Latent Class Regression Utilizing Fuzzy Clusterwise Generalized Structured Component Analysis

Seohee Park,Seongeun Kim,Ji Hoon Ryoo

doi:10.3390/math8112076

Abstract

Latent class analysis (LCA) has been applied in many research areas to disentangle the heterogeneity of a population. Despite its popularity, its estimation method is limited to maximum likelihood estimation (MLE), which requires large samples to satisfy both the multivariate normality assumption and local independence assumption. Although many suggestions regarding adequate sample sizes were proposed, researchers continue to apply LCA with relatively smaller samples. When covariates are involved, the estimation issue is encountered more. In this study, we suggest a different estimating approach for LCA with covariates, also known as latent class regression (LCR), using a fuzzy clustering method and generalized structured component analysis (GSCA). This new approach is free from the distributional assumption and stable in estimating parameters. Parallel to the three-step approach used in the MLE-based LCA, we extend an algorithm of fuzzy clusterwise GSCA into LCR. This proposed algorithm has been demonstrated with an empirical data with both categorical and continuous covariates. Because the proposed algorithm can be used for a relatively small sample in LCR without requiring a multivariate normality assumption, the new algorithm is more applicable to social, behavioral, and health sciences.

Highlights

Latent class analysis (LCA [1,2,3]) is a popular statistical tool to identify the relationship between categorical latent and observed categorical variables in a variety of research areas such as education [4], psychology [5], sociology [6], medicine [7,8], and public health [9]
All analyses were executed in the gscaLCA package on the R program [47] that we created by implementing the gscaLCR functions generated
When the gender covariate was added into the generalized structured component analysis (GSCA) model in Step 1, more subjects were in the smoking and drinking class (Class 1) and less subjects were involved in the substance user class (Class 3)

Summary

Introduction

Latent class analysis (LCA [1,2,3]) is a popular statistical tool to identify the relationship between categorical latent and observed categorical variables in a variety of research areas such as education [4], psychology [5], sociology [6], medicine [7,8], and public health [9]. LCA has been used to classify mutually exclusive heterogenous subpopulations, known as latent classes, based on participants’. Responses collected as a set of observed categorical variables. LCA enumerates the latent classes in which sample units respond in similar patterns in terms of observed categorical variables. Model specification of LCA includes two sets of parameters: class membership and item-response probabilities within each class. We identified the characteristics of each class using item-response probabilities and predicted the participant’s likelihood of belonging to each class based on the parameter estimates. Owing to the advent of maximum likelihood estimation methods (MLE [10]) and the development of software packages including Mplus [11], Proc LCA [12], Latent

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