A Monte Carlo investigation of parameter estimation efficacy using modified fixed "C" three parameter log (3PL) item response theory models with small sample sizes

Faced with small sample sizes and short test lengths, obtaining stable item parameter estimates using the 3PL item response theory model has been unsuccessful. This study investigated parameter estimation efficacy in small sample data sets with two modified and one unmodified 3PL IRT models. "True" parameter values were generated using a Monte Carlo technique and compared to "estimated" item parameters obtained using XCALIBRE. Results indicated that XCALIBRE recovered item and ability parameters "comparably" to BILOG using 500 examines and 50 test items. Overall, holding the lower asymptote constant did not necessarily contribute better recovery in the modified models. Item discrimination was moderately estimated in all three models and the lower asymptote was still poorly estimated in the unmodified model. It is questionable whether the recommended standard of using 1000 examines and 50 test items can produce "reasonably" stable parameter estimates. It is concluded that applying artificial changes to the 3PL IRT model is largely unsuccessful.