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 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.
Holt, 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:10.1177/014662168901300301
Holt, Judith A.; Macready, George B..
A simulation study of the difference chi-square statistic for comparing latent class models under violation of regularity conditions.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.