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Two-Step Estimation of Models Between Latent Classes and External Variables

Published online by Cambridge University Press:  01 January 2025

Zsuzsa Bakk  and
Jouni Kuha
Zsuzsa Bakk*
Affiliation:
Leiden University
Jouni Kuha
Affiliation:
London School of Economics and Political Science
*
Correspondence should be made to Zsuzsa Bakk, Leiden University, Leiden, The Netherlands. Email: [email protected]
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Abstract

We consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables. We propose a two-step method of estimating such models. In its first step, the measurement model is estimated alone, and in the second step the parameters of this measurement model are held fixed when the structural model is estimated. Simulation studies and applied examples suggest that the two-step method is an attractive alternative to existing one-step and three-step methods. We derive estimated standard errors for the two-step estimates of the structural model which account for the uncertainty from both steps of the estimation, and show how the method can be implemented in existing software for latent variable modelling.

Keywords

latent variablesmixture modelsstructural equation modelspseudo-maximum likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 4 , December 2018 , pp. 871 - 892
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-017-9592-7) contains supplementary material, which is available to authorized users.

References

Anderson, J. C., &Gerbing, D. W.(1988).Structural equation modeling in practice: A review and recommended two-step approach.Psychological Bulletin,103,411423.CrossRefGoogle Scholar
Asparouhov, T., &Muthén, B.(2014).Auxiliary variables in mixture modeling: Three-step approaches using Mplus.Structural Equation Modeling,21,329341.CrossRefGoogle Scholar
Asparouhov, T., & Muthén, B.(2015).Auxiliary variables in mixture modeling: Using the BCH method in Mplus to estimate a distal outcome model and an arbitrary secondary model (Mplus Web Notes No. 21).Google Scholar
Bakk, Z.,Oberski, D., &Vermunt, J.(2014).Relating latent class assignments to external variables: Standard errors for correct inference.Political Analysis,22,520540.10.1093/pan/mpu003CrossRefGoogle Scholar
Bakk, Z., Oberski, D. L., & Vermunt, J. K.(2014b). Replication data for: Relating latent class assignments to external variables: Standard errors for correct inference.Harvard Dataverse. Retrieved from https://doi.org/10.7910/DVN/24497.CrossRefGoogle Scholar
Bakk, Z.,Tekle, F. T., &Vermunt, J. K.(2013).Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches.Sociological Methodology,43,272311.CrossRefGoogle Scholar
Bakk, Z., &Vermunt, J. K.(2016).Robustness of stepwise latent class modeling with continuous distal outcomes.Structural Equation Modeling,23,2031.CrossRefGoogle Scholar
Bandeen-Roche, K.,Miglioretti, D. L.,Zeger, S. L., &Rathouz, P. J.(1997).Latent variable regression for multiple discrete outcomes.Journal of the American Statistical Association,92,13751386.CrossRefGoogle Scholar
Bartolucci, F.,Montanari, G. E., & Pandolfi, S.(2014).A comparison of some estimation methods for latent Markov models with covariates.In Proceedings of COMPSTAT 2014—21st International Conference on Computational Statistics(531–538).Google Scholar
Bolck, A.,Croon, M., &Hagenaars, J.(2004).Estimating latent structure models with categorical variables: One-step versus three-step estimators.Political Analysis,12,327.CrossRefGoogle Scholar
Bollen, K. A.(1989).Structural equations with latent variables,New York:WileyCrossRefGoogle Scholar
Bollen, K. A.(1996).An alternative two stage least squares (2SLS) estimator for latent variable equations.Psychometrika,61,109121.CrossRefGoogle Scholar
Burt, R. S.(1973).Confirmatory factor-analytic structures and the theory construction process.Sociological Methods & Research,2,131190.CrossRefGoogle Scholar
Burt, R. S.(1976).Interpretational confounding of unobserved variables in structural equation models.Sociological Methods & Research,5,352.CrossRefGoogle Scholar
Cameron, A. C., &Trivedi, P. K.(2005).Microeconometrics: Methods and applications,Cambridge:Cambridge University PressCrossRefGoogle Scholar
Chan, T. W., &Goldthorpe, J. H.(2007).European social stratification and cultural consumption: Music in England.Sociological Review,23,1119.Google Scholar
Clogg, C. C.,Jackson, D. J., &Borgotta, E. F.(1981).New developments in latent structure analysis.Factor analysis and measurement in sociological research,London:SageGoogle Scholar
Croon, M.,Marcoulides, G. A., &Moustaki, I.(2002).Using predicted latent scores in general latent structure models.Latent variable and latent structure models,Mahwah, NJ:Lawrence Erlbaum 195223.Google Scholar
Dayton, C. M., &Macready, G. B.(1988).Concomitant-variable latent class models.Journal of the American Statistical Association,83,173178.CrossRefGoogle Scholar
