Holt, Judith A.Macready, George B.2011-06-102011-06-101989Holt, Judith A & Macready, George B. (1989). A simulation study of the difference chi-square statistic for comparing latent class models under violation of regularity conditions. Applied Psychological Measurement, 13, 221-231. doi:10.1177/014662168901300301doi:10.1177/014662168901300301https://hdl.handle.net/11299/107310This study explored the robustness of the likelihood ratio difference statistic to the violation of a regularity condition when used to assess differences in fit provided 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). However, 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 x². The effects of three independent variables 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 produced according to the types of model comparisons; these effects negate the application of a simple correction to the statistic to achieve a x² distribution. Recommendations are made regarding how this statistic might reasonably be used under violation of the regularity condition. Index terms: latent class model, likelihood ratio chi-square, mixture model, regularity conditions, tests of fit.enArticle