Latent Class Analysis for Multiple Discrete Latent Variables: A Study on the Association Between Violent Behavior and Drug-Using Behaviors

This article proposes a new type of latent class analysis, joint latent class analysis (JLCA), which provides a set of principles for the systematic identification of the subsets of joint patterns for multiple discrete latent variables. Inferences about the parameters are obtained by a hybrid method of expectation-maximization and Newton–Raphson algorithms. We apply JLCA in an investigation of adolescent violent behavior and drug-using behaviors. The data are from 4,957 male high-school students who participated in the Youth Risk Behavior Surveillance System in 2015. The JLCA approach identifies the different joint patterns of 4 latent variables: violent behavior, alcohol consumption, tobacco cigarette smoking, and other drug use. The JLCA uncovers 4 common violent behaviors and 3 representative behavioral patterns for each of 3 other latent variables. In addition, the JLCA supports 3 common joint classes, representing the most probable simultaneous patterns for being violent and being a drug user among adolescent males.     

Relating Latent Class Membership to Continuous Distal Outcomes: Improving the LTB Approach and a Modified Three-Step Implementation

Latent class analysis often aims to relate the classes to continuous external consequences (“distal outcomes”), but estimating such relationships necessitates distributional assumptions. Lanza, Tan, and Bray (2013) suggested circumventing such assumptions with their LTB approach: Linear logistic regression of latent class membership on each distal outcome is first used, after which this estimated relationship is reversed using Bayes’ rule. However, the LTB approach currently has 3 drawbacks, which we address in this article. First, LTB interchanges the assumption of normality for one of homoskedasticity, or, equivalently, of linearity of the logistic regression, leading to bias. Fortunately, we show introducing higher order terms prevents this bias. Second, we improve coverage rates by replacing approximate standard errors with resampling methods. Finally, we introduce a bias-corrected 3-step version of LTB as a practical alternative to standard LTB. The improved LTB methods are validated by a simulation study, and an example application demonstrates their usefulness.     

A Comparison of Three-Step Approaches for Auxiliary Variables in Latent Class and Latent Profile Analysis

In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.     

Covariates and Mixture Modeling: Results of a Simulation Study Exploring the Impact of Misspecified Effects on Class Enumeration

For some time, there have been differing recommendations about how and when to include covariates in the mixture model building process. Some have advocated the inclusion of covariates after enumeration, whereas others recommend including them early on in the modeling process. These conflicting recommendations have led to inconsistent practices and unease in trusting modeling results. In an attempt to resolve this discord, we conducted a Monte Carlo simulation to examine the impact of covariate exclusion and misspecification of covariate effects on the enumeration process. We considered population and analysis models with both direct and indirect paths from the covariates to the latent class indicators. As expected, misspecified covariate effects most commonly led to the overextraction of classes. Findings suggest that the number of classes could be reliably determined using the unconditional latent class model, thus our recommendation is that class enumeration be done prior to the inclusion of covariates.     

Estimating Latent Variable Interactions with the Unconstrained Approach: A Comparison of Methods to Form Product Indicators for Large,Unequal Numbers of Items

This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the smaller scale, multiplying the three most reliable indicators of each scale matched by reliability, and matching items by reliability to create as many product indicators as the number of indicators of the smallest scale. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. All methods considered provided unbiased parameter estimates. Unbiased standard errors were obtained in all conditions with the LMS approach and when the sample size was large with the unconstrained approach. Power levels to test the latent interaction and Type I error rates were similar for all methods but slightly better for the LMS approach.