semrefs

Jason Newsom's
Structural Equation Modeling Reference List
(Journal Articles and Chapters on Structural Equation Models)

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INTRODUCTORY CHAPTERS

Alwin, D.F., & Jackson, D.J. (1979). Measurement models for response errors in surveys: Issues and applications. Sociological Methodology, 1980. San Francisco, CA: Jossey-Bass.

Anderson, J. C., & Gerbing, D. W. (1988). Structural Equation modeling in practice : A review and recommended two-step approach. Psychological Bulletin, 103(3), 411-423.

Bentler, P. M., & Chou, C. (1987). Practical issues in structural modelling. Sociological Methods and Research, 16, 78-117.

Bentler, P.M., & Chou, C.-P. (1988). Practical issues in structural modeling. In J.S. Long (Ed.), Common problems/proper solutions (pp. 161-192). Beverly Hills, CA: Sage.

Glaser, D. (2002). Structural Equation Modeling Texts: A primer for the beginner. Journal of Clinical Child Psychology, 31(4), 573-578.

Diamantopoulos, A.(1994), 'Modeling with LISREL: A guide for the uninitiated', Journal of Marketing Management, 10, 105-136.

Kelm, L. (2000). Structural equation modeling. In L. G. Grimm & P. R. Yarnold (Eds.) Reading and understanding more multivariate statistics (pp.

227-260). Washington, DC: American Psychological Association.

MacCallum, R. (1986). Specification searches in covariance structure modeling. Psychological Bulletin, 100, 107-120.

Mueller, R. (1997). Structural equation modeling: Back to basics. Structural Equation Modeling, 4, 353-369.

Tanaka, J.S., Panter, A.T., Winborne, W.C., & Huba, G.J. (1990). Theory testing in personality and social psychology with structural equation models: A primer in 20 questions. In C. Hendrick, & M.S. Clark (Eds.), Review of personality and social psychology (Vol 11, pp. 217-241). Newbury Park, CA: Sage.

INTRODUCTORY TEXTS
(See the SEMbooks list also)

Arbuckle, James (1997). AMOS Users' Guide Version 3.6. Smallwaters Corporation. (1-56827-125-5)

Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.

Hoyle, Rick (1995). Structural Equation Modeling: Concepts, Issues and Applications. Sage Publications (0-8039-5318-6).

Kline, R. B. (2004). Principles and practice of structural equation modeling (Second Edition). New York: Guilford Press. (1572306904)

Loehlin, John C. (1998). Latent Variable Models: An Introduction to Factor, Path, and Structural Analysis. 3^rd ed. Mahwah, N.J.: Lawrence Erlbaum Associates.

Maruyama (1998).Basics of Structural Equation Modeling. Thousand Oaks: Sage.

Mueller, Ralph (1996). Basic Principles of Structural Equation Modeling: An introduction to LISREL and EQS, Springer Press (0-387-94516-4).

Schumacker, Randall & Lomax, Richard (1996). A Beginner's Guide to Structural Equation Modeling. Lawrence Erlbaum. (0-8058-1766-2).

HISTORY OF STRUCTURAL EQUATION MODELING

Aigner, D.J., Hsiao, C., Kapteyn, A., & Wansbeek, T. (1984). Latent variable models in econometrics. IN Z. Griliches & M.D. Intriligator (Eds.), Handbook of Econometrics (Vol. 2, pp. 1321-1393). Amsterdam: North-Holland.

Austin, J.T., & Wolfle, D. (1991). Theoretical and technical contributions to structural equation modeling: An updated annotated biliography. Structural Equation Modeling, 3, 105-175.

Bentler, P.M. (1980). Multivariate analysis with latent variables: Causal modeling. Annual Review of Psychology, 31, 419-456.

Bentler, P.M. (1986). Structural equation modeling and Psychometrika: An historical perspective on growth and achievements. Psychometrika, 31, 35-51.

Bielby, W.T., & Hauser, R.M. (1977). Structural equation models. Annual Review of Sociology, 3, 137-161.

Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley. [Chapter 1]

Epstein, R.J. (1987). A history of econometrics. Amsterdam: Elsevier.

Tremblay, P.F., & Gardner, R.C. (1996). On the growth of structural equation modeling in psychological journals. Structural Equation Modeling, 3, 93-104.

PATH ANALYSIS, PATH MODELS
(see also mediation, indirect effects)

Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American Sociological Review, 40, 37-47.

Bollen, K.A. (1987). Total, direct, and indirect effects in structural equation models. In C.C. Clogg (Ed.), Sociological methodology 1987 (pp. 37-69). Washington, D.C.: American Sociological Association.

DeShon, R.P. (1998). A cautionary note on measurement error corrections in structural equation models. Psychological Methods, 3, 412-423.

Everitt, B. S., and G. Dunn, G. (1991). Applied multivariate data analysis. London: Edward Arnold.

Duncan, O.D. (1966). Path analysis: Sociological examples. American Journal of Sociology, 72, 219-316.

Duncan, O.D. (1975). Introduction to structural equation models. New York: Academic Press.

Freedman, D.A. (1987). As others see us: A case study in path analysis. Journal of Educational Statistics, 12, 101-128.

Kelm, L. (2000). Path Analysis. In L. G. Grimm & P. R. Yarnold (Eds.) Reading and understanding multivariate statistics (pp. 65-97). Washington, DC: American Psychological Association.

Loehlin, John C. (1998). Latent Variable Models: An Introduction to Factor, Path, and Structural Analysis. 3^rd ed. Mahwah, N.J.: Lawrence Erlbaum Associates.

Maassen, G. H., & Bakker, A. B. (2001). Suppressor variables in path models: Definitions and interpretations. Sociological Methods and Research, 30, 241-270.

McDonald, R.P. (1996). Path analysis with composite variables. Multivariate Behavioral Research, 31, 239-270.

Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. Sociological Methodology, 18, 449-493.

Pedhazur, Elazer J. (1982). Multiple regression in behavioral research, 2nd edition. NY: Holt. Chapter 15 (pp. 577-635) covers path analysis. Widely used textbook.

Wolfe, L.M. (1999). Sewall Wright on the method of path coefficients: An annotated bibliography. Structural Equation Modeling, 6, 280-291.

Wright, S. (1934). The method of path coefficients. Annals of Mathematical Statistics, Vol. 5: 161-215.

CRITICAL REVIEWS, CRITIQUES, and GENERAL COMMENTARY

Baumrind, D. (1983). Specious causal attributions in the social sciences: The reformulated stepping-stone theory of heroin use as an exemplar. Journal of Personality and Social Psychology, 45, 1289-1298.

Berk, R.A. (1988). Causal inference for sociological data. In N.J. Smelser (Ed.), Handbook of Sociology. Newbury Park, CA: Sage.

Biddle, B. J., & Marlin, M. M. (1987). Causality, confirmation, credulity, and structural equation modeling. Child Development, 58, 4-17.

Breckler, S. J. (1990). Applications of covariance structure modeling in psychology: Cause for Concern? Psychological Bulletin, 107, 260-273.

Cliff, N. (1983). Some cautions concerning the application of causal modeling methods. Multivariate Behavioral Research, 18, 81-105.

Cohen, Cohen, Teresi, Marchi, and Velez (1990). Problems in the measurement of latent variables in structural equations casual models. Applied Psychological Measurement, vol 14,(2), 183-196.

Freedman, D.A. (1987). As others see us: A case study in path analysis. Journal of Educational Statistics, 12, 101-128.

MacCallum, R. C., Roznowski, M., & Necowitz, L. B. (1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin. 111, 490-504

MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R.(1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114, 185-199.

Mueller, R. (1997). Structural equation modeling: Back to basics. Structural Equation Modeling, 4, 353-369.

Rogosa, D. (1987). Casual models do not support scientific conclusions: A comment in support of Freedman. Journal of Educational Statistics, 12, 185-195.

Williams, L. J., Bozdogan, H., & Aiman-Smith, L. (1996). Inference problems with equivalent models. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp.279-314). Mahwah, NJ: Erlbaum.

SAMPLE SIZE ISSUES

Anderson, J. C., & Gerbing, D. W. (1988). Structural Equation modeling in practice : A review and recommended two-step approach. Psychological Bulletin, 103(3), 411-423.

Barrett, P. T., & Kline, P. (1981). The observation to variable ratio in factor analysis. Personality Study and Group Behavior, 1, 23-33.

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246.

Bentler, P. M., & Chou, C. (1987). Practical issues in structural modelling. Sociological Methods and Research, 16, 78-117.

Bollen, K.A. (1990) Overall fit in covariance structure models: Two types of sample size effects. Psychological Bulletin, 107, 256-259.

Boomsma, A. (1982). The robustness of LISREL against small sample size in factor analysis models. In K. G. JF6reskog & H. Wold (Eds.), Systems under indirect observation, Part 1 (pp. 149-173). Amsterdam: North-Holland.

Fan, X., Thompson, B., & Wang, L. (1999). Effects of sample size, estimation methods, and model specification on structural equation modeling fit indexes. Structural Equation Modeling, 6, 56-83.

Finch, J. F., West, S. G., & MacKinnon, D. P. (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models. Structural Equation Modeling, 4(2), 87-107.

Gerbing, D.W., & Anderson, J.C. (1993). Monte Carlo evaluations of goodness-of-fit indices for structural equation modeling. In

Gerbing, D.W., & Anderson, J.C. (1993). Monte Carlo evaluations of goodness-of-fit indices for structural equation models. In K.A. Bollen, & J.S. Long (eds.), Testing structural equation models. Newbury Park, CA: Sage.

Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103(2),265-275.

Hu, L.-T., & Bentler, P. (1995). Evaluating model fit. In R. H. Hoyle (Ed.), Structural Equation Modeling. Concepts, Issues, and Applications (pp. 76-99). London: Sage.

Hu, L.-T., & Bentler, P. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.

Tanaka, J.S. (1987). "How big is big enough?": Sample size and goodness of fit in structural equation models with latent variables. Child Development, 58, 134-146.

Tanaka, J.S. (1993). Multifaceted conceptions of fit in structural equation models. In K.A. Bollen, & J.S. Long (eds.), Testing structural equation models. Newbury Park, CA: Sage.

CORRELATION VS. COVARIANCE MATRICES

Cudek, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 2, 317-327.

MISSING DATA, MISSING DATA IMPUTATION, MISSING DATA ESTIMATION, MULTIPLE IMPUTATION

Allison, P.D. (1987) Estimation of linear models with incomplete data. In C.C. Clogg [Ed.] Sociological Methodology (pp. 71-103). San Francisco: Jossey-Bass,

Arbuckle, J.L. (1996) Full information estimation in the presence of incomplete data. In G.A. Marcoulides and R.E. Schumacker [Eds.] Advanced structural equation modeling: Issues and Techniques. Mahwah, NJ: Lawrence Erlbaum Associates.

Duncan, T.E., Duncan, S.C. and Li, F. (1998) A comparison of model and multiple imputation-based approaches to longitudinal analyses with partial missingness. Structural Equation Modeling: A Multidisciplinary Journal, 5(1), 1-21.

Enders, C.K. (2001). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling, 8, 128-141.

Enders, C.K. (2001). The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data. Psychological Methods, 6, 352-370.

Enders, C. K., Peugh, J.L. (2004). Using an EM covariance matrix to estimate structural equation models with missing data: Choosing an adjusted sample size to improve the accuracy of inferences. Structural Equation Modeling: A Multidisciplinary Journal, 11, 1-19.

Enders, C. K. (2005). A SAS macro for implementing the modified Bollen-Stine bootstrap for missing data: Implementing the bootstrap using existing structural equation modeling software. Structural Equation Modeling: A Multidisciplinary Journal, 12(4), 620-641.

Enders, C. K. (2006). Analyzing structural equation models with missing data. In G.R. Hancock & R.O. Mueller (Eds.), Sstructural equation modeling: A second course. Greenwich, CT: .Information Age.

Ford, B. L. (1983). An overview of hot-deck procedures. In W. G. Madow, I. Olkin, & D. B. Rubin (Eds.), Incomplete Data in Sample Survey. Volume II: Theory and Bibliographies (pp. 185-207). New York: Academic Press.

Gold, M.S., & Bentler, P.M. (2000). Treatments of missing data: A Monte Carlo comparison of RBHDI, iterative stochastic regression imputation, and expectation-maximization. Structural Equation Modeling, 7, 319-355.

Graham, J. W., Hofer, S.M., Donaldson, S.I., MacKinnon, D.P., & Schafer, J.L. (1997). Analysis with missing data in prevention research. In K. Bryant, M. Windle, & S. West (Eds.), The science of prevention: methodological advances from alcohol and substance abuse research. (pp. 325-366). Washington, D.C.: American Psychological Association.

Graham, J. W., Hofer, S. M., & MacKinnon, D. P. (1996). Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures. Multivariate Behavioral Research, 31, 197-218.

Hedeker & Gibbons (1997). Application of random-effects pattern-mixture models for missing data in longitudinal studies. Psychological Methods, 2, 64-78.

Jinn, J.H., & Sedransk, J. (1989). Effect on secondary data analysis of common imputation methods. Sociological Methodology. Washington, DC: American Sociological Association.

Jones, M. P. (1996). Indicator and Stratification Methods for Missing Explanatory Variables in Multiple Linear Regression. Journal of the American Statistical Association, 91, 222-230.

Kaplan, D. (1995). The impact of BIB-spiraling induced missing data patterns on goodness-of-fit tests in factor analysis. Journal of Educational and Behavioral Statistics, 20, 69-82.

Lepkowski, J. M., Landis, J. R., & Stehouwer, S. A. (1987). Strategies for the analyses of imputed data from a sample survey: The national medical care utilization and expenditure survey. Medical Care, 25, 705-716.

Little, R.J.A., & Rubin, d.B. (1989). The analysis of social science data with missing values, Sociological Methods and Research, 18, 292-326.

Little, RJA & Rubin, D (1987). Statistical analysis with missing data. Wiley.

