Multilevel Structural Equation Modeling

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  • Byrd, J. K. (2008). A Monte Carlo Investigation of Three Different Estimation Methods in Multilevel Structural Equation Modeling under Conditions of Data Nonnormality and Varied Sample SizesUnpublished dissertation, Texas A & M University, College Station, TX. (pdf
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  • Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529-569. (pdf)
  • Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62, 583-619. (pdf coming soon) 
  • Das, S., Chen, M.-H., Kim, S., & Warren, N. (2008). A Bayesian structural equation model for multilevel data with missing responses and missing covariates. Bayesian Analysis, 3(1), 197-224. (pdf)
  • Duncan, T. E., Duncan, S. C., Alpert, A., Hops, H., Stoolmiller, M., & Muthén, B. (1997). Latent variable modeling of longitudinal and multilevel substance abuse data. Multilevel Behavioral Research, 32(3), 275-318. (pdf)
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  • Frontiers in Psychology: Multilevel Structural Equation Modeling Research Topic Page
  • Fall, E. (2011). Modeling heterogeneity in indirect effects: Multilevel structural equation modeling strategies. Unpublished doctoral dissertation. Lawrence, Kansas: University of Kansas. (pdf)
  • Geiser, C., Bishop, J., Lockhart, G., Shiffman, S., & Grenard, J. L. (2013). Analyzing latent state-trait and multiple-indicator latent growth curve models as multilevel structural equation models.  Frontiers in Psychology: Quantitative Psychology and Measurement. (pdf)
  • Geldhof, G. J., Preacher, K. J., & Zyphur, M. J. (in press). Reliablility estimation in a mutlilevel confirmatory factor analysis framework. Psychological Methods. (pdf)
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  • Hox, J. J. (1993). Factor analysis of multilevel data: Gauging the Muthén model. In J. H. L. Oud & R. A. W. Blokland-Vogelesang (Eds.). Advances in longitudinal and multivariate analysis in the behavioral sciences. (pp. 141-156).  Nijmegen, NL: ITS. (pdf)
  • Hox, J. J. (2002). Multilevel multivariate and structural equation models: Some missing links. In J. Blassius, J. J. Hox, E. de Leeuw, & P. Schmidt (Eds.), Social science methodology in the new millenium. Proceedings of the Fifth International Conference on Logic and Methodology, second expanded edition. Opladen: Leske - Budrich. (pdf)
  • Hox, J. J. (2010). Multilevel path models. In J. Hox, Multilevel Analysis: Technique and Applications. (2nd ed.). New York: Routledge. (pdf)
  • Hox, J. J., & Maas, C. J. M. (2009). The accuracy of multilevel structural equation modeling with pseudobalanced groups and small samples. Structural Equation Modeling, 8(2), 157-174. (pdf coming soon)
  • Hox, J. J., Maas, C. J. M., & Brinkhuis, M. J. S. (2010). The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64, 157-170. (pdf).
  • Hox, J. J. (2013). Multilevel regression and multilevel structural equation modeling. In T. Little (Ed.), Oxford Handbook of Quantitative Methods,Volume 2 (pp. 281-294). Oxford University Press. (pdf)
  • Jak, S., Oort, F.J. & Dolan, C.V. (2014). Measurement bias in multilevel data. Structural Equation Modeling, 21, 31-39. (pdf coming soon)
  • Jak, S. (2014). Testing strong factorial invariance using three-level structural equation modeling. Frontiers in Psychology, 5, 745. (pdf coming soon)

  • Jak, S., Oort, F.J. & Dolan, C.V. (2013). A test for cluster bias: Detecting violations of measurement invariance across clusters in multilevel data. Structural Equation Modeling, 20, 265-282. (pdf coming soon)

  • Jak, S., Oort, F.J. & Dolan, C.V. (2014). Measurement bias in multilevel data. Structural Equation Modeling, 21,31 - 39. (pdf coming soon)

  • Jedidi, K., & Ansari, A. (2001). Bayesian structural equation models for multilevel data. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 129-157). New York, NY: Erlbaum. (pdf)
  • Kamata, A. J., Bauer, D. J., & Miyazaki, Y. (2008). Multilevel measurement models. In A. A. O'Connell & B. D. McCoach (Eds.) Multilevel modeling of educational data (pp. 345-388). Charlotte, NC: Information Age. (pdf)
  • 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), 1-24.(pdf coming soon)
  • Kaplan, D., Kim, J.-S., & Kim, S.-Y.  (2009). Multilevel latent variable modeling: Current research and recent developments. In R. Millsap & A. Maydeu-Olivares (Eds.),Sage handbook of quantitative methods in psychology (pp. 592-612). Thousand Oaks, CA: Sage. (pdf)
  • Kaplan, D., & Kreisman, M. B. (2000). On the validation of indicators of mathematics education using TIMSS: An application of multilevel covariance structure analysis. International Journal of Educational Policy, Research, and Practice, 1, 217-242. (pdf)
  • Kelava, A., Moosbrugger, H., Dimitruk, P., & Schermelleh-Engel, K. (2008). Multicollinearity and MSEM for moderation missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects. Methodology, 4, 51-66. (pdf)
  • Lachowicz, M. J., Sterba, S. K., & Preacher, K. J. (2015). Investigating multilevel mediation with fully or partially nested dataGroup Processes & Intergroup Relations18, 274-289(pdf coming soon)
  • Lee, S.-Y., & Poon, W. Y. (1998). Analysis of two-level structural equation models via EM type algorithms. Statistica Sinica, 8, 749-766. (pdf)
  • Lee, S. Y., & Song, X.-Y. (2001). Hypothesis testing and model comparison in two-level structural equation modeling. Multivariate Behavioral Research, 36, 639-655. (pdf)
  • Lee, S.-Y., & Tsang, S. Y. (1999). Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms Psychometrika, 64, 435-450. (pdf)
  • Leite, W. L., & Zuo, Y. (2011). Modeling latent interactions at level 2 in multilevel structural equation models: An evaluation of mean-centered and residual-centered unconstrained approaches. Structural Equation Modeling, 18, 449-464. 
