Robustness of Identifying Item–Trait Relationships Under Non-Normality in MIRT Models

Abstract

Identifying item–trait relationships is a core task in multidimensional item response theory (MIRT). Common empirical approaches include exploratory item factor analysis (EIFA) with rotations, the expectation maximization-based $L_1$ regularization (EML1) algorithm, and the expectation model selection (EMS) algorithm. While these methods typically assume multivariate normality of latent traits, empirical data often deviate from this assumption. This study evaluates the robustness of EIFA, EML1, and EMS, when latent traits violate normality assumptions. Using the independent generator transform, we generate latent variables under varying levels of skewness, excess kurtosis, numbers of non-normal dimensions, and inter-factor correlations. We then assess the performance of each method in terms of the F1-score for identifying item–trait relationships and mean squared error (MSE) of parameter estimations. The results indicate that non-normality leads to a reduction in F1-score and an increase in MSE generally. For F1-score, EMS performs best with small samples (e.g., $N=500$), whereas EIFA with rotations yields the highest F1-score in larger samples. In terms of estimation accuracy, EMS and EML1 generally yield lower MSEs than EIFA. The effects of non-normality are also demonstrated by applying these methods to a real data set from the Depression, Anxiety, and Stress Scale.