Marsh, H.W. (1998). Pairwise deletion for missing data in structural equation models with missing data: Nonpositive definite matrices, parameter estimates, goodness of fit, and adjusted sample sizes. Structural Equation Modeling, 5, 22-36.

Muthen, B., Kaplan, D., & Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 51,431-462.

Roth, P. L. (1994). Missing data: A conceptual review from applied psychologists. Personnel Psychology, 47, 537-560.

Roth, P.L. (1994). Missing data: A conceptual review for applied psychologists. Personnel Psychology, 47, 537-560.

Roth, P. L., Switzer, F. S. , & Switzer, D. (1999). Missing data in multiple item scales: A monte carlo analysis of missing data techniques. Organizational Research Methods, 2(3), 211-232.

Rubin, D. (1987). Multiple imputation for nonresponse in surveys. Wiley.

Santos, R. (1981). Effects of imputation on regression coefficients. Proceedings of the Section on Survey research Methods, American Statistical Association, 1981, 1401. (Cited in Lepkowski et al, 1987).

Schafer, J (1997). Analysis of incomplete multivariate data. Chapman & Hall.

Schafer, J.L., & Graham, J.W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147-177.

Wothke, W. (in press) Longitudinal and multi-group modeling with missing data. In T.D. Little, K.U. Schnabel, and J. Baumert [Eds.] Modeling longitudinal and multiple group data: Practical issues, applied approaches and specific examples. Mahwah, NJ: Lawrence Erlbaum Associates. (forthcoming Summer1999, also available at http://www.smallwaters.com/whitepapers)

LATENT CLASS ANALYSIS

Dillon, W.R., & Goldstein, M. (1984). Latent structure analysis (pp. 491-520). In Multivariate analysis: Methods and applications. New York: Wiley.

Collins, L. M. (1991). Measurement in longitudinal research. In L. M.Collins and J. L. Horn (Eds.), Best methods for the analysis of change (pp. 137-148). Washington, DC: American Psychological Association.

Goodman, L. A. (1974). The analysis of systems of qualitative variables when some of the variables are unobservable. Part I—A modified latent structure approach. American Journal of Sociology, 79, 1179-1259.

Langeheine, R. (1994). Latent variables Markov models. In A.von Eye and C. C. Clogg (Eds.), Latent variables analysis (pp. 373-395). Thousand Oaks, CA: Sage Publications.

Macready, G. B., & Dayton, C. M. (1994). Latent class models for longitudinal assessment of trait acquisition. In A. von Eye and C. C. Clogg (Eds.), Latent variables analysis (pp. 245-273). Thousand Oaks, CA: Sage Publications.

McCutcheon, A. L. (1994). Latent logit models with polytomous effects variables. In A. von Eye and C. C. Clogg (Eds.), Latent variables analysis (pp. 353-372). Thousand Oaks, CA: Sage Publications.

von Eye, A., & Clogg, C. C. (1995, Editors). Latent variables analysis. Thousand Oaks, CA: Sage Publications.

CROSS-LAGGED PANEL MODELS, LONGITUDINAL MODELS, LONGITUDINAL ANALYSIS GENERAL (see also latent growth curve models)

Allison, P. (1990). Change scores as dependent variables in regression analysis. Sociological Methodology, 20, 93-114.

Collins, L.M., & Horn, J.L. (1991). Best Methods for the Analysis of Change . Washington, D.C: American Psychological Association.

Collins, L.M., & Sayer, A.G. (2001). New methods for the analysis of change. Washington, D.C.: American Psychological Association. (ISBN: 1557987548)

Finkel, S.E. (1995). Causal analysis with panel data. Thousand Oaks, CA: Sage. (QASS #105).

Kessler, R.C., Greenberg, D.F. (1981). Linear panel analysis: Models quantitative change. New York: Academic Press.

Gottman J.M. (1995). The Analysis of Change (pp. 261-276). Mahwah, NJ: Lawrence Erlbaum).

Marsh, H. W. (1993). Stability of individual differences in multiwave panel studies: Comparison of simplex models and one-factor models. Journal of Educational Measurement, 30, 157-183.

Menard, S. (1991). Longitudinal research. Newbury Park, NJ: Sage. (QASS #76).

Nielsen, F., & Rosenfeld, R. (1981). Substantive Interpretation of Differential Equation Models. American Sociological Review 46:159-174.

Sivo, S.A, & Willson, V.L. (2000). Modeling causal error structures in longitudinal panel data: A Monte Carlo study. Structural Equation Modeling, 7(2), 174-205.

Willett, J.B. (1988).Questions and answers in the measurement of change. Review of Research in Education, 15, 345-422.

Williams, L. J., & Podsakoff, P. M. (1989). Longitudinal field methods for studying reciprocal relationships in organizational behavior research: Toward improved causal analysis. In B. M. Staw & L. L. Cummings (Eds.), Research in organizational behavior, vol. 11. Greenwich, CT: JAI Press.

SIMPLEX MODELS

Jones, M. B. (1959). Simplex Theory . Pensacola: U.S. Naval Aviation Medicine Monograph No. 3.

Jones, M. B. (1960). Molar Correctional Analysis. Pensacola, FL: U.S. Naval Aviation Medicine Monograph No. 4.

Jöreskog, K. G. (1970). Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 23, 121-145.

Joreskog, K. G. (1979). Statistical models and methods for analysis of longitudinal data. In J. Magidson (ed.) Advances in Factor Analysis and Structural Equation Models. Cambridge, MA: Abt Books.

Marsh, H. W. (1993). Stability of individual differences in multiwave panel studies: Comparison of simplex models and one-factor models. Journal of Educational Measurement, 30, 157-183.

LATENT GROWTH CURVE MODELS (LGC)

Bock, R. D. (1991). Prediction of growth. In L. M. Collins & J. L. Horn(Eds.), Best Methods for the Analysis of Change . Washington, D.C: American Psychological Association.

Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach incorporating longitudinal mean and covariance structures analysis (LMACS) and multiple indicator latent growth modeling (MLGM). Organizational Research Methods, 1,421-483.

Duncan, S.C., & Duncan, T.E. (1994). Modeling in complete longitudinal substance use data using latent variable growth curve methodology. Multivariate Behavioral Research, 29, 313-338.

Duncan, S.C., & Duncan, T.E. (1996). A multivariate growth curve analysis of adolescent substance use. Structural Equation Modeling, 3, 323-347.

Duncan, T. E., Duncan, S. C., & Li, F. (1998). A comparison of model- and multiple imputation-based approaches to longitudinal analyses with partial missingness. Structural Equation Modeling, 5(1), 1-21.

Duncan, T.E., Duncan, S.C., & Hops, H. (1994). The effects of family cohesiveness and peer encouragement on the development of adolescent alcohol use: A cohort-sequential approach to the analysis of longitudinal data. Journal of Studies on Alcohol, 55, 588-599.

Duncan, T.E., Duncan, S.C., Alpert, A., Hops, H., Stoolmiller, M., & Muthen, B. (1997). Latent variable modeling of longitudinal and multilevel substance use data. Multivariate Behavioral Research, 32, 275-318.

Duncan, T.E., Duncan, S.C., Strycker, L.A., Li, F., & Alpert, A. (1999). An introduction to latent variable growth curve modeling: Concepts, issues, and applications. Mahwah, NJ: Erlbaum.

Hancock, G.R., Kuo, W.-L., & Lawrence, F.R. (2001). An illustration of second-order latent growth models. Structural Equation Modeling, 8, 470-489.

Hancock, G. R., & Lawrence, F. R. (2006). Using latent growth models to evaluate longitudinal change. In G. R. Hancock & R. O. Mueller (Eds.), Structural Equation Modeling: A Second Course. Greenwood, CT: Information Age Publishing, Inc.

Lawrence, F. R., & Hancock, G. R. (1998). Assessing change over time using latent growth modeling. Measurement and Evaluation in Counseling and Development, 30, 211-224.

Lawrence, F. R., & Hancock, G. R. (1998). Methods, plainly speaking. Assessing change over time using latent growth modeling. Measurement and Evaluation in Counseling and Development, 30, 211-224.

Marsh, H. W., & Grayson, D. (1994). Longitudinal stability of latent means and individual differences: A unified approach. Structural Equation Modeling, 1, 317-359.

McArdle, J.J. (1986). Dynamic but structural equation modeling of repeated measures data. In Nesselroade, J.R., and Cattel, R.B. (eds.), Handbook of Multivariate Experimental Psychology (2nd ed.). New York: Plenum Press.

McArdle, J.J. (1996). Current directions in structural factor analysis. Current Directions, 5, 11-18.

Meredith, W, & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.

Muthen, B.O. (1997). Latent variable modeling of longitudinal and multilevel data. In A.E. Raftery (Ed.), Sociological methodology (pp.453-480). Washington, DC: Blackwell.

Muthen, B.O., & Curran, P.J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2, 371-402.

Muthen, B. O., & Khoo, S.-T. (1998). Longitudinal studies of achievement growth using latent variable modeling. Learning and Individual Differences, 10, 73-101.

Rogosa, D. R. (1995). Myths and methods: "Myths about longitudinal research," plus supplemental questions. In J. M. Gottman, (Ed.), The analysis of change (pp. 3-66) Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Raykov, T. (1997). Growth curve analysis of ability means and variances in measures of fluid intelligence of older adults. Structural Equation Modeling,4(4), 283-319.

Sayer, A.G., Cumsille, P. E. (2001). Second-order latent growth models. In L.M. Collins,& A.G. Sayer (Eds). New methods for the analysis of change. Decade of behavior. (pp. 179-200). Washington, DC: American Psychological Association.

Steyer, R., Eid, M., & Schwenkmezger, P. (1997). Modeling true intraindividual change: True change as a latent variable. Methods of Psychological Research, 2(1).

Tisak, J, & Meredith, W. (1990). Descriptive and associative developmental models. In A. von Eye (Ed.), Statistical methods in developmental research (Vol. 2, pp. 387-406). San Diego, CA: Academic Press.

Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363-381.

Willett, J. B., & Sayer, A. G. (1996). Cross-domain analysis of change overtime: Combining growth modeling and covariance structure analysis. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced Structural Equation Modeling. Issues and Techniques (pp.125-157). Mahwah, NJ: Lawrence Erlbaum.

Willett, JB, Ayoub, CC, Robinson, D. (1991). using growth modelling to examine systematic differences in growth: An example of change in the functioning of families at risk of maladaptive parenting, child abuse or neglect. Journal of Consulting & Clinical Psychology, 59, 38-47.

LATENT GROWTH CURVE EXAMPLES

Curran, P.J., Harford, T., & Muthen, B.O. (1996). The relation between heavy alcohol use and bar patronage: A latent growth model. Journal of Studies on Alcohol, 57, 410-418.

Curran, P.J., Stice, E., & Chassin, L. (1997). The relation between adolescent alcohol use and peer alcohol use: A longitudinal random coefficients model. Journal of Consulting and Clinical Psychology,65, 130-140.

Duncan, T. E. & Duncan, S. C. (1994) Modeling developmental processes using latent growth structural equation methodology. Applied Psychological Measurement, 18(4), 343-354.

Stoolmiller, M. (1995). Using latent growth curve models to study developmental processes. In J. M. Gottman (Ed.), The analysis ofchange. Mahwah, NJ: Lawrence Erlbaum.

Wickrama, K. A. S., Lorenz, F. O., & Conger, R. D. (1997). Parental support and adolescent physical health status: A latent growth-curve analysis. Journal of Health and Social Behavior, 38, 149-163.

LATENT STATE-TRAIT MODELS, LATENT TRAIT-STATE MODELS

Dumenci, L, & Windle, M. (1996). A latent trait-state model of adolescent depression using the center for epidemiologic studies-depression scale. Multivariate Behavioral Research, 31, 313-330.

Dumenci, L, & Windle, M. (1998). A multitrait-multioccassion generalization of the latent trait-state model: Description and application. Structural Equation Modeling, 5, 391-410.

Kenny, D.A., & Zautra, A. (1995). The trait-state-error model for multiwave data. Journal of Consulting and Clinical Psychology, 63, 52-59.

Kenny, D.A., & Zautra, A. (2001). Trait-state models for longitudinal data. In L.M. Collins & A.G. Sayer (Eds.), New methods for the analysis of change. Decade of behavior (pp. 243-263). Washington, DC: American Psychological Association .

Steyer, R., Majcen, A.-M., Schwenkmezger, P. & Buchner, A. (1989). A latent state-trait anxiety model and its application to determine consistency and specificity coefficients. Anxiety Research, 1, 281-231.

Steyer, R., Ferring, D., & Schmitt, M. J. (1992). States and traits in psychological assessment. European Journal of Psychological Assessment, 8, 79-98.

POWER, POWER ANALYSIS, SAMPLE SIZE

sem power analysis software by Paul Dudgeon www.psych.unimelb.edu.au/people/staff/DudgeonP.html

Hancock, G. R. (2006). Power analysis in covariance structure models. In G. R. Hancock & R. O. Mueller (Eds.), Structural Equation Modeling: A Second Course. Greenwood, CT: Information Age Publishing, Inc.

Hu, L-T., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.

Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling, 8(2), 205-223.

Kaplan, D. (1995). Statistical power in structural equation modeling. In R. Hoyle (Ed). Structural Equation Modeling: Concepts, Issues, and Applications. pp. 100-117. Thousand Oaks, CA: Sage.

Kaplan, D., & George, R. A study of the power associated with testing factor mean differences under violations of factorial invariance. Structural Equation Modeling: A Multidisciplinary Journal, 2, 101-118.

Kaplan, D., & Wenger, R. N. (1993). Asymptotic independence and separability in covariance structure models: Implications for specification error, power, and model modification. Multivariate Behavioral Research, 28, 483-498.

MacCallum, R. C., & Hong, S. (1997). Power analysis in covariance structure modeling using GFI and AGFI. Multivariate Behavioral Research, 32(2), 193-210.

MacCallum, R. C., Browne, M. W., & Sugawara, H.M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods. 1(2), 130-149.