  • Liang, J., & Bentler, P. M. (2004). An EM algorithm for fitting two-level structural equation models. Psychometrika, 69, 101-122. (pdf)
  • Little, J. (2013). Multilevel confirmatory ordinal factor analysis of the Life Skills Profile-16. Psychological Assessment25(3), 810-825. (pdf)
  • Longsford, N. T., & Muthén, B. (1992). Factor analysis for clustered observations. Psychometrika, 57, 581-597. (pdf)
  • Lüdtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203-229. (pdf)
  • Lüdtke, O., Marsh, H. W., Robitzsch, A., & Trautwein, U. (2011). A 2 × 2 taxonomy of multilevel latent contextual models: Accuracy-bias trade-offs in full and partial error correction models. Psychological Methods, 16, 444-467. (pdf coming soon)  
  • McDonald, R. P. (1993). A general model for two-level data with responses missing at random. Psychometrika, 58, 575-585. (pdf)
  • McDonald, R. P. (1994). The bilevel reticular action model for path analysis with latent variables. Sociological Methods and Research, 22, 399-413. (pdf)
  • McDonald, R. P., & Goldstein, H. L. (1989). Balanced versus unbalanced designs for linear structural relations in two-level data. British Journal of Mathematical and Statistical Psychology, 42, 215-232. (pdf)
  • Mehta, P. D., & Neale, M. C. (2005). People are variables too:  Multilevel structural equation modeling. Psychological Methods, 10, 259-284(pdf)
  • Merz, E. L., & Roesch, S. C. (2011). Modeling trait and state variation using multilevel factor analysis with PANAS daly diary data. Journal of Research in Personality, 45, 2-9. (pdf)
  • Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrica, 54, 557-585. (pdf)
  • Muthén, B. (1990). Mean and covariance structure analysis of hierarchical data (UCLA Statistics Series No. 62). Los Angeles: University of California. (pdf)
  • Muthén, B. (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28, 338-354. (pdf)
  • Muthén, B. (1994). Multilevel covariance structure analysis. Sociological Methods and Research, 22, 376-398. (pdf)
  • Muthén, B. (2007). Latent variable modeling of longitudinal and multilevel data. Sociological Methodology, 27, 453-480. (pdf)
  • Muthén, B., & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In G. Fitzmaurice, M. Davidian, G. Verbeke, & G. Molenberghs (Eds.), Longitudinal Data Analysis (pp. 143-165). Boca Raton, FL: Chapman & Hall/CRC. (pdf)
  • Muthén, B., & Asparouhov, T. (2011). Beyond multilevel regression modeling: Multilevel analysis in a general latent variable context. In J. J. Hox & J. K. Roberts (Eds.), Handbook of advanced multilevel analysis. (pp. 15-40). New York: Routledge. (pdf)
  • Muthén, B., & Satorra, A. (1989). Multilevel aspects of varying parameters in structural models. In D. R. Bock (Ed.), Multilevel analysis of educational data (pp. 87-99). San Diego, CA: Academic Press. (pdf)
  • Muthén, B., & Satorra, A. (1995) Complex sample data in structural equation modeling. Sociological Methodology, 25, 267-316. (pdf)
  • Peugh, J.L. (2006). Specification Searches in Multilevel Structural Equation Modeling: A Monte Carlo Investigation. (Unpublished doctoral dissertation).  University of Nebraska, Lincoln. (pdf)
  • Peugh, J.L., & Enders, C.K. (2010). Specification searches in multilevel structural equation modeling: A Monte Carlo investigation. Structural Equation Modeling: A Multidisciplinary Journal, 17, 42-65. (pdf)
  • Preacher, K. J., Zhang, Z., & Zyphur, M. J. (2011). Alternative methods for assessing mediation in multilevel data: The advantages of multilevel SEMStructural Equation Modeling18, 161-182. (pdf)
  • Preacher, K. J. (2011). Multilevel SEM strategies for evaluating mediation in three-level data. Multivariate Behavioral Research46, 691-731. (pdf)
  • Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods15, 209-233. (pdf)
  • Preacher, K. J., Zhang, Z., & Zyphur, M. J. (in press). Multilevel structural equation models for assessing moderation within and across levels of analysisPsychological Methods (pdf coming soon)
  • Rabe-Hesketh, S., Skrondal, A., & Pickles, A. (2004). Generalized multilevel structural equation modeling. Psychometrika, 69, 167-190. (pdf)
  • Rabe-Hesketh, S., Skrondal, A., & Zheng, X. (2012). Multilevel structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 512-531). New York: The Guilford Press. (pdf)
