The main purposes of this study were to investigate, by means of simulation: (1) whether the difference likelihood ratio chi-square statistic (G2-dif) for comparing item response theory (IRT) models is asymptotically distributed as a chi-square distribution; and (2) the accuracy rate of applying G2-dif in selection of nested IRT models. Two hundred replications of simulated test data for 2 test lengths and 2 sample sizes were generated. The results of this study demonstrate that the usual practice of treating the G2-dif as distributed as a central chi-square distribution is not sound. For short test length, the proportion of times the correct model is being selected can be very low. It appears that the G2-dif is more likely to be distributed as a noncentral chi-square distribution. Discussion concerning the proportion of the right model is being selected by the difference statistic as well as its relative merits in comparison to the Akaike Information Criteria (AIC) and the m(k) indices is also included in this study. (Contains 12 tables and 26 references.) (Author/SLD)