MacCallum, R.C., Widaman, K.F., Zhang, S., & Hong, S. (1999). ``Sample Size in Factor Analysis.'' Psychological Methods 4:84-99

MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11, 19-35.

Matsueda, R. L. and Bielby, W. T. (1986). Statistical power in covariance structure models. pp. 120-158 in Sociological Methodology 1986, edited by Nancy B. Tuma. Washington, DC: American Sociological Association.

Muthén, L.K., & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.

Preacher, K. J., & Coffman, D. L. (2006, May). Computing power and minimum sample size for RMSEA [Computer software]. Available from http://www.quantpsy.org/.

Saris, W. E. and Stronkhorst, H. (1984). Causal modelling in nonexperimental research: An introduction to the LISREL approach. Amsterdam, The Netherlands: Sociometric Research Foundation.

Saris. W. E., Satorra, A., and Sorbom, D. (1987). The detection and correction of specification errors in structural equation models. pp. 105-129 in Sociological Methodology 1987, edited by Clifford Clogg. Washington, DC: American Sociological Association.

Sarris, W. E., & Satorra, A. (1993). Power evaluations in structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 181-204). Newbury Park, CA: Sage.

Satorra, A. and Saris, W. E. (1985). The power of the likelihood ratio test in covariance structure analysis. Psychometrika 50: 83-90.

SOFTWARE

Kline, R. B. (1998). Software programs for structural equation modeling: Amos, EQS, and LISREL. Journal of Psychoeducational Assessment,16, 302-323.

ALPHA INFLATION, FAMILYWISE ERROR

Green, Samuel B; Thompson, Marilyn S; Babyak, Michael A. (1998). A Monte Carlo investigation of methods for controlling Type I errors with specification searches in structural equation modeling. Multivariate Behavioral Research, 33, 365-383.

Green, Samuel B; Babyak, Michael A. (1997). Control of Type I errors with multiple tests of constraints in structural equation modeling. Multivariate Behavioral Research, 32, 39-51.

EXAMPLES OF SECOND-ORDER FACTOR MODELS
(HIEARCHICAL FACTOR MODELS)

Bunting, B, Saris, W.E. and McCormack, J.A (1987). Second-order factor analysis of the reliability and validity of the 11 plus examination in Northern Ireland. The Economic and Social Review, 18, 137-147.

Catalano, R. F., Kosterman, R., Hawkins, J. D., Newcomb, M. D., & Abbott, R. D. (Spring, 1996). Modeling the etiology of adolescent substance use: A test of the social development model. Journal of Drug Issues, 26 429-455.

Gerbing, D.W., Hamilton, J.G., & Freeman, E.B. (1994). A large-scale second-order structural equation model of the influence of management participation on organizational planning benefits. Journal of Management, 20, 859-885.

Goldman, M. S., Greenbaum, P. E., & Darkes, J. (1997). A confirmatory test of hierarchical expectancy structure and predictive power: Discriminant validation of the Alcohol Expectancy Questionnaire. Psychological Assessment, 9, 145-157.

Gustafson, J. E., & Balke, G. (1993). General and specific abilities as predictors of school achievement. Multivariate Behavioral Research, 28, 407-434.

Kaplan, D. & Elliott. P. R. (1997) A model-based approach to validating education indicators using multilevel structural equation modeling. Journal of Educational and Behavioral Statistics, 22, 323-348.

Kaplan, D., & Elliott, P. R. (1997) A didactic example of multilevel structural equation modeling applicable to the study of organizations. Structural Equation Modeling, 4, 1-24.

McGrew, K. S., Flanagan, D. P., Keith, T. Z., & Vanderwood, M. (1997). Beyond g: The impact of Gf-Gc specific cognitive abilities research on the future use and interpretation of intelligence test batteries in the schools. School Psychology Review, 26, 189-210.

Mulaik, S. A. & Quartetti, D. A. (1997). First order or higher order general factor? Structural Equation Modeling, 4, 193-211.

Rindskopf, D., & Rose, T. (1988). Some theory and applications of confirmatory second-order factor analysis. Multivariate Behavioral Research, 23, 51-67.

Russell, D., & Cutrona, C. E. (1991). Social support, stress, and depressive symptoms among the elderly: Test of a process model. Psychology and Aging, 6, 190-201.

COEFFICIENT ALPHA, RELIABILITY, CRONBACH’S ALPHA

Rasmussen, J. L. (1989). Analysis of Likert-scale data: A reinterpretation of Gregoire and Driver. Psychological Bulletin, 105, 167-170.

Bandalos, D. L., & Enders, C. K. (1996). The effects of nonnormality and number of response categories on reliability. Applied Measurement in Education, 9, 151-160.

Bollen, K., & Lennox, R. (1991). Conventional Wisdom on Measurement: A structural equation perspective. Psychological Bulletin, Vol. 110(2): 305-314.

Cortina, J.M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98-104.

Enders, C. K., & Bandalos, D. L. (1999). The effects of heterogeneous item distributions on reliability. Applied Measurement in Education,12, 133-150.

Enders, C. K. (2001). The impact of nonnormality on full information maximum likelihood estimation for structural equation models with missing data. Psychological Methods, 6, 352-370.

Enders, C. K. (2003). Using the EM algorithm to estimate coefficient alpha for scales with item level missing data. Psychological Methods, 8, 322-337.

Enders, C. K. (2004). The impact of missing data on sample reliability estimates: Implications for reliability reporting practices. Educational and Psychological Measurement, 64, 419-436.

Green, S.B., Lissitz, R.W., & Mulaik, S.A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37, 827-837.

Greene, V.L., & Carmines, E.G. (1979). Assessing the reliability of linear composites. Sociological Methodology, 1980. San Francisco: Jossey-Bass.

Guttman, L. (1953). Reliability formulas that do not assume experimental independence. Psychometrika, 18, 225-239.

Jenkins, G. D., & Taber, T. D. (1977). Monte Carlo study of factors affecting three indices of composite scale reliability. Journal of Applied Psychology, 62, 392-398.

Joreskog, K.G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36, 109-133.

Komaroff, E. (1996). Coefficient alpha under simultaneous violations of essential tau-equivalence and uncorrelated errors. (Doctoral dissertation, University of Miami, 1996). Dissertation Abstracts International, 57-05, 2013.

Komaroff, E. (1997). Effect of simultaneous violations of essential tau-equivalence and uncorrelated error on coefficient alpha. Applied Psychological Measurement, 21(4) (in press).

Levine (1994). Trues scores, error, reliability, and unit of analysis in environment and behavior research. Environment and Behavior, 26, 261-293.

Li, Heng; Rosenthal, Robert; Rubin, Donald B. Reliability of measurement in psychology: From Spearman-Brown to maximal reliability. Psychological Methods. Vol 1(1) 98-107, Mar 1996.

Matell, M. S., & Jacoby, J. (1972). Is there an optimal number of alternatives for Likert-scale items? Effects of testing time and scale properties. Journal of Applied Psychology, 56, 506-509.

Matell, M. S., & Jacoby, J. (1971). Is there an optimal number of alternatives for Likert scale items? I. Reliability and validity. Educational & Psychological Measurement, 31, 657-674.

Miller, M. B. (1995). Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling. Structural Equation Modeling, 2(3), 255-273.

Novick, M.R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32, 1-13.

Okleshen-Peters, C. & Enders, C. K. (2002). A primer for the estimation of structural equation models in the presence of missing data: Maximum likelihood algorithms. Journal of Targeting, Measurement, and Analysis for Marketing, 11, 81-95.

Preston, C. C., & Colman, A. M. (2000). Optimal number of response categories in rating scales: Reliability, validity, discriminating power, and respondent preferences. Acta Psychologica, 104, 1-15.

Raykov, T. (1997). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21, 173-184.

Raykov, T. (2004). Estimation of maximal reliability: A note on a covariance structure modelling approach. British Journal of Mathematical & Statistical Psychology, 57, 21-27.

Raykov, T. (2001). Estimation of congeneric scale reliability using covariance structure analysis with nonlinear constraints. British Journal of Mathematical & Statistical Psychology, 54, 315-323.

Reuterberg, S.E., & Gustafsson, J.E. (1992). Confirmatory factor analysis and reliability: Testing measurement model assumptions. Educational and Psychological Measurement, 52, 795-811.

Richards, et al. (1991.) Units of analysis and the psychometrics of environmental assessment scales. Environment and Behavior, 23, 423-437.

Rozeboom, W.W. (1966). Foundations of the theory of prediction. Homewood, IL: Dorsey.

Smith, D. A., & Davidson, L. A. (1986). Interfacing Indicators and Constructs in Criminological Research: A Note on the Comparability of Self-Report Violence Data for Race and Sex Groups. Criminology,24, 473-488.

Van Zyl, J. M., Neudecker, H., & Nel, D. G. (2000). On the distribution of the maximum likelihood estimator of Cronbach's Alpha. Psychometrika,65(3), 271--280.

Zimmerman, D.W., Zumbo, B.D., & Lalonde, C. (1993). Coefficient alpha as an estimate of test reliability under violation of two assumptions. Educational and Psychological Measurement, 53, 33-49.

LIKERT RESPONSE SCALES, SCALING, ORDINAL MEASUREMENT

Champney, H., & Marshall, H. (1939). Optimal refinement of the rating scale. Journal of Applied Psychology, 23, 323-331.

Cox, E. P. (1980). The optimal number of response alternatives for a scale: A review. Journal of Marketing Research, 17, 407-422.

Ghiselli, E. E. (1939). All or none versus graded response questionnaires. Journal of Applied Psychology, 23, 405-413.

Green, P. E., & Rao, V. R. (1970). Rating scales and information recovery - how many scales and response categories to use? Journal of Marketing, 34, 33-39.

Jenkins, G. D., & Taber, T. D. (1977). Monte Carlo study of factors affecting three indices of composite scale reliability. Journal of Applied Psychology, 62, 392-398.

Johnson, D.R., & Creech, J.C. (1983). Ordinal measures in multiple indicator models: A simulation study of categorization error. American Sociological Review, 48, 398-407.

Lissitz, R. W., & Green, S. B. (1975). Effect of the number of scale points on reliability: A monte carlo approach. Journal of Applied Psychology, 60, 10-13.

Matell, M. S., & Jacoby, J. (1971). Is there an optimal number of alternatives for Likert scale items? Study I: Reliability and validity. Educational and Psychological Measurement, 31, 657-674.

Matell, M. S., & Jacoby, J. (1972). Is there an optimal number of alternatives for Likert-scale items? Effects of testing time and scale properties. Journal of Applied Psychology, 56, 506-509.

Michell, J. (1986). Measurement scales and statistics: A clash of paragdigms. Psychological Bulletin, 100, 398-407.

Michell, J. (1990). An introduction to the logic of psychological measurement. Hillsdale, NJ: Lawrence Erlbaum Associates.

Narens, L., & Luce, R. D. (1986). Measurement: The theory of numerical assignments. Psychological Bulletin, 99, 166-180.

Ramsay, J. O. (1973). The effect of number of categories in rating scales on precision of estimation of scale values. Psychometrika, 38,513-532.

Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 667-680.

Suppes, P., & Zinnes, J. L. (1963). Basic measurement theory. In R. D. Luce & R. Bush & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1, pp. 3-76). New York: Wiley.

Symonds, P. M. (1924). On the loss of reliability in rating due to coarseness of the scale. Journal of Experimental Psychology, 456-461.

Trout, J. D. (1999). Measurement. In W. H. Newton-Smith (Ed.), A companion to the philosophy of science. Oxford: Blackwell.

ADF, AGLS, and WLS ESTIMATION METHODS

Browne, M.W. (1984). Asymptotic distribution free methods in analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.

McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman Hall.

Muthen, B. (1993). Goodness of fit with categorical and other nonnormal variables. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 205-234). Newbury Park, CA: Sage.

Muthen, B., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171-189.

Olsson, U.H., Foss, T., Troye, S. V., & Roy D. Howell (2000). The Performance of ML, GLS and WLS Estimation in Structural Equation Modeling Under Conditions of Misspecification and Nonnormality. Structural Equation Modeling, 7 (4), 557-595.

Sugawara, Hazuki M. and Robert C. MacCallum (1993), "Effect of Estimation Method on Incremental Fit Indexes for Covariance Structure Models," Applied Psychological Measurement, 17, 365-77.

Yuan, K.-H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92, 767-774.

NONNORMALITY, DISTRIBUTIONAL ASSUMPTIONS, CATEGORICAL DATA, ORDINAL, MULTIVARIATE KURTOSIS

Babakus, E., Ferguson, C.E., Jr., and Joreskog, K.G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24, 222-28.

Bandalos, D. L., & Enders, C. K. (1996). The effects of nonnormality and number of response categories on reliability. Applied Measurement in Education, 9, 151-160.

Curran, P. J., West, S. G, & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.

D'Agostino, R. B., Belanger, A., & D'Agostino, R. B. (1990). A suggestion for using powerful and informative tests of normality. American Statistician, 44, 316-321.

DeCarlo, L. T. (1997), On the meaning and use of kurtosis. Psychological Methods, 2, 292-307.

Enders, C. K. (2001). The impact of nonnormality on full information maximum likelihood estimation for structural equation models with missing data. Psychological Methods, 6, 352-370.

Fan, X., Thompson, B., & Wang, L. (1999). Effects of sample size, estimation method, and model specification on structural equation modeling fit indexes. Structural Equation Modeling, 6, 56-83.

Finch, J.F., West, S.G., & MacKinnon, D. (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variables models. Structural Equation Modeling, 4, 87-107.

Fouladi, R.T. (2000) Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality. Structural Equation Modeling, 7(3), 356-410.

Hoogland & Boomsma (1998). Robustness studies in Covariance Structure Modeling: An overview and a meta-analysis. Sociological Methods and Research, 26, 329-3

Hosking, J. R. M. (1997). Regional frequency analysis. An approach base on L-Moments. Cambridge, UK: Cambridge University Press.

Hu, L-T., & Bentler, P.M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424-453. Nevitt, J., & Hancock, G.R. (2000). Improving the root mean square error of approximation for nonnormal conditions in structural equation modeling. Journal of Experimental Education, 68(3), 251-268.

