Recovery of Two- and Three-Parameter Logistic Item Characteristic Curves: A Monte Carlo Study

This monte carlo study assessed the accuracy of simultaneous estimation of item and person parameters in item response theory. Item responses were simulated using the two- and three-parameter logistic models. Samples of 200, 500, 1,000, and 2,000 simulated examinees and tests of 15, 30, and 60 items were generated. Item and person parameters were then estimated using the appropriate model. The root mean squared error between recovered and actual item characteristic curves served as the principal measure of estimation accuracy for items. The accuracy of estimates of ability was assessed by both correlation and root mean squared error. The results indicate that minimum sample sizes and tests lengths depend upon the response model and the purposes of an investigation. With item responses generated by the two-parameter model, tests of 30 items and samples of 500 appear adequate for some purposes. Estimates of ability and item parameters were less accurate in small sample sizes when item responses were generated by the three-parameter logistic model. Here samples of 1,000 examinees with tests of 60 items seem to be required for highly accurate estimation. Tradeoffs between sample size and test length are apparent, however.