Abstract
Latent class (LC) analysis is used by social, behavioral, and medical science researchers among others as a tool for clustering (or unsupervised classification) with categorical response variables, for analyzing the agreement between multiple raters, for evaluating the sensitivity and specificity of diagnostic tests in the absence of a gold standard, and for modeling heterogeneity in developmental trajectories. Despite the increased popularity of LC analysis, little is known about statistical power and required sample size in LC modeling. This paper shows how to perform power and sample size computations in LC models using Wald tests for the parameters describing association between the categorical latent variable and the response variables. Moreover, the design factors affecting the statistical power of these Wald tests are studied. More specifically, we show how design factors which are specific for LC analysis, such as the number of classes, the class proportions, and the number of response variables, affect the information matrix. The proposed power computation approach is illustrated using realistic scenarios for the design factors. A simulation study conducted to assess the performance of the proposed power analysis procedure shows that it performs well in all situations one may encounter in practice.
Highlights
Latent class (LC) analysis was initially introduced in the 1950s by Lazarsfeld (1950) as a tool for identifying subgroups of individuals giving similar responses to sets of dichotomous attitude questions
Statistical software for LC analysis has become generally available—e.g., Latent GOLD (Vermunt and Magidson 2013b), Mplus (Muthen and Muthen 2012), LEM (Vermunt 1997), the SAS routine PROC LCA (Lanza, Collins, Lemmon, and Schafer 2007), and the R package poLCA (Linzer and Lewis 2011)—which has contributed to the increased popularity of this model among applied researchers
Applications of LC analysis include building typologies of respondents based on social survey data (McCutcheon 1987), identifying subgroups based on health risk behaviors (Collins and Lanza 2010), identifying phenotypes of stalking victimization (Hirtenlehner, Starzer, and Weber 2012), and finding symptom subtypes of clinically diagnosed disorders (Keel et al 2004)
Summary
Latent class (LC) analysis was initially introduced in the 1950s by Lazarsfeld (1950) as a tool for identifying subgroups of individuals giving similar responses to sets of dichotomous attitude questions. In the literature on LC analysis, methods for sample size and/or power computation as well as a thorough study on the design factors affecting the power of statistical tests used in LC analysis, are lacking. We present a method for assessing the power of tests related to the class-specific response probabilities, which in confirmatory LC analysis are the parameters of main interest. An important difference compared to standard logistic regression analysis is that in a LC analysis the predictor in the logistic models for the responses, the latent class variable, is unobserved This implies that the uncertainty about the individuals’ class memberships should be taken into account in the power and sample size computation. We provide a brief discussion of the main results of our study
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