The Sensitivity of Parameter Estimates to the Latent Ability Distribution

Estimation of item response model parameters and ability distribution parameters has been, and will remain, an important topic in the educational testing field. Much research has been dedicated to addressing this task. Some studies have focused on item parameter estimation when the latent ability was assumed to follow a normal distribution, whereas others have utilized nonparametric or semiparametric techniques to substitute the normal ability assumption. However, both approaches have their limitations. A normal ability assumption is not flexible enough to reflect possible deviations from symmetry, whereas the nonparametric and semiparametric techniques used to capture possible nonnormal features of the latent ability have difficulty in reaching satisfactory estimates for certain quantities of the ability distribution such as quantiles. Hence a continuous generalized skew normal (GSN) distribution was applied in this study to better capture the possible underlying asymmetric ability distribution. In addition, simultaneous estimation of both the item parameters and the distributional parameters was employed. The performance of the GSN was compared with the normal ability assumption in terms of item parameter and distributional parameter recoveries, based on a series of simulation studies. The results showed that (a) under the Rasch model, both the item parameter estimates and the distributional parameter estimates are robust to the misspecification of the ability distribution, and (b) under the two-parameter logistic model, although the distributional parameter estimates are fairly robust, the item parameter estimates are slightly more sensitive to the misspecification of the ability distribution, especially when the underlying ability distribution is highly skewed.