The Heteroscedastic Skew Graded Response Model: An Answer to the Non-Normality Predicament?

As item response theory models are more frequently applied to psychological assessment, understanding the ramifications of failing to account for non-normality is of utmost importance, especially, considering the likelihood of encountering traits that are non-normally distributed in the population (e.g., anxiety, depression). Previous research has established concerns with regard to bias in item parameter and trait score estimates when non-normality is ignored, and, as such developed models to aid in minimizing bias. Once such model is the heteroscedastic GRM with a skewed latent trait (HSGRM). This research provides an in-depth examination of the viability and utility of the HSGRM. Under various degrees of skew and heteroscedasticity, including extreme on both, this research addresses the consequences of ignoring non-normality and how to address it. A simulation study was conducted to evaluate the ability of the HSGRM to provide improved item parameter estimates, and recover the shape of the distribution (i.e., skew). Results support the HSGRM as a major improvement over the traditional GRM when faced with non-normality in data due to skew in the trait and heteroscedastic errors