• The Pure and Applied Mathematics
• /
• v.20 no.1
• /
• pp.59-70
• /
• 2013

The purpose of this study was to develop a zero-inflated Rasch (ZI-Rasch) model, a combination of the Rasch model and the ZIP model. The ZI-Rasch model was considered in this study as an appropriate alternative to the Rasch model for zero-inflated data. To investigate the relative appropriateness of the ZI-Rasch model, several analyses were conducted using PROC NLMIXED procedures in SAS under various simulation conditions. Sets of criteria for model evaluations (-2LL, AIC, AICC, and BIC) and parameter estimations (RMSE, and $r$) from the ZI-Rasch model were compared with those from the Rasch model. In the data-model fit indices, regardless of the simulation conditions, the ZI-Rasch model produced better fit statistics than did the Rasch model, even when the response data were generated from the Rasch model. In terms of item parameter ${\lambda}$ estimations, the ZI-Rasch model produced estimates similar to those of the Rasch model.