Effects of Statistical Models and Items Difficulties on Making Trait-Level Inferences: A Simulation Study

Researchers dealing with the task of estimating locations of individuals on continuous latent variables may rely on several statistical models described in the literature. However, weighting costs and benefits of using one specific model over alternative models depends on empirical information that is not always clearly available. Therefore, the aim of this simulation study was to compare the performance of seven popular statistical models in providing adequate latent trait estimates in conditions of items difficulties targeted at the sample mean or at the tails of the latent trait distribution. Results suggested an overall tendency of models to provide more accurate estimates of true latent scores when using items targeted at the sample mean of the latent trait distribution. Rating Scale Model, Graded Response Model, and Weighted Least Squares Mean-and Variance-adjusted Confirmatory Factor Analysis yielded the most reliable latent trait estimates, even when applied to inadequate items for the sample distribution of the latent variable. These findings have important implications concerning some popular methodological practices in Psychology and related areas.