Muthén, B., & Kaplan, D. (1985). A comparison of methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171-189.

Muthén, B., & Kaplan, D. (1992). A comparison of some methodologies for the factor analysis of non-normal Likert variables: A note on the size of the model. British Journal of Mathematical and Statistical Psychology, 45, 19-30.

Olsson, U. H, Troye, S. V., and Howell, R. D. (1999). Theoretic fit and empirical fit: The performance of maximum likelihood versus generalized least squares estimation in structural equation models. Multivariate Behavioral Research, 34, 31-58.

Satorra, A., & Bentler, P.M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. 1988 Proceedings of the Business and Economic Statistics Section of the American Statistical Association, 308-313.

Satorra, A., & Bentler, P.M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye and C.C. Clogg (eds.), Latent Variable Analysis: Applications to Developmental Research (pp. 399-419). Newbury Park: Sage.

Stuart, A., & Ord, J. K. (1987). Kendall's advanced theory of statistics (Vol. 1). London: Charles Griffin and Co.

West, S. G., Finch, J.F, & Curran, P.J. (1995). Structural equation models with nonnormal variables: Problems and remedies. In R.H. Hoyle (Ed), (1995). Structural equation modeling: Concepts, issues, and applications. (pp. 56-75). Thousand Oaks, CA: Sage Publications.

Xie, Yu (1989) Structural equation models for ordinal variables, Sociological Methods & Research, 17, 325-352.

Yuan, K.-H., & Bentler, P. M. (1997). Improving parameter tests in covariance structure analysis. Computational Statistics & Data Analysis, 26, 177-198.

Yuan, K.-H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92, 767-774.

Yuan, K-H., & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51, 289-309.

ASSUMPTIONS, MULTICOLLINEARITY, NONCONSTANT VARIANCE, HETEROSCEDASTICITY, OUTLIERS

Rensvold, R. B., & Cheung, G. W. (1999). Identification of influential cases in structural equation models using the jackknife method. Organizational Research Methods, 2(3), 293-308.

POLYCHORIC CORRELATIONS, TETRACHORIC CORRELATIONS, POLYSERIAL CORRELATIONS, and NONNORMALITY

Babakus, Ferguson and Joreskog (1987), The Sensitivity of Confirmatory Maximum Likelihood Factor Analysis to Violations of Measurement Scale and Distributional Assumptions, J. of Marketing Research, 24, 222-228.

Bentler (1990), Comparative Fit Indices in Structural Models, Psychological Bulletin, 107, 238-246.

Brown. R.L. (1989). Using Covariance Modeling for Estimating Reliability on Scales with Ordered Polytomous Variables, Educational and Psychological Measurement, 49, 385-398.

Fornell and Larcker (1981), Evaluating Structural Equation Models with Unobservable Variables and Measurement Error, J. of Marketing Research, 18, 39-50.

Muthen, B., & Hofacker, C. (1988). Testing the assumptions underlying tetrachoric correlations. Psychometrika, 53, 563-578.

Ollson (1979), On the Robustness of Factor Analysis Against Crude Classification of the Observations, Multivariate Behavioral Research, 14, 485-500.

Rigdon, E.E. and Ferguson, C.E., Jr. (1991), The Performance of the Polychoric Correlation Coefficient and Selected Fitting Functions in Confirmatory Factor Analysis with Ordinal Data, Journal of Marketing Research, 28, 491-497.

MTMM (MULTI-TRAIT MULTI-METHOD MATRIX)

Bagozzi, R. P., & Yi, Y. (1990). Assessing method variance in multitrait-multimethod matrices: The case of self-reported affect and perceptions at work. Journal of Applied Psychology, 75, 547-560.

Bagozzi, R. P., & Yi, Y. (1991). Multitrait-multimethod matrices in consumer research. Journal of Consumer Research, 17, 426-439.

Bagozzi, R. P., & Yi, Y. (1992). Testing hypotheses about methods, traits, and commonalties in the direct-product model. Applied Psychological Measurement, 16, 373-380.

Bagozzi, R. P., Yi, Y., & Phillips, L. W. (1991) Assessing construct validity in organizational research. Administrative Science Quarterly, 36, 421-458. Byrne, B & Goffin (1993). Modeling MTMM data from additive and multiplicative covariance structures: An audit of construct validity concordance. Multivariate Behavioral Research, 28, 67-96.

Bollen, K.A. & Joreskog, K.G. (1985). Uniqueness does not imply identification. Sociological Methods and Research, 14, 155-163.

Bollen, K.A., & Paxton, P. (1998). Detection and determinants of bias in subjective measures. American Sociological Review, 63, 465-478.

Cook, W.L. (1994). A structural equation model of dyadic relationships within the family system. Journal of Consulting and Clinical Psychology, 62, 500-509.

Cook, W. L. & Goldstein, M. J. (1993). Multiple perspectives on family relationships: A latent variables model. Child Development, 64,1377-1388.

Coovert, M. D., & Craiger, J. P., Teachout, M. S. (1997). Effectiveness of the direct product versus confirmatory factor model for reflecting the structure of multimethod-multirater job performance data. Journal of Applied Psychology, 82, 271-280.

Kenny, D. A., & Kashy, D. A. (1992). Analysis of the multitrait-multimethod matrix by confirmatory factor analysis. Psychological Bulletin, 112, 165-172.

Marsh, H. W. & Bailey, M. (1991). Confirmatory factor analysis of multitrait-multimethod data: A comparison of alternative models. Applied Psychological Measurement, 15, 47-70.

Marsh, H. W. (1989). Confirmatory factor analysis of multitrait-multimethod data: Many problems and a few solutions. Applied Psychological Measurement, 13, 335-361.

Marsh, H. W. (1993). Multitrait-multimethod analyses: Inferring each trait/method combination with multiple indicators. Applied Measurement in Education, 6, 49-81.

Marsh, H. W., & Bailey, M. (1991). Confirmatory factor analysis of multitrait-multimethod data: A comparison of alternative models. Applied Psychological Measurement, 15, 47-70.

Marsh, H. W., & Grayson, D. (1995). Latent-variable models of multitrait-multimethod data. In R. H. Hoyle (Ed.), Structural equation modeling: Issues and applications (pp. 177-198). Newbury, CA,. Sage.

Marsh, H. W., & Hocevar, D. (1988). A new, more powerful approach to multitrait-multimethod analyses: Application of second order confirmatory factor analysis. Journal of Applied Psychology, 73, 107-117.

Marsh, H. W., Byrne, B. M., & Craven, R. (1992). Overcoming problems in confirmatory factor analyses of MTMM data: The correlated uniqueness model and factorial invariance. Multivariate Behavioral Research, 27, 489-507.

Millsap, R.E. (1992) Sufficient conditions for rotational uniqueness in the additive MTMM model. British Journal of Mathematical and Statistical Psychology, 45, 125-138.

Scullen, S. E. (1999). Using confirmatory factor analysis of correlated uniqueness to estimate method variance in multitrait-multimethod matrices. Organizational Research Methods, 2(3), 275-292.

Widaman, K. F. (1985). Hierarchically nested covariance structure models for multitrait-multimethod data. Applied Psychological Measurement, 9, 1-26.

Wothke, W. (1996). Models for multitrait-multimethod matrix analysis. In G. A. Marcoulides & R. E. Schumacher (Eds.) Advanced Structural Equation Modelling. Mahwah, NJ: Erlbaum.

VALIDITY

Cronbach, L. J. (1971). Test validity. In R. L. Thorndike (Ed.)Educational Measurement (2nd ed., pp. 443-507) Washington, D.C.: American Council on Education.

Goodman, N. (1979). Fact fiction and forecast (4th ed.). Cambridge, MA: Harvard University press.

Hubley, A. M., & Zumbo, B. D. (1996). A dialectic on validity: Where we have been and where we are going. The Journal of General Psychology, 123,207-215.

Hubley, A.M. & Zumbo, B.D. (1996). A dialectic on validity: Where we have been and where we are going. The Journal of General Psychology, 123, 207-215.

Loevinger, J. (1967). Objective tests as instruments of psychological theory. In D. N. Jackson & S. Messick (Eds.) Problems in Human Assessment (pp. 78-123). New York: Krieger.

Messick, S. (1989). Validity. In R. L. Linn (Ed.) Educational measurement(3rd ed., pp. 13-103). New York: American Council on Education.

STANDARDIZED SOLUTIONS

Chou, C. P., & Bentler, P. M. (1993). Invariant standardized estimated parameter change for model modification in covariance structure analysis. Multivariate Behavioral Research, 28, 97-110.

Raykov, T., & Marcoulides, G.A. (2000). A method for comparing completely standardized solutions in multiple groups. Structural Equation Modeling, 7, 292-308.

Kim, J. O., & Ferree, G. D., Jr. (1981). Standardization in causal analysis. Sociological Methods and Research, 10, 187-210.

Kim, J. O., & Mueller, C. W. (1976). Standardized and unstandardized coefficients in causal analysis: An expository note. Sociological Methods and Research, 4, 428-438.

SAMPLE WEIGHTING, COMPLEX SURVEY DESIGNS, SAMPLING ADJUSTMENTS

Kaplan, D., & Ferguson, A.J. (1999). On the utilization of sample weights in latent variable models. Structural Equation Modeling, 6, 305-321.

Muthen, B., & Satorra, A. (1995). Complex sample data in structural equation modeling. Sociological methodology, 25, 267-316.

REGRESSION DIAGNOSTICS, SEM DIAGNOSTICS, OUTLIERS, MULTICOLLINEARITY

Belsley, D.A., Kuh, e., & Welsch, R.E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York: John Wiley.

Bollen, K.A. and G. Arminger. 1991. Observational Residuals in Factor Analysis and Structural Equation Models (pp. 235-62). In P.M. Marsden (Ed.), Sociological Methodology 1991. Oxford: Basil-Blackwell.

Bollen, K.A., & Jackman, R.W. (1990). Regression diagnostics: An expository treatment of outliers and influential cases. In J. Fox, J.S. Long (Eds.), Modern methods of data analysis. Newbury Park, CA: Sage.

Cook, R.D., & Weisberg, S. (1994). An introduction to regression graphics. New York: Wiley.

Fox, J. (1991). Regression diagnostics. Newbury Park, CA: Sage.

Kaplan, D. (1995). Estimator conditioning diagnostics for covariance structure models. Sociological Methods and Research, 23, 200-229.

Neter, J., Kutner, M.H., Nachtsheim, C.J., & Wasserman, W. (1996). Applied linear regression models (3^rd Ed.). Chicago, IL: Irwin.

Rensvold, R. B., & Cheung, G. W. (1999). Identification of influential cases in structural equation models using the jackknife method. Organizational Research Methods, 2(3), 293-308.

Yuan, Ke-Hai; Bentler, Peter M. (2001). Effect of outliers on estimators and tests in covariance structure analysis. British Journal of Mathematical & Statistical Psychology, 54(1), 161-175.

REVERSED ITEMS, SCALING, ACQUIESCENCE, RESPONSE BIAS, SOCIAL DESIRABILITY, METHODS FACTORS

Andrich, D. (1988) The application of an unfolding model of the PIRT type to the measurement of attitude. Applied Psychological Measurement, 12, 33-51.

Goldsmith, R. E. (1987). Two Studies of Yeasaying, Psychological Reports, 60, 239-244.

J. J. Ray (1983). Reviving the Problem of Acquiescent Response Bias. Journal of Social Psychology, 121, 81-96.

J. J. Ray (1985). Acquiescence and response skewness in scale constructional paradox," Person. Individual Differences, 6, 655-656.

Marsh, H. W. (1996). Positive and negative global Self-Esteem: A substantively meaningful distinction or artifactors? Journal of Personality and Social Psychology, 70, 810-819.

Mitchell, J. (1994). Measuring dimensions of belief by unidimensional unfolding. Journal of Mathematical Psychology, 38, 244-273

Russo, J. (1994). Thurstone's scaling model applied to assessment of self-reported depression severity. Psychological Assessment, 6, 159-171.

Spector (1976). Choosing response categories for summated rating scales. Journal of Applied Psychology, 61, 374-375.

Spector (1980). Ratings of equal and unequal response choice intervals. Journal of Social Psychology,112, 115-119.

Spector, P.E., Van Katwyk, P.T., Brannick, M.T., & Chen, P.Y. (1997). When two factors don't reflect two constructs: How item characteristics can produce artificial factors. Journal of Management, 23, 659-677.

Tomas, J.M., & Olivers, A. (1999). Rosenberg's self-esteem scale: Two factors or method effects. Structural Equation Modeling, 6, 84-98.

van Schuur, H. and Kiers, H. (1994). Why factor analysis is often the incorrect model for analyzing bipolar concepts, and what model to use instead. Applied Psychological Measurement, 18, 2, 97-110.

ITEM PARCELING, ITEM PARCELS

Bandalos, D.L. (2002). The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling. Structural Equation Modeling, 9, 78-102.

Bogozzi, R. P., & Heatherton, T. F. (1994). A general approach to representing multifaceted personality constructs: Application to state self-esteem. Structural Equation Modeling, 1, 35-67.

Hall, R. J., Snell, A. F., & Foust, M. S. (1999). Item parceling strategies in SEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods 2(3), 233-256.

Kishton, J. M; Widaman, K. F. (1994). Unidimensional versus domain representative parceling of questionnaire items: An empirical example. Educational & Psychological Measurement, 54, 757-765.

Marsh HW. Hau KT. Balla JR. Grayson D. (1998). Is more ever too much: The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33, 181-220.

Russell, D. W., Kahn, J. H., Spoth, R., & Altmaier, E. M. (1998). Analyzing data from experimental studies: A latent variable structural equation modeling approach. Journal of Counseling Psychology, 45, 18-29.

META-ANALYSIS

Erez, A., Bloom, M.C., and Wells, M.T. (1996). Using random rather than fixed effects models in meta-analysis: Implications for situational specificity and validity generalization. Personnel Psychology 49:275-306.

