Applications Of IRT Models For Estimating Latent Variable Distributions

Item response theory(IRT)serves as a cornerstone of modern psychometrics.In the standard application of IRT,the population distribution of latent trait is typically assumed to be normally distributed(denoted as,Gaussian IRT),however,this normal distribution assumption might be unrealistic,and can potentially lead to seriously misleading results,including inaccurate and imprecise estimates of item and person parameters.Therefore,researchers have proposed a variety of models for estimating the distribution of latent trait in IRT.Previous studies on the Montreal Cognitive Assessment(MoCA)using IRT were typically under the assumption that the population distribution of latent trait is normally distributed,which might be problematic.The purpose of this study was to investigate the item parameters and the ability parameters of the MoCA data using IRT with estimation of latent trait distribution.The purpose of the first part of this study was to explore the availability of the functions for estimating the item parameters of the IRT with estimation of latent trait distribution in the mirt package,and to compare the relative fit indices of the IRT model with or without the estimation of latent trait distribution when fitting the simulated observed response data generated under the normally distributed or non-normally distributed conditions.The simulation results showed that:(1)the functions for estimating the item parameters of the IRT with estimation of latent trait distribution in the mirt package showed stable item parameter recovery.(2)for the simulated observed response data generated under the normally distributed conditions,the IRT with latent trait normally distributed assumption had better fit,and for the simulated observed response data generated under the non-normally distributed conditions,the best fitted mode was DC-IRT(k=4).The main purpose of the second part of this study was to compare the performance of the relative fit indices and the item parameter estimated of the IRT models investigated in this study by taking the MoCA data as an example.Real-world data analyses showed that:(1)the IRT with estimation of latent trait distribution had better fit than that of the Gaussian IRT,and the DC-IRT(k=8)model had the best fit among the model investigated in this study.(2)most of the item discrimination and difficulty parameter estimates of the DC-IRT(k=8)had good performance.The main purpose of the third part of this study was to demonstrate the application of the IRT model with the estimation of latent trait distribution in the estimation of the ability parameter in the MoCA data.Real-world data analyses showed that:(1)the latent ability parameters estimated using the DC-IRT(k=8),which is the best fitted model for the MoCA data in this study,were different from those estimated using other DC-IRT models.(2)for the ability parameter estimates of the DC-IRT(k=8)and Gaussian IRT,the same trends hold.The DC-IRT(k=8)is recommended for estimating item parameters and ability parameters in the MoCA data in this study.