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Abstract: Bayesian Inferencefor Growth Mixture ModelsWith Nonignorable Missing DataZhenqiu Laura Lu a , Zhiyong Johnny Zhang a & GittaLubke aa Department of Psychology , University of NotreDamePublished online: 20 Dec 2010.

To cite this article: Zhenqiu Laura Lu , Zhiyong Johnny Zhang & Gitta Lubke(2010) Abstract: Bayesian Inference for Growth Mixture Models With NonignorableMissing Data, Multivariate Behavioral Research, 45:6, 1028-1029, DOI:10.1080/00273171.2010.534381

To link to this article: http://dx.doi.org/10.1080/00273171.2010.534381

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Multivariate Behavioral Research, 45:1028–1029, 2010

Copyright © Taylor & Francis Group, LLC

ISSN: 0027-3171 print/1532-7906 online

DOI: 10.1080/00273171.2010.534381

Abstract: Bayesian Inference for Growth MixtureModels With Nonignorable Missing Data

Zhenqiu (Laura) Lu, Zhiyong (Johnny) Zhang, and Gitta LubkeDepartment of PsychologyUniversity of Notre Dame

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing

attention in psychological research communities but have not been fully studied. Whenthe assumption of ignorable missingness mechanism does not hold, it becomes neces-

sary to model missingness mechanisms. However, few studies have discussed how todeal with nonignorable missing data in the framework of GMMs. Also, most of previous

studies have relied on maximum likelihood method for parameter estimation and carriedout inferences through conventional likelihood procedures. Bayesian methods providegreat advantages in the analysis of complex models with complicated data structure.

The goal of this paper is to propose and to evaluate a Bayesian method to estimate theGMM with nonignorable missing data.

In this study, an extended GMM (see Figure 1) is first presented in which classprobabilities are predicted by some observed explanatory variables and data missingness

depends on both the explanatory variables and a categorical latent class variable.Through the data augmentation algorithm, conditional posterior distributions for allmodel parameters and missing data are obtained. A Gibbs sampling procedure is then

used to generate Markov chains of model parameters for statistical inference. Theapplication of the model and the method is first demonstrated through the analysis

of the Peabody Individual Achievement Test Mathematics Assessment data from theNational Longitudinal Survey of Youth 1997 cohort (Bureau of Labor Statistics, U.S.

Department of Labor, 2005). Based on our real data analysis, a simulation studyconsidering three main factors (the sample size, the class probability, and the missingdata mechanism) is then conducted to evaluate the performance of the model and the

Bayesian estimation method. Results show that the proposed Bayesian method can(a) recover model parameters very well, (b) estimate the standard errors very well, and

(c) work equally well for both the nonignorable and the ignorable missing mechanisms.Finally, some implications of this study, including the sensitivity of the model, the

misspecified missingness mechanism, the sample size, and the future directions, arediscussed.

Bureau of Labor Statistics, U.S. Department of Labor. (2005). National Longitudinal Survey of Youth 1997 cohort,

1997–2003 (rounds 1–7) [computer file]. Columbus, OH: Center for Human Resource Research.

The first author appreciates her SMEP sponsor, Gitta Lubke. The first author also thanks Johnny Zhang,

Ke-Hai Yuan, and Scott Maxwell for their help.

Correspondence concerning this abstract should be addressed to Laura Lu, University of Notre Dame,

Department of Psychology, 118 Haggar Hall, Notre Dame, IN 46556. E-mail: Lu.30@nd.edu

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