Several complex sample standard error estimators based on linearization and resampling for the latent regression model of the National Assessment of Educational Progress (NAEP) are studied with respect to design choices such as number of items, number of regressors, and the efficiency of the sample. This paper provides an evaluation of the extent these estimators are appropriate for the models and test lengths often encountered in NAEP and what the effect is on the NAEP imputation model. It is shown that in general the resampling method used in this study provides the most accurate standard errors. However, the differences with the linearization method chosen in this study are relatively small if only small models are used with respect to the independent variables of the latent regression. Illustration is provided through several small simulation studies and NAEP data analysis.