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  • Raykov, T., & Mehls, G. (2007). Lower level mediation effect analysis in two-level studies: A note on a multilevel structural equation modeling approach. Structural Equation Modeling, 14(4), 636-648. (pdf coming soon)
  • Reise, S. P., Ventura, J., Nuechterlein, K. H., & Kim, K. H. (2005). An illustration of multilevel factor analysis. Journal of Personality Assessment, 84(2), 126-136. (pdf)
  • Roesch, S. C., Aldridge, A. A., Stocking, S. N., Vilodas, F., Leung, Q., Bartley, C., & Black, L. J. (2010). Multilevel factor analysis and structural equation modeling of daily diary coping data: Modeling trait and state variation. Multivariate Behavioral Research, 45, 767-789. (pdf)
  • Ryu, E. (2008). Evaluation of Model Fit in Multilevel Structural Equation Modeling: Level-Specific Model Fit Evaluation and the Robustness to Nonnormality. Unpublished dissertation, Arizona State University, Tempe, AZ. (pdf)
  • Ryu, E. (2011). Effects of skewness and kurtosis on normal-theory based maximum likelihood test statistic in multilevel structural equation modeling. Behavior Research Methods, 43, 1066-1074. (link)
  • Ryu, E. (2014). Model fit evaluation in multilevel structural equation models. Frontiers in Psychology: Quantitative Psychology and Measurement, 5. (pdf)
  • Ryu, E. (2014). Factorial invariance in multilevel confirmatory factor analysis British Journal of Mathematical and Statistical Psychology, 67, 172-194. (pdf)
  • Ryu, E., & West, S. G. (2009). Level-specific evaluation of model fit in multilevel structural equation modeling. Structural Equation Modeling, 16, 583-601. (pdf)
  • Ryu, E. (in press). The role of centering for interaction of level 1 variables in multilevel structural equation models. Structural Equation Modeling, YY-ZZ (pdf coming soon)
  • Schermelleh-Engel, K., Klein, A. & Moosbrugger, H. (1998). Estimating nonlinear effects using a latent moderated structural equations approach. In R.E. Schumacker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 203-238). Mahwah, NJ: Lawrence Erlbaum Associates. (pdf coming soon)  
  • Schermelleh-Engel, K., Kerwer, M., & Klein, A. G. (2014). Evaluation of model fit in nonlinear multilevel structural equation modeling. Frontiers in Psychology: Quantitative Psychology and Measurement. doi: 10.3389/fpsyg.2014.00181 (pdf coming soon)
  • Schmidt, W. H. (1969). Covariance structure analysis of the multivariate random effects model (Unpublished doctoral dissertation). University of Chicago. (pdf)
  • Skrondal, A., & Rabe-Hesekth, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, F:L Chapman & Hall/CRC. (link)
  • SSI Session 12 Document about Multilevel Structural Equation Modeling in LISREL
  • SSI Multilevel Structural Equation Modeling Technical Document
  • Stapleton, L. M. (2002). The incorporation of sample weights into multilevel structural equation modeling. Structural Equation Modeling, 9(4), 475-502. (pdf)
  • Stapleton, L. M. (2013). Using multilevel structural equation modeling techniques with complex sample data. In Hancock, G. R., & Mueller, R. (Eds). A Second Course in Structural Equation Modeling, 2nd Ed. (pp. 521-562). Greenwich, CT: Information Age Publishing. (pdf)
  • Sterba, S. K., Preacher, K. J., Forehand, R., Hardcastle, E., Cole, D. A., & Compas, B. E. (2014). Structural equation modeling approaches for analyzing partially nested dataMultivariate Behavioral Research49, 93-118. (pdf)
  • Wu, J.-Y., & Kwok, O.-m. (2012). Using SEM to analyze complex survey data: A comparison between design-based single-level and model-based multilevel approaches. Structural Equation Modeling, 19(1), 16-35. (pdf coming soon)
  • Yuan, K.-H., & Bentler, P. M. (2007). Multilevel covariance structure analysis by fitting multiple single-level models. Sociological Methodology, 37, 53-82. (pdf)
  • Zhang, Z., Zyphur, M. J., & Preacher, K. J. (2009). Testing multilevel mediation using hierarchical linear models: Problems and solutionsOrganizational Research Methods12, 695-719. (pdf)
  • More to come...(if you have suggestions, feel free to send references)
  • slides
  • Mplus code
  • xxM in R for multilevel SEM (manual)
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