An Alternative Way to Model Population Ability Distributions in Large-Scale Educational Surveys

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and the high model complexity. The approach introduced here to identify multiple groups that can account for the variation among students is to conduct a latent class analysis (LCA). In the LCA, one or more latent nominal variables are identified that can be used to classify respondents with respect to their background characteristics. These classifications are then introduced as predictors in the latent regression. The primary goal of this study was to explore whether this approach yields similar estimates of group means and standard deviations compared with the operational procedure. The alternative approaches based on LCA differed regarding the number of classes, the items used for the LCA, and whether manifest class membership information or class membership probabilities were used as independent variables in the latent regression. Overall, recovery of the operational approach's group means and standard deviations was very satisfactory for all LCA approaches. Furthermore, the posterior means and standard deviations used to generate plausible values derived from the operational approach and the LCA approaches correlated highly. Thus, incorporating independent variables based on an LCA of background data into the latent regression model appears to be a viable alternative to the operational approach.