To make the GDM more applicable to NAEP data analysis, which requires a fairly large subgroups analysis, this study developed a log-linear model to reduce the number of parameters in the latent skill distribution without sacrificing the accuracy of inferences. This paper describes such a model and applies the model in the analysis of NAEP reading assessments for 2003 and 2005. The comparisons between using this model and the unstructured model were made through the use of various results, such as the differences between item parameter estimates and the differences between estimated latent class distributions. The results in general show that using the log-linear model is efficient.