More than a dozen statistical models have been developed for the purpose of cognitive diagnosis. These models are supposed to extract a much finer level of information from item responses than traditional unidimensional item response models. In this paper, a general diagnostic model (GDM) was used to analyze a set of simulated sparse data and real data from National Assessment of Educational Progress (NAEP) assessments. The purpose of this study was to find out (a) whether the parameters can be recovered for a sparse data matrix in the framework of the GDM and (b) how to estimate group characteristics for large survey data, such as NAEP, in the framework of the GDM. The results of the simulation study show that GDM parameters can be recovered satisfactorily. The GDM under single group and multiple group assumptions were employed to fit NAEP assessment data. The results under these two assumptions and between the GDM and the statistics derived using the operational NAEP model were compared. The findings indicate that it is possible to conduct cognitive diagnosis for NAEP proficiency data.