Comparing Conditional and Marginal Direct Estimation of Subgroup Distributions

Many large-scale assessment programs in education utilize “conditioning models” that incorporate both cognitive item responses and additional respondent background variables relevant for the population of interest. The set of respondent background variables serves as a predictor for the latent traits (proficiencies/abilities) and is used to obtain a conditional prior distribution for these traits. This is done by estimating a linear regression, assuming normality of the conditional trait distributions given the set of background variables. Multiple imputations, or plausible values, of trait parameter estimates are used in addition to or, better, on top of the conditioning model—as a computationally convenient approach to generating consistent estimates of the trait distribution characteristics for subgroups in complex assessments. This report compares, on the basis of simulated and real data, the conditioning method with a recently proposed method of estimating subgroup distribution statistics that assumes marginal normality. Study I presents simulated data examples where the marginal normality assumption leads to a model that produces appropriate estimates only if subgroup differences are small. In the presence of larger subgroup differences that cannot be fitted by the marginal normality assumption, however, the proposed method produces subgroup mean and variance estimates that differ strongly from the true values. Study II extends the findings on the marginal normality estimates to real data from large-scale assessment programs such as the National Assessment of Educational Progress (NAEP) and the National Adult Literacy Survey (NALS). The research presented in Study II shows differences between the two methods that are similar to the differences found in Study I. The consequences of relying upon the assumption of marginal normality in direct estimation are discussed.