Multilevel Latent Class Models with Dirichlet Mixing Distribution

Chong Zhi Di, Karen J Bandeen Roche

Research output: Contribution to journalArticle

Abstract

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.

Original languageEnglish (US)
Pages (from-to)86-96
Number of pages11
JournalBiometrics
Volume67
Issue number1
DOIs
StatePublished - Mar 2011

Fingerprint

Mixing Distribution
Dirichlet Distribution
Latent Class Model
Multilevel Models
Latent Class Analysis
Maximum likelihood
Pairwise Likelihood
Maximum Likelihood
Expectation-maximization Algorithm
Likelihood Functions
obsessive-compulsive disorder
Latent Class
social sciences
Social sciences
Random Effects Model
Model Fitting
Social Sciences
Multilevel Analysis
Standard error
Maximum Likelihood Estimate

Keywords

  • Dirichlet distribution
  • EM algorithm
  • Latent class analysis (LCA)
  • Multilevel models
  • Pairwise likelihood

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

Multilevel Latent Class Models with Dirichlet Mixing Distribution. / Di, Chong Zhi; Bandeen Roche, Karen J.

In: Biometrics, Vol. 67, No. 1, 03.2011, p. 86-96.

Research output: Contribution to journalArticle

@article{5a47c50334a946b7b1888aa92d676ca7,
title = "Multilevel Latent Class Models with Dirichlet Mixing Distribution",
abstract = "Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.",
keywords = "Dirichlet distribution, EM algorithm, Latent class analysis (LCA), Multilevel models, Pairwise likelihood",
author = "Di, {Chong Zhi} and {Bandeen Roche}, {Karen J}",
year = "2011",
month = "3",
doi = "10.1111/j.1541-0420.2010.01448.x",
language = "English (US)",
volume = "67",
pages = "86--96",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "1",

}

TY - JOUR

T1 - Multilevel Latent Class Models with Dirichlet Mixing Distribution

AU - Di, Chong Zhi

AU - Bandeen Roche, Karen J

PY - 2011/3

Y1 - 2011/3

N2 - Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.

AB - Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.

KW - Dirichlet distribution

KW - EM algorithm

KW - Latent class analysis (LCA)

KW - Multilevel models

KW - Pairwise likelihood

UR - http://www.scopus.com/inward/record.url?scp=79952615101&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952615101&partnerID=8YFLogxK

U2 - 10.1111/j.1541-0420.2010.01448.x

DO - 10.1111/j.1541-0420.2010.01448.x

M3 - Article

C2 - 20560936

AN - SCOPUS:79952615101

VL - 67

SP - 86

EP - 96

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -