Estimation of Standard Error of Regression Effects in Latent Regression Models Using Binder's Linearization. Research Report. ETS RR-07-09

Two versions of a general method for approximating standard error of regression effect estimates within an IRT-based latent regression model are compared. The general method is based on Binder's (1983) approach, accounting for complex samples and finite populations by Taylor series linearization. In contrast, the current National Assessment of Educational Progress procedure assumes a simple random sample for standard error of regression effects and applies a jackknife estimator to statistics of interest as a way to account for NAEP's complex sample. In this study, the versions of the general method are formally defined and the general method is extended to multiple dimensions. Furthermore, they are applied in an empirical study to the 2004 NAEP long-term trend data comparing both large, nearly saturated, and small models. Subsequently, the results are compared to the operational-based imputation method. Results show no impact on the imputation-based results, limited impact on large models, and reasonable impact on small models. While it is not readily apparent to what this differential impact can be attributed, several explanations are discussed.