A Simulation Study of the Difference Chi-Square Statistic for Comparing Latent Class Models Under Violation of Regularity Conditions

Abstract

This study explored the robustness of the likelihood ratio difference statistic to the violation of a regularity condition when used to assess differences in fit pro vided by pairs of latent class models. Under regularity conditions, the additive property of the likelihood ratio statistic can be used to assess the statistical difference between pairs of hierarchically related models (i.e., one model is a constrained form of the other). How ever, when one of the two models being compared is obtained by fixing parameters of the other model at boundary values (i.e., 0 or 1), a regularity condition is violated and the difference statistic is not necessarily distributed as χ². The effects of three independent var iables on the distribution of the difference statistics were studied for two generation models and a variety of subsuming models. Differential effects in terms of the direction and the extent of deviation were pro duced according to the types of model comparisons; these effects negate the application of a simple correc tion to the statistic to achieve a χ² distribution. Rec ommendations are made regarding how this statistic might reasonably be used under violation of the regu larity condition.