Xu and von Davier (2006) demonstrated the feasibility of using the general diagnostic model (GDM) to analyze National Assessment of Educational Progress (NAEP) proficiency data. Their work showed that the GDM analysis not only led to conclusions for gender and race groups similar to those published in the NAEP Report Card, but also allowed flexibility in estimating multidimensional skills simultaneously. However, Xu and von Davier noticed that estimating the latent skill distributions will be much more challenging with this model when there is a large number of subgroups to estimate. 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.