A semi-parametric approach to estimating item response functions
In Item Response Theory, although the one parameter (1PL), two parameter (2PL) or three parameter logistic models have been shown to be useful in a variety of situations, there are cases where these models do not produce a good fit to the data. The Logistic function of a Monotonic Polynomial (L-MP) is a model proposed aiming to improve the model-data fit. The L-MP model replaces the linear exponent of the 1PL or 2PL model with a monotonic polynomial. It is a general model which includes the 1PL or 2PL model as a special case. A surrogate-based two-stage approach is used to obtain the estimates from the L-MP model. The L-MP model is illustrated using both simulation studies and two real world examples. Performance of the L-MP model in the simulation studies is evaluated by examining the Root Integrated Mean Square Error (RIMSE) for the item curves and the ability estimates, and also the rank correlations between the estimated and true abilities. The L-MP model is compared with the 2PL model with Marginal Maximum Likelihood (MML) estimates and Joint Maximum Likelihood (JML) estimates. It is also compared with two nonparametric approaches, namely TESTGRAF which uses a kernel smoothing method, and the Nonparametric Bayesian model. Results show that: (1) The L-MP estimation method is able to recover the true values of person and of item parameters reasonably well. (2) If a standard logistic model holds, the L-MP method can provide very close estimated ICCs to those of the MML method and much better estimated ICCs than those of the JML method. For ability parameters, the L-MP method can provide slightly better estimates than MML and much better estimates than JML. (3) When the true models are not standard logistic functions, the L-MP model with a higher order polynomial is preferable to the 2PL model and the results from the L-MP model are comparable to the best of those from other approaches considered. This demonstrates that the surrogate ability approach, adapted from TESTGRAF and used in L-MP, yields results that are completely suitable for practical use.
School:The Ohio State University
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:item response theory semi parametric approach logistic function monotonic polynomial
Date of Publication:01/01/2007