Knight, G. P; Fabes, R. A; Higgins, D. A. (1996). Concerns about drawing causal inferences from meta-analyses: An example in the study of gender differences in aggression. Psychological Bulletin, 119, 410-421.

Rice, N. and Leyland, A. (1996). Multilevel models: Applications to health data. Journal of Health Services Research and Policy1(3):154-164.\

Shadish, W. R. (1996). Meta-analysis and the exploration of causal mediating processes: A primer of examples, methods, and issues. Psychological Methods, 1, 47-65.

Viswesvaran, C., & Ones, D.S. (1995). Theory testing: Combining psychometric meta-analysis and structural equation modeling. Personnel Psychology, 48, 865-883.

EXAMPLES OF META-ANALYSIS with SEM

Becker, B. J. (1992). Models of science achievement: Forces affecting male and female performance in school science. In T. D. Cook, H.M. Cooper, D. S. Cordray, H. Hartmann, L. V. Hedges, R. J. Light, T. A. Louis, & F. Mosteller (Eds.), Meta-analysis for explanation: A casebook(pp. 209-281). New York: Russell Sage Foundation.

Brown, S. P., & Peterson, R. A. (1993). Antecedents and consequences of salesperson job satisfaction: Meta-analysis and assessment f causal effects. Journal of Marketing Research, 30, 63-77.

Harris, M. J., & Rosenthal, R. (1985). Mediation of interpersonal expectancy effects: 31 meta-analyses. Psychological Bulletin, 97, 363-386.

Hom, P. W., Caranikas-Walker, F., Prussia, G. E., & Griffeth, R. W.(1992). A meta-analytical structural equations analysis of a model of employee turnover. Journal of Applied Psychology, 77, 890-909.

Peters, L. H., Hartke, D. D., & Pohlmann, J. T. (1985). Fiedler's contingency theory of leadership: An application of the meta-analysis procedures of Schmidt and Hunter. Psychological Bulletin, 103, 223-234.

Premack, S. L., & Hunter, J. E. (1988). Individual unionization decisions. Psychological Bulletin, 103, 223-234.

Rooney & Murray (1996). A meta-analysis of smoking prevention programs after adjustment for errors in the unit of analysis. Health Education Quarterly,23(10, 48-64.

Schmidt, F. L., Hunter, J. E., & Outerbridge, A. N. (1986). The impact of job experience and ability on job knowledge, work sample performance, and supervisory ratings of job performance. Journal of Applied Psychology, 71, 432-439.

IRT, FULL-INFORMATION ML FACTOR ANALYSIS, DIF

Bock, R.D., Gibbons, R., and Muraki, E. Full-Information Item Factor Analysis. Applied Psychological Measurement 12(3):261-280, 1988.

Bock, RD (1989). Multilevel Analysis of Educational Data. San Diego: Academic Press.

Bollen, K. A., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110, 305-314.

Christensen, H., Jorm, A. F., Mackinnon, A. J., Korten, A. E., Jacomb, P. A., Henderson, A. S., & Rodgers, B. (1999). Age differences in depression and anxiety symptoms: a structural equation modeling analysis of data from a general population sample. Psychological Medicine, 29(2), 325-39.

Clark, L. A., & Watson, D. (1995). Constructing validity: Basic issues in objective scale development. Psychological Assessment, 7, 309-319.

Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, N.J.: Lawrence Erlbaum Associates.

Floyd, F. J., & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment, 7, 286-299.

Gallo, J. J., Anthony, J. C., & Muthén, B. O. (1994). Age differences in the symptoms of depression: a latent trait analysis. Journals of Gerontology, 49(6), 251-64.

Gallo, J. J., Rabins, P. V., & Anthony, J. C. (1998). Sadness in older persons: 13-year follow-up of a community sample in Baltimore, Maryland. Psychological Medicine, 29, 341-350.

Hambleton, R. K., Swaminathan, H., & Rogers, H. (1991). Item and Test Information Functions, Fundamentals of Item Response Theory (pp. 91-98). Thousand Oaks, CA: Sage.

Hambleton, R. K., & Swaminathan, H. (1985). Item Response Theory: Principles and applications. Boston: Kluwer-Nijhoff.

Harnqvist, K, et al. (1994). Hierarchical models of ability at individual and class levels. Intelligence, 18, 165-187.

Linden, W. J., & Hambleton, R. K. (1997). Handbook of modern item response theory. New York: Springer.

Mellenbergh, G. J. (1994). Generalized Linear Item Response Theory. Psychological Bulletin, 115, 300-307.

Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58, 525-543.

Mislevy, RJ (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56, 177-196.

Muthén, B. (1988). Some uses of structural equation modeling in validity studies: Extending IRT to external variables. In H. Wainer & H. Braun (Eds.), Test Validity (pp. 213-238). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations. Meetings of Psychometric Society (1989, Los Angeles, California and Leuven, Belgium). Psychometrika, 54(4), 557-585.

Muthén, B. O., Kao, C. F., & Burstein, L. (1991). Instructionally sensitive psychometrics: Application of a new IRT-based detection technique to mathematics achievement test items. Journal of Educational Measurement, 28 (1), 1-22.

Muthén, B., & Lehman, J. (1985). Multiple group IRT modeling: Applications to item bias analysis. Journal of Educational Statistics, 10(2), 133-142.

Muthen, BO (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28, 338-354.

Oort, F. (1996). Using restricted factor analysis in test construction. Amsterdam: Faculteit der Psychologie, Universiteit van Amsterdam.

Raudenbush, S (1995). A multivariate hierarchical model for studying change within married couples. Journal of Family Psychology, 9,161-174.

Teresi, J. A., Kleinman, M., & Ocepek-Welikson, K. (2000). Modern psychometric methods for detection of differential item functioning: Application to cognitive assessment measures. Statistics in Medicine, 19, 1651-1683.

van der Linden, W.J. and Hambleton, R.K. Handbook of modern Item Response Theory, Berlin: Springer, 1997.

Weiss, D., & Yoes, M. (1990). Item Response Theory (Chapter 3). In R. Hambleton & J. Zaal (Eds.), Advances in educational and psychological testing: Theory and applications . Boston: Kluwer Academic Publishers.

RASCH MODELS

Bond, T. G, & Christine, M. (2001). Applying the Rasch model: fundamental measurement in the human sciences. Mahwah, NJ: L. Erlbaum Associates.

Fischer, G. H., & Molenaar, I. W. (1993). Rasch Models. New York:Springer-Verlag.

Fischer, G.H., & I. W. Molenaar (Eds.) (1996), Rasch Models: Foundations, Recent Developments, and Applications. Berlin: Springer

Fischer, G.H., & Molenaar, I.W. (1995). Rasch models: Foundations, recent developments, and Applications. New York: Springer-Verlag.

SUPPRESSION EFFECTS, SUPPRESSOR VARIABLES

Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. Mahway, NJ: Erlbaum

Maassen, G.H., & Bakker, A.B. (2001). Suppressor variables in path models: Definitions and interpretations. Sociological Methods and Research, 30, 241-270.

Smith, R. L., Ager, J. W., & Williams, D. L. (1992). Suppressor variables in multiple regression/correlation. Educational and Psychological Measurement, 52, 17-29.

CORRELATED ERRORS, CORRELATED UNIQUENESS

Gerbing, D. W., & Anderson, J.C. (1984). On the meaning of within-factor correlated measurement errors. Journal of Consumer Research, 11, 572-580.

Gillespie, M. W., & Fox, J. (1980). Specification errors and negatively correlated disturbances in "parallel" simultaneous-equation models. Sociological Methods and Research, 8, 273-308.

Green, S.B., & Hershberger, S.L. (2000). Correlated errors in true score models and their effect on coefficient alpha. Structural Equation Modeling, 7, 251-270.

Meng, X., Rubin, D.B., & Rosenthal, R. (1992) Comparing correlated correlation coefficients. Psychological Bulletin, 111(1), 172-175.

Rigdon, E. E. (1994). Demonstrating the effects of unmodeled random measurement error. Structural Equation Modeling, 1, 375-80.

Sivo, S.A., & Willson, V.L. (2000). Structural Equation Modeling, 7, 174-205.

Steiger, J.H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245-251.

FACTOR SCORES

Bentler & Yuan "Optimal conditionally unbiased equivariant factor score estimators." In M. Berkane (ed.) Latent variable modeling with applications to causality (pp. 259-281). New York: Springer Verlag.

Bernstein, I. H., & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evidence for multidimensionality due to item categorization. Psychological Bulletin, 105, 467-477.

HIERARCHICAL LINEAR MODELING (HLM) and MULTILEVEL MODELS

Bentler, P. M., & Satorra, A. (2000). Hierarchical regression without phantom factors. Structural Equation Modeling: A Multidisciplinary Journal, 7(2), 287-291.

Cook, W.L. (1994). A structural equation model of dyadic relationships within the family system. Journal of Consulting and Clinical Psychology, 62, 500-509.

de Jong, P. F. (1999). Hierarchical regression analysis in structural equation modeling. Structural Equation Modeling, 6(2), 198-211.

Florin et al. (1990). Levels of analysis and effects: Clarifying group influence and climate by separating individual and group effects. Journal of Applied Social Psychology, 20(11), 881-900.

Haney, W. (1980). Units and levels of analysis in large-scale evaluation. New Directions for Methodology of Social and Behavioral Science, 6, 1-15.

Harnqvist, K., Gustafsson, J.E., Muthen, B, & Nelson, G. (1994). Hierarchical models of ability at class and individual levels. Intelligence, 18, 165-187.

J.J. Hox (1995). Applied Multilevel Analysis. Amsterdam: TT-Publikaties.

Kaplan, D., & Elliott, P.R. (1997). A didactic example of multilevel structural equation modeling applicable to the study of organizations. Structural Equation Modeling, 4, 1-24.

Kenny, David A; Kashy, Deborah A; Bolger, Niall. Data analysis in social psychology. In D.T. Gilbert, S.T. Fiske et al. (1998). The handbook of social psychology, Vol. 2 (4th ed.). (pp. 233-265). Boston, MA, USA: Mcgraw-Hill. x, 1085 pp.

Kenny, D. A., & La Voie, L. (1985). Separating individual and group effects. Journal of Personality and Social Psychology, 48, 339-348.

Klein, K.J., Dansereau, F., & Hall, R.J. (1994). Levels issues in theory development, data collection, and analysis. Academy of Management Review, 19, 195-229.

McArdle, JJ., & Hamagami, F. (1996). Multilevel models from a multiple group structural equation perspective. In G.A. Marcoulides & R.E. Schumacker (eds.), Advanced Structural Equation Modeling: Issues and Techniques (pp. 89-124). Mahway, NJ: Erlbaum.

Muthen, B. (1994). Multilevel covariance structure analysis. In J. Hox &I. Kreft (eds.), Multilevel Modeling, a special issue of Sociological Methods & Research, 22, 376-398.

Muthen, B. & Satorra, A. (1995). Complex sample data in structural equation modeling. In P. Marsden (ed.), Sociological Methodology 1995, 216-316.

Muthen, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.

Muthen, B. (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28, 338-354.

Muthen, B. (1997). Latent variable growth modeling with multilevel data. In M. Berkane (ed.), Latent Variable Modeling with Applications to Causality (149-161), New York: Springer Verlag.

Muthen, B. (1997). Latent variable modeling with longitudinal and multilevel data. In A. Raftery (Ed.), Sociological Methodology (pp.453-480). Boston: Blackwell Publishers.

Newsom, J.T. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9, 431-447.

Rooney & Murray (1996). A meta-analysis of smoking prevention programs after adjustment for errors in the unit of analysis. Health Education Quarterly,23(10, 48-64.

DYADIC DATA, SOCIAL RELATIONS MODELS

Cook, W.L. (1994). A structural equation model of dyadic relationships within the family system. Journal of Consulting and Clinical Psychology, 62, 500-509.

Cook, W. L. & Goldstein, M. J. (1993). Multiple perspectives on family relationships: A latent variables model. Child Development, 64,1377-1388.

Kenny, D.A., Kashy, D.A., Bolger, N. (1998). Data analysis in social psychology. In D.T. Gilbert, S.T. Fiske et al. The handbook of social psychology, Vol. 2 (4th ed., pp. 233-265). Boston, MA: Mcgraw-Hill.

Kenny, D. A., & La Voie, L. (1984). The social relations model. In L. Berkowitz (Ed.), Advances in experimental social psychology (Vol. 18, pp 141-182). San Diego, CA: Academic Press.

Kenny, D. A., & La Voie, L. (1985). Separating individual and group effects. Journal of Personality and Social Psychology, 48, 339-348.

Neale, M.C., Eaves, L.J., Kendler, K.S., Heath, A.C., & Kessler, R.C. (1994). Multiple regression with data collected from relatives: Testing assumptions of the model. Multivariate Behavioral Research, 29, 33-61.

Newsom, J.T. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9, 431-447.

EXPLORATORY DATA ANALYSIS

Hartwig, F. & Dearing, B. E. (1979). Exploratory data analysis. Beverly Hills, CA: Sage. (QASS #16)

Mulaik, S. A. (1985). Exploratory statistics and empiricism. Philosophy of Science, 52, 410-430.

Tukey, J. W. (1977) Exploratory data analysis. Reading, MA: Addison-Wesley.

NONRECURSIVE MODELS, RECIPROCAL PATHS, RECIPROCAL CAUSES, FEEDBACK LOOPS

Berry, W.D. (1984). Nonrecursive causal models. Newbury Park, CA: Sage. QASS #37).

Pesaran, M.H. and R.J. Smith (1994). A Generalized R² Criterion for Regression Models Estimated by the Instrumental Variables Method. Econometrica, 62, 705-710.

Teel, J.E.J., Beardon, W.O., & Sharma, S. (1986). Interpreting LISREL estimates of explained variance in nonrecursive structural equation models. Journal of Marketing Research, 23, 164-168.

Wong, C., & Law, K.S. (1999). Testing reciprocal relations by nonrecursive structural equation models using cross-sectional data. Organizatonal Research Methods, 2, 69-87.

