Investigating factors that affect the performance of the EM algorithm and examining the power of model selection criteria in latent class models : Monte Carlo study

Abstract

Latent Class Models have been used extensively in literature to divide a heterogenous population into smaller, homogenous clusters relative to similar characteristics. The main advantage of these models over traditional clustering techniques lies in the simultaneous segmentation and parameter estimation, which is carried out using the EM algorithm. In this research study, a data set (Lia 2013) is used to analyse preferences of iPad attributes using Latent Class Procedures. The sample comprises the rating responses of 364 respondents to 24 iPad profiles described by three item attributes including the capacity of the iPad, the price and the connectivity of the iPad. Using the facilities of the GLIM software, three latent class models are fitted by varying the number of clusters from 2 to 4. The parameter estimates of these class models are used to simulate a number of data sets to conduct two Monte-Carlo studies. The first Monte-Carlo study examines the performance of latent class models when modifying several factors, including the sample size, the number of segments and the size of a perturbation constant multiplied to the error term which is assumed to have a normal distribution. Using the simulated data sets, four measures will be used to assess segment classification recovery, parameter recovery and recovery of segment membership probabilities. These measures include the percentage of correctly classified subjects into their true segments and three 𝑅𝑀𝑆 statistics used to assess parameter recovery, segment membership probability recovery and the predictive power for each latent class model. The second Monte-Carlo study examines several information criteria to identify which one is best in predicting the number of true segments in latent class models. These information criteria have distinct penalty terms that depend on the number of parameters, sample size and entropy.