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Structural Equation Modeling: A

Multidisciplinary Journal

Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/hsem20

Causal Inference in Latent Class Analysis

Stephanie T. Lanza a , Donna L. Coffman a & Shu Xu b a The Pennsylvania State University b New York University

Published online: 22 Jul 2013.

To cite this article: Stephanie T. Lanza , Donna L. Coffman & Shu Xu (2013) Causal Inference in

Latent Class Analysis, Structural Equation Modeling: A Multidisciplinary Journal, 20:3, 361-383, DOI: 10.1080/10705511.2013.797816

To link to this article: http://dx.doi.org/10.1080/10705511.2013.797816

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Structural Equation Modeling, 20:361–383, 2013

Copyright © Taylor & Francis Group, LLC

ISSN: 1070-5511 print/1532-8007 online

DOI: 10.1080/10705511.2013.797816

Causal Inference in Latent Class Analysis

Stephanie T. Lanza,1 Donna L. Coffman,1 and Shu Xu2 1The Pennsylvania State University 2New York University

The integration of modern methods for causal inference with latent class analysis (LCA) allows social, behavioral, and health researchers to address important questions about the determinants of latent class membership. In this article, 2 propensity score techniques, matching and inverse propensity weighting, are demonstrated for conducting causal inference in LCA. The different causal questions that can be addressed with these techniques are carefully delineated. An empirical analysis based on data from the National Longitudinal Survey of Youth 1979 is presented, where college enrollment is examined as the exposure (i.e., treatment) variable and its causal effect on adult substance use latent class membership is estimated. A step-by-step procedure for conducting causal inference in LCA, including multiple imputation of missing data on the confounders, exposure variable, and multivariate outcome, is included. Sample syntax for carrying out the analysis using

SAS and R is given in an appendix.

Keywords: average causal effect, causal inference, latent class analysis, propensity scores

Latent class analysis (LCA), a technique for identifying underlying subgroups (i.e., latent classes) in a population, is a statistical method that is now widely accessible to and frequently used by social, behavioral, and health researchers. With this technique, a model with a userspecified number of latent classes is fit to a data set, yielding a vector of latent class membership probabilities and a matrix of class-specific probabilities of each response to the set of observed variables used to measure the latent variable. Recent software advances, including PROC LCA (Lanza, Dziak, Huang, Wagner, & Collins, 2013) and Mplus (Muthén & Muthén, 1998–2010), make conducting LCA and its extensions straightforward. In addition, finite mixture models more complex than LCA are becoming widely adopted by applied researchers. These models include latent transition analysis (Collins & Lanza, 2010), associative latent transition analysis (Bray, Lanza, & Collins, 2010), growth mixture modeling (Muthén & Shedden, 1999; Nagin, 2005), and finite mixture regression (Wedel & DeSarbo, 2002). All of these models share the characteristic that underlying heterogeneity is explained by a latent grouping variable, but that individuals’ actual group membership cannot be known with certainty. Rather, each individual has a (typically nonzero) probability of membership in each latent class.

Correspondence should be addressed to Stephanie T. Lanza, The Methodology Center, The Pennsylvania State

University, 204 E. Calder Way, Suite 400, State College, PA 16801. E-mail: SLanza@psu.edu 361

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L au rie r U niv ers ity ] a t 1 3:2 4 1 0 S ep tem be r 2 01 3 362 LANZA, COFFMAN, XU

A well-understood extension of finite mixture models that holds great practical importance is the ability to include observed covariates, which serve as predictors of latent class membership.

This extension is important in that it allows scientists to better understand the composition of each subgroup. For example, researchers could use LCA to identify latent classes of substance use behavior in adolescence. In this case, the identification of factors that are significantly related to increased odds of membership in classes characterized by high-risk behavior would allow for preventive interventions to be targeted toward individuals with high levels on those factors.