HISTORY OF STATISTICS

Cowles, M. (1989). Statistics in psychology: An historical perspective. Hillsdale NJ: Erlbaum.

Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L. Beatty, J. and Kruger, L. (1989). The empire of chance. Cambridge: Cambridge University Press.

Mackenzie, Donald A. (1981). Statistics in Britain 1865-1930 The social construction of scientific knowledge. Edinburgh: Edinburgh University Press.

Porter, T. M. (1986). The rise of statistical thinking 1820-1900. Princeton: Princeton University Press.

Stigler, S.M. (1986). The history of statistics: The treatment of uncertainty before 1900. Cambridge, MA: Harvard Univ. Press

PSYCHOMETRICS, PSYCHOMETRIC THEORY

Alwin & Jackson (1979). Measurement Models of Response Errors in Surveys: Issues and Applications. Sociological Methodology, 1980,68-119.

Carmines, E. G., & Zeller, R. A. (1979). Reliability and Validity Assessment. Newbury Park, CA: SAGE.

Cronbach (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.

Heise & Bohrnstedt (1970). Validity, Invalidity, and Reliability. Sociological Methodology, 1970, 104-129.

Hinkin, T. R. (1995). A review of scale development practices in the study of organizations. Journal of Management, 21, 967-988.

Janda, L. (1998). Psychological testing: theory and applications(Allyn & Bacon)

Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

Nunnally, J. C. (1978). Psychometric Theory. New York: McGraw-Hill.

Nunnally, J.C., & Bernstein, I.H. (1994). Psychometric theory (3^rd Ed.). New York: McGraw-Hill.

Pedhazur, E.J., & Schmelkin, L.P. (1991). Measurement, design, and Analysis: An integrated approach. Hillsdale, NJ: Erlbaum.

Reise, Widaman, and Pugh (1993). Confirmatory Factor Analysis and item Response Theory: Two Approaches for Exploring Measurement Invariance. Psychological Bulletin, 114, 552-566.

Steyer, R. (1989). Models of Classical Psychometric Test Theory as Stochastic Measurement Models: Representation, Uniqueness, Meaningfulness, Identifiability, and Testability. Methodika, 3, 25-60.

ten Berge, J. M. F. (1995). Review: Psychometric theory. Psychometrika, 60, 313-315.

EFFECTS OF MEASUREMENT ERROR

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.

P. M. Bentler, (1983). Simultaneous equation systems as moment structure models: With an introduction to latent variable models. Journal of Econometrics, 22, 13-42.

Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.

DeShon, R.P. (1998). A cautionary note on measurement error corrections in structural equation models. Psychological Methods, 3, 412-423.

Fergusson, D. M., & Horwood, L. J. (1984). Life events and depression in women: A structural equation model. Psychological Medicine, 14, 881-889.

Gillespie, M. W., & Fox, J. (1980). Specification errors and negatively20correlated disturbances in "parallel" simultaneous-equation models. Sociological Methods and Research, 8, 273-308.

Rigdon, .E. E. (1994). Demonstrating the Effects of Unmodeled Random Measurement Error, Structural Equation Modeling, 1, 375-80.

EXTENSION ANALYSIS

Dwyer, P.S. (1937). The determination of the factor loadings of a given test from the known factor loadings of other tests. Psychometrika, 2,173-178.

McDonald, R.P. Some checking procedures for extension analysis. Multivariate Behavioral Research, 13, 319-325.

PARTIAL CORRELALATIONS

Olkin, I., and Finn, J.D. (1995). Correlation Redux. Psychological Bulletin, 118,155-164.

Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. Mahway, NJ: Erlbaum

MEDIATION, INDIRECT EFFECTS (with sem)

Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American Sociological Review, 40, 37-47.

Brown, R.L. (1997). Assessing specific mediational effects in complex theoretical models. Structural equation modeling, 4, 142-156.

Finch, J. F., West, S. G., & MacKinnon, D. P. (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models. Structural Equation Modeling, 4, 87-107.

Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. Sociological Methodology, 18, 449-493.

Holmbeck, G. N. (1997). Toward terminological, conceptual, and statistical clarity in the study of mediators and moderators: Examples from the

child-clinical and pediatric psychology literatures. Journal of Consulting and Clinical Psychology, 65, 599-610.

Hoyle, R.H. & Kenny, D.A. (1999). Sample size, reliability, and tests of statistical mediation. In R. Hoyle (Ed.) Statistical Strategies for Small Sample Research. Thousand Oaks, CA: Sage Publications.

Maruyama, Chapter 5, “Effects of random and nonrandom error on path models.” Maruyama (1998).Basics of Structural Equation Modeling. Thousand Oaks: Sage.

MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002, A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83-104).

MEDIATION, INDIRECT EFFECTS (with regression)

Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology,51, 1173-1182.

Davis, J. A. (1985). The logic of causal order. SAGE Quantitative Psychology Series Paper 55. Newbury Park, CA.

Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55, 708-713.

Holmbeck, G. N. (1997). Toward terminological, conceptual, and statistical clarity in the study of mediators and moderators: Examples from the child-clinical and pediatric psychology literature. Journal of Consulting and Clinical Psychology, 65, 599-610.

James, L. R., & Brett, J. M. (1984). Mediators, moderators, and tests for mediation. Journal of Applied Psychology, 69, 307-321.

Judd, C. M., & Kenny, D. A. (1981). Process analysis: Estimating mediation in treatment evaluations. Evaluation Review, 5, 602-619.

Judd, C.M., Kenny, D.A., & McClelland, G.H. (2001). Estimating and testing mediation and moderation in within-subjects designs. Psychological Methods, 7, 115-134.

MacKinnon, D. P. (in press). Contrasts in multiple mediator models. In J. Rose & L. Chassin (Eds.), Multivariate applications in substance use research. New York: Lawrence Erlbaum.

MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158.

MacKinnon, D.P. (1994). Analysis of mediating variables in prevention and intervention research. In A. Cazares and L. A. Beatty, Scientific Methods in Prevention Research. NIDA Research Monograph 139. DHHS Pub. No. 94-3631. Washington, DC: U.S. Govt. Print. Office, pp. 127-153.

MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41-62.

MacKinnon, D.P., Lockwood, C.M., Hoffman, J. M.,West, S.G., & Sheets, V. (2002) A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-104.

Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7(4), 422-445.

Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhart (Ed.), Sociological methodology 1982 (pp. 290-312). San Francisco: Jossey-Bass.

Sobel, M.E. (1986). Some new results on indirect effects and their standard errors in structural equation models. In N.B. Tuma (Ed.) Sociological Methodology (pp. 159-186). San Francisco: Jossey-Bass.

INTERACTIONS, MODERATOR, MODERATION, LATENT MODERATORS (SEM)
(see also: NONLINEAR sem and 2SLS)

Algina, J., & Moulder, B.C. (2001). A Note on Estimating the Jöreskog-Yang Model for Latent Variable Interaction Using LISREL 8.3. Structural Equation Modeling, 8, 40-52.

Amemiya, Y., & Yalcin, I. ( 1997). Model fitting procedures for nonlinear factor analysis using the errors-in-variables parameterization. In M. Berkane (Eds.), Latent variable modeling and applications to causality (pp. 195-210). New York, Springer-Verlag.

Bollen, K. A. (1995). Structural equation models that are nonlinear in latent variables: A least-squares estimator. Sociological Methodology, 25, 223-251.

Bollen, K. A., & Paxton, P. (1998). Two-stage least squares estimation of interaction effects. In R. E. S. G. A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 125-151). Mahwah, NJ, Lawrence Erlbaum Associates.

Bollen, K.A., & Paxton, P. (1998). Interactions of latent variables in structural equation models. Structural Equation Modeling, 5, 267-293.

Busemeyer, J. & Jones, L. R., (1983). Analysis of multiplicative causal rules when the causal variables are measured with error. Psychological Bulletin, 93, 549-562.

Fuzhong, L. et al. (1998). Approaches to testing interaction effects using structural equation modeling methodology. Multivariate Behavioral Research, 33, 1-39.

Jaccard, J., & Wan, C. K. (1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator and structural equation approaches. Psychological Bulletin, 117(2), 348-357.

Joreskog, K. G. (1998). Interaction and nonlinear modeling: Issues and approaches. In G. A. M. R. E. Schumacker (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 239-250). Mahwah, NJ, Lawrence Erlbaum Associates.

Jaccard, J. & Wan, C. K. (1996). LISREL Approaches to interaction effects in multiple regression. Thousand Oaks, Calif.: Sage Publications. (Quantitative Applications in the Social Sciences, Vol. 114 ISBN: 0-8039-7179-6).

Jöreskog, K. G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In G. A. Marcoulides and R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 57-88). Mahwah, NJ: Lawrence Erlbaum.

Kenny, D. A., & Judd, C. M. (1984). Estimating the nonlinear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.

Klein, A., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65(4), 457-474.

Kline, T. J. B., & Dunn, B. (2000). Analysis of interaction terms in structural equation models: A non-technical demonstration using the deviation score approach. Canadian Journal of Behavioral Science, 32(2), 127-132.

Laplante, B., Sabourin, S., Cournoyer, L.-G., & Wright, J. (1998). Estimating nonlinear effects using a structured means intercept approach. In G. A. Marcoulides and R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 183-202). Mahwah, NJ, Lawrence Erlbaum Associates.

Li, F., Duncan, T. E., & Acock, A. (2000). Modeling interaction effects in latent growth curve models. Structural Equation Modeling, 7(4), 497-533.

Li, F.Z., Harmer, P., Duncan, T.E., Duncan, S.C., Acock, A., & Boles S. (1998). Approaches to testing interaction effects using structural equation modeling methodology. Multivariate Behavioral Research, 33, 1-39.

Lubinsky, D, & Humphreys, L. G. (1990). Assessing spurious moderator effects: Illustrated substatively with the hypothesized ("synergistic") relation between spatial and mathematical ability. Psychological Bulletin, 107, 385-393.

McDonald, R. P. (1967). Factor Interaction in nonlinear factor analysis. British Journal of Mathematical & Statistical Psychology, 20(2), 205-215.

Moulder, B.C., & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, 9, 1-19.

Ping, R.A. (1995). A parsimonious estimating technique for interaction and quadratic latent variables Journal of Marketing Research, 32, 336-347.

Ping, R.A. (1996). Estimating latent variable interactions and quadratics: The state of this art Journal of Management, 22, 163-183. Ping, R.A. (1996). Latent variable regression: A technique for estimating interaction and quadratic coefficients Multivariate Behavioral Research, 31, 95-120.

Ping, R.A. (1996). Improving the detection of interactions in selling and sales management research. Journal of Personal Selling & Sales Management, 16(1), 53-64

Ping, R.A. (1996). Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis. Psychological Bulletin, 119, 166-175.

Ping, R. A. (1996). Latent variable regression: A technique for estimating interaction and quadratic coefficients. Multivariate Behavioral Research, 31(1), 95-120.

Rigdon, E. E., Schumacker, R. E., & Wothke, W. (1998). A comparative review of interaction and nonlinear modeling. In G. A. Marcoulides and R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 1-16). Mahwah, NJ, Lawrence Erlbaum Associates.

Schumaker, R.E. (2002). Latent variable interaction modeling. Structural Equation Modeling, 9, 40-54.

Tate, R. L. (1998). Effect decomposition in interaction and nonlinear models In G. A. Marcoulides and R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 167-181). Mahwah, NJ, Lawrence Erlbaum Associates.

Wall, M. M., & Amemiya, Y. (2000). Estimation for polynomial structural equation models. Journal of the American Statistical Association, 95(451), 929-940.

Wall, M. M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1-29.

Wen, Z., Marsh, H.W., & Hau, K.-T. (2002). Interaction effects in growth modeling: A full model. Structural Equation Modeling, 9, 20-39.

Yalcin, I., & Amemiya, Y. (2001). Nonlinear factor analysis as a statistical method. Statistical Science, 16(3), 275-294.

INTERACTIONS, MODERATOR, MODERATION (REGRESSION)

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.

Arnold, H.J. (1982). Moderator variables: A clarification of conceptual, analytic, and psychometric issues. Organizational Behavior and Human Performance, 29, 143-174.

Arnold, H.J. & Evans, M.G. (1979). Testing multiplicative models does not require ratio scales. Organizational Behavior and Human Performance, 24, 41-59.

Busemeyer, J.R., & Jones, L.E. (1983). Analysis of multiplicative combination rules when the causal variables are measured with error. Psychological bulletin, 93, 549- 562.

Cortina, J.M. (1993). Interaction, Nonlinearity, and Multicollinearity - Implications for Multiple- Regression. Journal of Management, 19, 915-922.

Evans, M.G. (1985). A Monte-Carlo study of the effects of correlated method variance in moderated multiple regression analysis. Organizational Behavior and Human Decision Processes, 36, 305-323.

Evans, M.G. (1991). The problem of analyzing multiplicative composites: Interactions revisited. American Psychologist, 46, 6-15. Evans, M.G. (1991). On the use of moderated regression. Canadian Psychology, 32, 116- 119.

Ganzach, Y. (1997). Misleading interaction and curvlinear terms. Psychological Methods, 2 (3), 235-247.

Jaccard, J. & Wan, C. K.(1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple-regression - multiple indicator and structural equation approaches. Psychological Bulletin, 117, 348-357.

Kanetkar, V., Evans, M.G., Everell, S.A., Irvine, D., & Millman, Z. (1995). The effect of scale changes on meta-analysis of multiplicative and main effects models. Educational & Psychological Measurement, 55, 206-224.

Judd, C.M., Kenny, D.A., & McClelland, G.H. (2001). Estimating and testing mediation and moderation in within-subjects designs. Psychological Methods, 7, 115-134.

McClelland, G.H., & Judd, C.M. (1993). Statistical difficulties of detecting interactions and moderator effects. Psychological bulletin , 114, 376-390.

Rosnow & Rosenthal (1995). Some things you learn aren't so: Cohen's paradox, Asch's paradigm, and the interpretation of the interaction. Psychological Science, 6, 3-9.