De Cuyper, N.,Rigotti, T.,Witte, H. D., &Mohr, G.(2008).Balancing psychological contracts: Validation of a typology.International Journal of Human Resource Management,19,543561.CrossRefGoogle Scholar
Dempster, A. P.,Laird, N. W., &Rubin, D. B.(1977).Maximum likelihood from incomplete data via the EM algorithm (with discussion).Journal of the Royal Statistical Society B,39,138.CrossRefGoogle Scholar
Devlieger, I.,Mayer, A., &Rosseel, Y.(2016).Hypothesis testing using factor score regression: A comparison of four methods.Educational and Psychological Measurement,76,741770.CrossRefGoogle ScholarPubMed
De Witte, H.,Bouwen, R.,De Witte, K.,De Witte, H., &Taillieu, T.(2000).Arbeidsethos en jobonzekerheid: Meting en gevolgen voor welzijn, tevredenheid en inzet op het werk [Work ethic and job insecurity: Measurement and consequences for well-being, satisfaction and performance].Van groep naar gemeenschap. Liber Amicorum Prof. Dr. Leo Lagrou,Leuven:Garant 325350.Google Scholar
Dias, J. G., &Vermunt, J. K.(2008).A bootstrap-based aggregate classifier for model-based clustering.Computational Statistics,23,64359.CrossRefGoogle Scholar
Einarsen, S.,Hoel, H., &Notelaers, G.(2009).Measuring exposure to bullying and harassment at work: Validity, factor structure and psychometric properties of the Negative Acts Questionnaire—Revised.Work & Stress,23,2444.CrossRefGoogle Scholar
Gong, G., &Samaniego, F. J.(1981).Pseudo maximum likelihood estimation: Theory and applications.The Annals of Statistics,76,861889.Google Scholar
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,79,11791259.CrossRefGoogle Scholar
Gourieroux, C., &Monfort, A.(1995).Statistics and econometric models,Cambridge:Cambridge University PressGoogle Scholar
Haberman, S.(1979).Analysis of qualitative data. vol. 2: New developments,New York:Academic PressGoogle Scholar
Hagenaars, J. A.(1993).Loglinear models with latent variables,Newbury Park, CA:SageCrossRefGoogle Scholar
Jöreskog, K. G., &Sörbom, D.(1986).LISREL VI: Analysis of linear structural relationships by maximum likelihood and least squares methods,Mooresville, IN:Scientific Software IncGoogle Scholar
Kam, J. A.(2011).Identifying changes in youth’s subgroup membership over time based on their targeted communication about substance use with parents and friends.Human Communication Research,37,324349.CrossRefGoogle Scholar
Lance, C. E.,Cornwell, J. M., &Mulaik, S. A.(1988).Limited information parameter estimates for latent or mixed manifest and latent variable models.Multivariate Behavioral Research,23,171187.CrossRefGoogle ScholarPubMed
Lanza, T. S.,Tan, X., &Bray, C. B.(2013).Latent class analysis with distal outcomes: A flexible model-based approach.Structural Equation Modeling,20(1).126.CrossRefGoogle ScholarPubMed
Lazarsfeld, P. F., &Henry, N. W.(1968).Latent structure analysis latent structure analysis,Boston:Houghton-MifflinGoogle Scholar
Lu, IRR, &Thomas, D. R.(2008).Avoiding and correcting bias in score-based latent variable regression with discrete manifest items.Structural Equation Modeling,15,462490.CrossRefGoogle Scholar
Magidson, J.(1981).Qualitative variance, entropy, and correlation ratios for nominal dependent variables.Social Science Research,10,177194.CrossRefGoogle Scholar
McCutcheon, A. L.(1985).A latent class analysis of tolerance for nonconformity in the American public.Public Opinion Quarterly,494,474488.CrossRefGoogle Scholar
McCutcheon, A. L.(1987).Latent class analysis,Newbury Park, CA:SageCrossRefGoogle Scholar
Muthén, L. K., &Muthén, B. O.(2017).Mplus user’s guide [Computer software manual],(8)Los Angeles, CA:Muthen and MuthenGoogle Scholar
Petersen, J.,Bandeen-Roche, K.,Budtz-Jørgensen, E., &Groes Larsen, K.(2012).Predicting latent class scores for subsequent analysis.Psychometrika,77,244262.CrossRefGoogle ScholarPubMed
Ping, R. A.(1996).Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis.Psychological Bulletin,119,166175.CrossRefGoogle Scholar
PSYCONES.(2006).Psychological contracts across employment situations, final report. DG Research, European Commission. Retrieved from http://cordis.europa.eu/documents/documentlibrary/100123961EN6.pdfGoogle Scholar
R Core Team.(2016).R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria.https://www.R-project.org.Google Scholar
Skrondal, A., &Kuha, J.(2012).Improved regression calibration.Psychometrika,77,649669.CrossRefGoogle Scholar
Skrondal, A., &Laake, P.(2001).Regression among factor scores.Psychometrika,66,563576.CrossRefGoogle Scholar
Vermunt, J. K.(2010).Latent class modeling with covariates: Two improved three-step approaches.Political Analysis,18,450469.CrossRefGoogle Scholar
Vermunt, J. K., &Magidson, J.(2005).Latent GOLD 4.0 user’s guide,Belmont, MA:Statistical InnovationsGoogle Scholar
Vermunt, J. K., &Magidson, J.(2016).Technical guide for Latent GOLD 5.1: Basic, Advanced and Syntax,Belmont, MA:Statistical InnovationsGoogle Scholar
Xue, Q. L., &Bandeen-Roche, K.(2002).Combining complete multivariate outcomes with incomplete covariate information: A latent class approach.Biometrics,58,110120.CrossRefGoogle ScholarPubMed
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