Rasch Model Parameter Estimation in the Presence of a Nonnormal Latent Trait Using a Nonparametric Bayesian Approach

Holmes Finch and Julianne M. Edwards   

Abstract

Standard approaches for estimating itemresponse theory (IRT) model parameters generally work under the assumption thatthe latent trait being measured by a set of items follows the normaldistribution. Estimation of IRT parameters in the presence of nonnormal latenttraits has been shown to generate biased person and item parameter estimates. Anumber of methods, including Ramsay curve item response theory, have beendeveloped to reduce such bias, and have been shown to work well for relativelylarge samples and long assessments. An alternative approach to the nonnormal latenttrait and IRT parameter estimation problem, nonparametric Bayesian estimation approach,has recently been introduced into the literature. Very early work with thismethod has shown that it could be an excellent option for use when fitting theRasch model when assumptions cannot be made about the distribution of the modelparameters. The current simulation study was designed to extend research in thisarea by expanding the simulation conditions under which it is examined and to comparethe nonparametric Bayesian estimation approach to the Ramsay curve item responsetheory, marginal maximum likelihood, maximum a posteriori, and the BayesianMarkov chain Monte Carlo estimation method. Results of the current study supportthat the nonparametric Bayesian estimation approach may be a preferred optionwhen fitting a Rasch model in the presence of nonnormal latent traits and itemdifficulties, as it proved to be most accurate in virtually all scenarios thatwere simulated in this study.

Keywords
item response theory, Rasch model, nonnormal latent trait, nonparametric Bayes, parameter estimation