Zedeck, S. (1971). Problems with the use of moderator variables. Psychological Bulletin, 76(4), 295-310.

NONLINEAR, QUADRATIC, CURVILINEAR, POLYNOMIAL
(see also moderation)

MacCallum, R. C., & Mar, C.M. (1995). Distinguishing between moderator and quadratic effect in multiple regression. Psychological Bulletin, 118, 405-421.

Joreskog, K.G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny-Judd model with interaction effects. In G.A. Marcoulides, & R.E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques. Mahwah, NJ: Erlbaum.

Schumacker, R. E., & Marcoulides, G.A. (Eds.) (1998). Interaction And Non-Linear Effects In Structural Equation. Mahwah, N.J.: Lawrence Erlbaum Associates.

Wall, M.M., and Amemiya, Y., (2000). Estimation for polynomial structural equation Models. The Journal of the American Statistical Association, 95, 929-940.

Wall, M. M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1-29.

TWO-STAGE LEAST SQUARES, 2SLS, TSLS
(see also moderation)

Bollen, K.A. (1995). Structural Equation Models that are Nonlinear in Latent Variables: A Least-Squares Estimator. Ch 6, pp223-252 in P. Marsden (ed) Sociological Methodology, Blackwell Publishers: Oxford.

Bollen, K.A. (1996). An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations. Psychometrika, 61, 109-121.

Bollen, K.A. (2001). Two-Stage Least Squares and Latent Variable Models: Simultaneous Estimation and Robustness to Misspecifications. Ch 7, pp 199-138 in R. Cudeck, S. du Toit and D. Sorbom (eds) Structural Equation Modeling: Present and Future: A Festschrift in honor of Karl Joreskog, Scientific Software International: Lincolnwood.

Bollen, K.A. and Paxton, P. (1998). Interactions of Latent Variables in Structural Equation Models. Structural Equation Modeling, 5, 267-293.

Oczkowski, E. (2001) Hedonic Wine Price Functions and Measurement Error. Economic Record, 77, 374-382.

Oczkowski, E. (2002) .Discriminating Between Measurement Scales using Non-nested Tests and 2SLS: Monte Carlo Evidence. Structural Equation Modeling, 9, 103-125.

Oczkowski, E. and M. Farrell (1998). Discriminating between Measurement Scales using Non-Nested Tests and Two-Stage Least Squares Estimators: The Case of Market Orientation. International Journal of Research in Marketing, 15, 349-366.

CONFIRMATORY FACTOR ANALYSIS (CFA)

Bollen, K.A. (1984). Multiple indicators: Internal consistency or no necessary relationship? Quality and Quantity, 18, 377-385.

Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.

Bollen, K. and Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110, 305-314.

Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53, 605-634.

Cohen, P., Cohen, J., Teresi, J., Marchi, M., & Velez, C.N. (1990). Problems in the measurement of latent variables in structural equations causal models. Applied Psychological Measurement, 14, 183-196.

Hayduk, L.A. (1987). Structural equation modeling with LISREL: Essentials and Advances. Baltimore, MD: Johns Hopkins University Press.

Hayduk, L.A. (1996). LISREL: Issues, Debates, and Strategies. Baltimore, MD: Johns Hopkins University Press.

MacCallum, R.C., & Brown, M.W. (1993). The use of causal indicators in covariance structure models: Some practical issues. Psychological Bulletin, 114, 533-541.

Millsap, R. A., & Everson, H. (1998). Confirmatory measurement model comparisons using latent means. Multivariate Behavioral Research, 26, 479-497.

Mulaik, Stanley A. Confirmatory factor analysis. In J.R. Nesselroade, R.B. Cattell, et al. (Eds) (1988). Handbook of multivariate experimental psychology (2nd ed.). Perspectives on individual differences. (pp.259-288). New York, NY, USA: Plenum Press.

EXPLORATORY FACTOR ANALYSIS, EFA
(see also comparing exploratory factor analysis and confirmatory factor analysis)

Cudeck, R. (2000). Exploratory factor analysis. In In H.E.A. Tinsley & S.D. Brown (Eds.), Handbook of applied multivariate statistics and mathematical modeling (pp. 265-296). San Diego, CA: Academic Press.

Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272-299.

Kim, J.-O., & Mueller, C.W. (1978). Introduction to factor analysis: What it is and how to do it. Newbury Park: Sage.

Kim, J.-O., & Mueller, C.W. (1978). Factor analysis: Statistical methods and practical issues. Newbury Park: Sage.

Tabachnick, B.G., & Fidell, L.S. (2000). Using multivariate statistics (4^th Ed.). New York: Harper-Collins.

Gorsuch, R.L. (1990). Common factor analysis versus component analysis: Some well and little known facts. Multivariate Behavioral Research, 25, 33-39.

Hurley, A.E. et al. (1997). Exploratory and confirmatory factor analysis: Guidelines, issues, and alternatives. Journal of Organizational Behavior, 18, 667-683.

Snook, S.C., & Gorsuch, R.L. (1989). Principal component analysis versus common factor analysis: A Monte Carlo study. Psychological Bulletin, 106, 148-154.

COMPARING EXPLORATORY FACTOR ANALYSIS (EFA) AND CONFIRMATORY FACTOR ANALYSIS (CFA)

Borkenau, P., & Ostendorf, F. (1990). Comparing exploratory and confirmatory factor analysis: A study on the 5-factor model of personality. Personality and Individual Differences, 11, 515-524.

Church, A. T., & Burke, P., J. (1994). Exploratory and confirmatory tests of the Big Five and Tellegen's three- and four-dimensional models. Journal of Personality and Social Psychology, 66, 93-114.

Hurley, A.E. et al. (1997). Exploratory and confirmatory factor analysis: Guidelines, issues, and alternatives. Journal of Organizational Behavior, 18, 667-683.

McCrae, R. R., Zonderman, A. B., Costa, P. T. J. r., Bond, M. H., & Paunonen, S. V. (1996). Evaluating replicability of factors in the revised NEO Personality Inventory: Confirmatory factor analyses versus procrustes rotation. Journal of Personality and Social Psychology, 70, 552-566.

CAUSAL INDICATORS
(FORMATIVE INDICATORS, FORMATIVE VS. REFLECTIVE INDICATORS, COMPOSITES, PRINCIPAL COMPONENTS)

Blalock, H.M. (1964). Causal inference in nonexperimental research. Chapel Hill, NC: University of North Carolina Press.

Bollen, K.A. & Lennox, (1991) Conventional Wisdom on Measurement: A Structural Equation Perspective, Psychological Bull, , 110,2

Bollen, K.A., & Ting, K-f. (2000). A tetrad test for causal indicators. Psychological Methods, 5, 3-22.

Diamontopoulos, A., & Winklhofer, H. M. (2001). Index construction with formative indicators: An alternative to scale development. Journal of Marketing Research, 38: 269-277.

Edwards, J.R., Bagozzi, R.P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155-174.

MacCallum and Browne, (1993). Use of Causal Indicators in Covariance Structure Models: Some, Psychological Bulletin, 114, 3

McDonald, (1996). Path Analysis with Composite Variables, Multivariate Behavioral Research, 31, 2,

COMPARING CORRELATIONS, COMPARING CORRELATION MATRICES

Meng, X., Rubin, D.B., & Rosenthal, R. (1992) Comparing correlated correlation coefficients. Psychological Bulletin, 111(1), 172-175.

Raghunathan, Rosenthal, & Rubin (1996). Comparing correlated but nonoverlapping correlations. Psychological Methods, 1, 178-183

Steiger (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 37, 245-251

Tatsuoka, M. M (1988). Multivariate analysis: Techniques for educational and Psychological Research. New York. MacMillan.

Green, J.A. (1992). Testing whether correlation matrices are different from each other. Developmental-Psychology, 28, 215-224.

INTERRATER RELIABILITY

Bartko, J.J.(1991). Measurement and Reliability: Statistical Thinking Considerations. Schizophrenia Bulletin, 17: 483-489.

Commenges, D., & Jacquin, H. (1994). The Intraclass Correlation Coefficient: Distribution-Free Definition and Test. Biometric, 50, 517-526.

Drewes, D. W. (2000). Beyond the Spearman-Brown: A Structural Approach to Maximal Reliability. Psychological Methods, 5, 214-227.

Guggenmoos-Holzmann, I. (1996) The Meaning of Kappa: Probabilistic Concepts of Reliability and Validity revisited. Journal of Clinical Epidemiology, 49: 775 - 782.

Li, H., Rosenthal, R., & Rubin, D.B. (1996). Reliability of measurement in psychology: From Spearman-Brown to maximal reliability. Psychological Methods, 1, 98-107.

Tinsley, H.E.A., & Weiss, D.J. (1975). Interrater reliability and agreement of subjective judgments. Journal of Counseling Psychology, 22(4),358-376.

FIT INDICES (FIT INDEXES)
(see also noncentrality parameter)

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246.

Bollen, 1990, Overall fit in covariance structure models: Two types of sample size effects. Psychological Bulletin, 107, 256-259.

Ding, L., Velicer, W. F., & Harlow, L. L. (1995). Effects of estimation methods, number of indicators per factor, and improper solutions on structural equation modeling fit indices. Structural Equation Modeling, 2,119-144.

Fan, X., Thompson, B., & Wang, L. (1999). Effects of sample size, estimation method, and model specification on structural equation modeling fit indexes. Structural Equation Modeling, 6, 56-83.

Haughton, D.M.A., Oud, J.H.L., & Jansen, R.A.R.G. (1997). Information and other criteria in structural equation model selection. Communications in Statistics: Simulation and Computation, 26, 1477-1516.

Hu, L., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424-453.

Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55.

Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness of fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391-410.

Marsh, H. W., Balla, J. W., & Hau, K. (1996). An evaluation of incremental fit indices: A clarification of mathematical and empirical properties. In G. A. Marcoulides and R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 315-353). Mahwah, NJ: Erlbaum.

Nevitt, J., & Hancock, G. R. (2000). Improving the root mean squared error of approximation for nonnormal conditions in structural equation modeling. Journal of Experimental Education, 68, 51-268.

Raykov, T. (2000). On the large-sample bias, variance, and mean squared error of the conventional noncentrality parameter estimator of covariance structure models. Structural Equation Modeling, 7, 431-441.

Steiger, J.H. (1989). EZPATH: A supplementary module for SYSTATand SYGRAPH. Evanston, IL: SYSTAT.

Tanaka, J.S. (1993). Multifaceted conceptions of fit in structural equation models. In K.A. Bollen, & J.S. Long (eds.), Testing structural equation models. Newbury Park, CA: Sage.

POST HOC MODEL MODIFICATION, MODIFICATION INDICES

Green, S.B., Thompson, M.S., & Poirer, J. (1999). Exploratory analysis to improve model fit: Errors due to misspecification and a strategy to reduce their occurrence. Structural Equation Modeling, 6, 113-126.

Green, S.B., Thompson, M.S., & Poirer, J. (2001). An adjusted Bonferroni method for the elimination of parameters in specification addition searches. Structural Equation Modeling, 8, 18-39.

Hancock, G.R. (1999). A sequential Scheffe-type respecification procedure for controlling Type I error in exploratory structural equation model modification. Structural Equation Modeling, 6, 158-168.

MacCallum, R. C., Roznowski, M., & Necowitz, L. B. (1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin. 111, 490-504

MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R.(1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114, 185-199.

NONCENTRALITY PARAMETER, NCP, DELTA, D

Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238-246.

McDonald, R.P., & Marsh, H.W. (1990). Choosing a multivariate model: Noncentrality and goodness of fit. Psychological Bulletin, 107, 247-255.

Steiger, J.H., & Lind, J. (1980, May). Statistically based tests ofr the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.

Steiger, J.H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25, 173-180.

TWO-STEP APPROACH TO SEM, FOUR-STEP DEBATE

Anderson, J.C., & Gerbing, D.W. (1988). Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach, Psychological Bulletin, 103, 411-23.

Anderson, J.C., & Gerbing, D.W. (1992). Assumptions and Comparative Strengths of the Two-Step Approach: Comment on Fornell and Yi. Sociological Methods & Research, 20, 321-33.

Fornell, C., & Yi, Y. (1992). Assumptions of the Two-Step Approach to Latent Variable Modeling. Sociological Methods & Research, 20, 291-320.

Fornell, C., & Yi, Y. (1992). Assumptions of the Two-Step Approach: Reply to Anderson and Gerbing, Sociological Methods & Research, 20, 334-339.

Hayduk, L.A. (1996). LISREL: Issues, Debates, and Strategies. Baltimore, MD: Johns Hopkins University Press.

Hayduk, LA., & Glaser, D.N. (2000). Jiving the four-step, waltzing around factor analysis, and other serious fun. Structural Equation Modeling, 7, 1-35. See also replies by Mulaik & Millsap, Bollen, Bentler, Herting & Costner in Vol. 7 of Structural Equation Modeling.

Markus, K.A. (2000). Comceptual shell games in the four-step debate. Structural Equation Modeling, 7, 163-173.

Mulaik, S.A., & Millsap, R.E. (2000). Doing the four-step right. Structural Equation Modeling, 7, 36-73.

BOOTSTRAPPING
(see also missing data section)

Bollen, K. A. & Stine, R. A. (1992). Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods & Research, 21, 205-229.

Bollen, K.A., & Stine, R.A. (1993). Bootstrapping goodness-of-fit measures in structural equation models. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 195-226). Newbury Park, CA: Sage. (Reprint of above 1992 reference)

Ichikawa, M. & Konishi, S. (2001). Efficient bootstrap tests for the goodness of fit in covariance structure analysis. Behaviormetrika, 28(2),103-110.

Johnson, T.R., & Bodner, T.E. (2007). A Note on the Use of Bootstrap Tetrad Tests for Covariance Structures. Structural Equation Modeling: A Multidisciplinary Journal, 14, 113-124.

Nevitt, J. & Hancock, G. R. (2001). Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling. Structural Equation Modeling,8, 353-377.

