An efficient standard error estimator of the DINA model parameters when analysing clustered data

Abstract

Cognitive diagnostic modelling is often used to analyse educational and psychological data, which are typically collected through cluster sampling with unequal selection probabilities. Jackknife is a resampling technique used to account for the sampling design. It typically gives unbiased estimates of the standard errors of the model parameters, but implementation can be vastly time-consuming. This study proposes an accurate and computationally fast approach for the standard errors of the parameters in the DINA model, one that incorporates the Huber-White sandwich estimator approach. Our simulation study suggests that the proposed sandwich estimator performs well when analysing clustered data structures specifically with moderate to large numbers of clusters. We also demonstrate its applicability to TIMSS 2011 mathematics.