Yung, Y.-F., & Bentler, P.M. (1994). Bootstrap-corrected ADF test statistics in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 47, 63-84.

Yung, Y.-F., & Bentler, P.M. (1996). Bootstrapping techniques in analysis of mean and covariance structures. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced Structural Equation Modeling. Issues and Techniques (pp.125-157). Mahwah, NJ: Lawrence Erlbaum.

CAUSALITY AND SEM, CAUSAL INFERENCE, CAUSATION

Blalock, H. M. Jr. Correlation and causality: The multivariate case. [Journal Article] Social Forces. 39 1961, 246-251. Univ. of North Carolina Press,

Berk, R.A. (1988). Causal inference for sociological data. In N.J. Smelser (Ed.), Handbook of Sociology. Newbury Park, NJ: Sage.

Chambers, W.V. (2000). Causation and corresponding correlations. The Journal of Mind and Behavior, 21, 437-460.

Duncan, Otis Dudley (1975). Introduction to structural equation models. New York: Academic Press. ISBN: 0-1222-41509.

Glymour, C. (2001). The mind's arrows. Cambridge, Massachusets: MIT Press.

Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. Sociological Methodology, 18, 449-493.

Jöreskog, Karl G. and Herman Wold, eds. (1982). Systems under indirect observation: causality, structure, prediction. Vol. I, II. Amsterdam: North-Holland. ISBN:

0-44486301X (set)

Kenny, David A. (1979). Correlation and causality. New York: John Wiley. ISBN: 0-471-02439-2.

Mulaik, S.A., & James, L.R. (1995). Objectivity and reasoning in science and structural equation modeling. In R. H. Hoyle (Ed.), Structural Equation Modeling. Concepts, Issues, and Applications (pp. 118-137). London: Sage.

Pearl, Judea (2000). Causality: models, reasoning, and inference. Cambridge: Cambridge University Press. ISBN: 0521773628.

Scheiblechner, H. (1999). Additive conjoint isotonic probabilistic models. Psychometrika, 64, 295-316.

Scheines, Richard, Peter Spirtes, Clark Glymour, and Christopher Meek (1994) TETRAD II: Tools for Discovery. Hillsdale, N.J.: Lawrence Erlbaum Associates.

Sobel, M.E. (1994). Causal inference in latent variable models. In von Eye, A., & Clogg, C.C. (Eds.). Latent variable Analysis: Applications for developmental research (pp. 3-35). Thousand Oaks, CA: Sage.

BAYESIAN INFORMATION CRITERIA (BIC)

Raftery, A.E. (1993). Bayesian model selection in structural equation models. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 163-180). Newbury Park, CA: Sage.

Raftery, A.E. (1995). Bayesian Model Selection in Social Research. Sociological Methodology, 25, 111-163.

PLS (PARTIAL LEAST SQUARES)

Fornell , C., & Bookstein, F.L (1982), Two structural equation models: LISREL and PLS applied to consumer exit-voice theory. Journal of Marketing Research, 19, 440-452.

Fornell, C., & Cha, J. (1994), Partial least squares. In R.P. Bagozzi (Ed.), Advanced Methods of Marketing Research (pp. 52-78), Cambridge, MA: Blackwell Business,

Joreskog, K.G., & Wold, H. (1982). The ML and PLS techniques for modeling with latent variables: Historical and comparative aspects. In K.G. Joreskog, & Ketterlinus, R.D. et al. (1990). Partial least squares analysis in developmental psychopathology. Development and psychopathology, 1, 351-371.

McDonald, R. P. (1996). Path analysis with composite variables. Multivariate Behavioral Research, 31, 239-270.

Wold, H. (1982). Soft modeling: the basic design and some extensions. In K.G. Joreskog & H. Wold (ed.), Systems under Indirect Observation: Causality, Structure, Prediction, Vol.2, North-Holland, Amsterdam, p1-54.

For basic information about PLS as an alternative to SEM, see the "Related Methods" page in the SEMNET FAQ: http://www.gsu.edu/~mkteer/relmeth.html#pls

TIME SERIES

Bakeman & Gottman (1997). Observing interaction: An introduction to sequential analysis (2nd ed., Cambridge University Press; New York, NY.

Gottman, J. M., & Roy, A. K. (1990). Sequential analysis: A guide forbehavioral researchers. Cambridge: Cambridge University Press.

Hershberger, S.L., Molenaar, P.C.M., & Corneal, S.E. (1996). A hierarchy of univariate and multivariate structural time series models. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced Structural Equation Modeling: Issues and Techniques (pp.159-194). Mahwah, NJ: Lawrence Erlbaum.

See also LATENT GROWTH CURVE ANALYSIS for related methods

FACTOR ANALYSIS WITH DICHOTOMOUS DATA

Bock, D., Gibbons, R., & Muraki, E (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261-280.

Muthen, B. (1983). Latent variable structural equation modeling with categorical data. Journal of Economics, 22, 43-65.

Muthen, B. (in press). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In A. Sayer & L. Collins (Eds.), New methods for the analysis of change.

Muthen, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 115-132.

http://www.ssicentral.com/irt/testfact.htm

Mplus software http://www.statmodel.com/

FACTORIAL SURVEYS

Hox, J.J., Kreft, G.G., & Hermkens, P.L.J. (1991). The analysis of factorial surveys. Sociological Methods & Research, 19, 493- 510.

MULTIGROUP SEM, STACKED MODELS, CROSS-GROUP ANALYSIS, MEASUREMENT INVARIANCE, FACTORIAL INVARIANCE

Alwin, D.F., & Jackson, D.J. (1981). Applications of simultaneous factor analysis to issues of factorial invariance. In D. Jackson & E. Borgotta (Eds.), Factor analysis and measurement in sociological research: A multi-dimensional perspective. Beverly Hills, CA: Sage.

Bloxom, B. (1972). Alternative approaches to factorial invariance. Psychometrika, 37, 425-40.

Byrne, B.M. & Shavelson, R.J. (1987). Adolescent self-concept: Testing the assumption of equivalent structure across gender. American Educational Research Journal, 24, 365-385.

Byrne, B.M., Shavelson, R.J., & Muthen, B. (1989). Testing for the equivalence of factorial covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin, 105, 456-466.

Cheung, G.W. & Rensvold, R.B. (1999). Testing factorial invariance across groups: A reconceptualization and proposed new method. Journal of Management, 25, 1-27.

Hayduk, L.A. (1987). Structural equation modeling with LISREL: Essentials and Advances. Baltimore, MD: Johns Hopkins University Press.

Hayduk, L.A. (1996). LISREL: Issues, Debates, and Strategies. Baltimore, MD: Johns Hopkins University Press.

Joreskog, K.G. (1971). Statistical analyses of sets of congeneric tests. Psychometrika, 36, 109-134.

Kaplan, D. (1989). A study of the sampling variability and z-values of parameter estimates from misspecified structural equation models. Multivariate Behavioral Research, 24, 41-57.

Kaplan, D. (1985). Statistical power in structural equation modeling. In R. H. Hoyle (Ed.), Structural Equation Modeling. Concepts, Issues, and Applications (pp. 100-117). London: Sage.

Kim, J. O., & Ferree, G. D., Jr. (1981). Standardization in causal analysis. Sociological Methods and Research, 10, 187-210.

Kim, J. O., & Mueller, C. W. (1976). Standardized and unstandardized coefficients in causal analysis: An expository note. Sociological Methods and Research, 4, 428-438.

Lennox, J.A., & Lennox, R.D. (1995). Sex-race differences in social support in depression in older low-income adults. In R. H. Hoyle (Ed.), Structural Equation Modeling. Concepts, Issues, and Applications (pp. 199-216). London: Sage.

Little, T. D. (1997). Mean and covariance structures (MACS) analyses of cross-cultural data: Practical and theoretical issues. Multivariate Behavioral Research, 32, 53-76.

Little, T. D. (2000). On the comparability of constructs in cross-cultural research: A critique of Cheung and Rensvold. Journal of Cross-Cultural Psychology, 31, 213-219.

Magidson, J. (1977). Toward a causal model approach for adjusting for preexisting differences in the nonequivalent control groupsituation. Evaluation Quarterly, 1, 399-420.

Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58, 525-543.

Millsap, R.E. (1995). Measurement invariance, predictive invariance, and the duality paradox. Multivariate Behavioral Research, 30, 577-605

Millsap, R. E. (1997). Invariance in measurement and prediction: Their relationship in the single-factor case. Psychological Methods, 2, 248-260.

Muthen, B. (1989). Latent variable modeling in heterogenous populations. Psychometrika, 54, 557-88.

Muthen, B., & Christofferson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46, 485-500.

Raykov, T., & Marcoulides, G.A. (2000). A method for comparing completely standardized solutions in muliple groups. Structural Equation Modeling, 7, 292-308.

Steenkamp, J-B.E.M. & Baumgartner, H. (1998). Assessing measurement invariance in cross-national consumer research. Journal of Consumer Research, 25, 78-90.

Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4-69.

Werts, C.E., Rock, D.A., Linn, R.L., & Joreskog, K.G. (1977). Validating psychometric assumptions within and between several populations. Educational and Psychological Measurement, 37, 863-872.

STRUCTURAL MEANS, MEAN STRUCTURES, LATENT MEANS

Aiken, L.S., Stein, J.A., & Bentler, P.M. (1994). Structural equation analyses of clinical subpopulation differences and comparative treatment outcomes: Characterizing the daily lives of drug addicts. Journal of Consulting and Clinical Psychology, 62, 488-499.

Browne, M.W., & Arminger, G. (1995). Specification and estimation of mean- and covariance-structure models. In G. Arminger, C.C. Clogg, & M.E. Sobel (eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-241). New York: Plenum Press.

Cole, D.A., Maxwell, S.E., Arvey, R., & Salas, E. (1993). Multivariate group comparisons of variable systems: MANOVA and structural equation modeling. Psychological Bulletin, 114, 174-184.

Hancock, G.R., Lawrence, F.R., & Nevitt, J. (2000). Type I error and power of latent mean methods and MANOVA in factorially invariant and noninvariant latent variable systems. Structural Equation Modeling, 7, 534-556.

Marsh, H. W., & Grayson, D. (1994). Longitudinal stability of latent means and individual differences: A unified approach. Structural Equation Modeling, 1, 317-359.

Millsap, R. A., & Everson, H. (1998). Confirmatory measurement model comparisons using latent means. Multivariate Behavioral Research, 26, 479-497.

Sorbom, D. (1974) A general method for studying differences in factor means and factor structure across groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.

Sorbom, D. (1978). An alternative to the methodology for analysis of covariance. Psychometrika , 43, 381-396.

Sorbom, D. (1982). Structural equation models with structured means. In K.G. Joreskog & H. Wold (Eds.) Systems under indirect observation: Causality, structure, prediction_. (pp. 183-195). Amsterdam: North-Holland.

PARSIMONY

Markus, K. A. (1998). Judging Rules. The Journal of Experimental Education, 66, 261-265.

Marsh, H. W., & Hau, K-T. (1996). Assessing goodness of fit: Is parsimony always desirable? Journal of Experimental Education, 64, 364-390.

Marsh, H. W., & Hau, K-T. (1998). Is parsimony always desirable: Response to Hoyle, Sivo & Willson, Markus, Mulaik, Tweedledee, Tweedledum, the Cheshire Cat, and others. Journal of Experimental Education

Mulaik, S.A., James, L.R., Van Alstine, J., Bennett, N., Lind, S., & Stillwell, C.D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105, 430-445.

Raykov, T., & Marcoulides, G.A. (1999). On desirability of parsimony in structural equation model selection. Structural Equation Modeling, 6, 292-300.

HEYWOOD CASES, NEGATIVE ERROR VARIANCES, NONPOSITIVE DEFINITE MATRIX, IDENTIFICATION

Bekker, Merckens & Wansbeek (1994). Identification, Equivalent Models, and Computer Algebra. New York: Academic Press.

Bentler, P.M., & Chou, C.-P. (1988). Practical issues in structural modeling. In J.S. Long (Ed.), Common problems/proper solutions (pp. 161-192). Beverly Hills, CA: Sage.

Bollen, K.A., & Jöreskog, K.G. (1985). Uniqueness Does Not Imply Identification: A Note on Confirmatory Factor Analysis. Sociological Methods and Research, 14, 155-63.

Chen, F., K.A. Bollen, P. Paxton, P. Curran, and J. Kirby. 2001. Improper Solutions in Structural Equation Models: Causes, Consequences, and Strategies. Sociological Methods and Research, 29, 468-508.

Dillon, W.R., Kumar, A., & Mulani, N. (1987). Offending estimates in covariance structure analysis: Comments on the causes of and solutions to Heywood cases. Psychological Bulletin, 101, 126-135.

Johnson, T.R., & Bodner, T.E. (2007). A Note on the Use of Bootstrap Tetrad Tests for Covariance Structures. Structural Equation Modeling: A Multidisciplinary Journal, 14, 113-124.

Rigdon, E E. (1995). A necessary and sufficient identification rule for structural models estimated in practice. Multivariate Behavioral Research, 30, 359-384.

Steiger, J.H. (2002). When constraints interact: A caution about reference variables, identification constraints, and scale dependencies in structural equation modeling. Psychological Methods, 7, 210-227.

Wothke, W. (1993). Nonpositive definite matrices in structural equation modeling. In K.A. Bollen & J.S. Long (Eds.), Testing structural equation models (pp. 205-234). Newbury Park, CA: Sage.

WRITING ABOUT SEM, WRITE-UP, REPORTING SEM ANALYSES

Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7, 461-483.

Hoyle, R.H., & Panter, A.T. (1995). Writing about structural equation models. In In R. H. Hoyle (Ed.), Structural equation modeling: Comments, issues, and applications. (pp. 56-77). Thousand Oaks, CA: Sage.

McDonald, R.P., Ho, M-H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.

Raykov, T., Tomer, A., & Nesselrode, R.J. (1991). Reporting structural equation modeling results in psychology and aging: Some proposed guidelines. Psychology and Aging, 6, 499-501.