title: Estimation of a four-parameter item response theory model.
abstract: We explore the justification and formulation of a four-parameter item response theory model (4PM) and employ a Bayesian approach to recover successfully parameter estimates for items and respondents. For data generated using a 4PM item response model, overall fit is improved when using the 4PM rather than the 3PM or the 2PM. Furthermore, although estimated trait scores under the various models correlate almost perfectly, inferences at the high and low ends of the trait continuum are compromised, with poorer coverage of the confidence intervals when the wrong model is used. We also show in an empirical example that the 4PM can yield new insights into the properties of a widely used delinquency scale. We discuss the implications for building appropriate measurement models in education and psychology to model more accurately the underlying response process.
authors.affiliation: Pennsylvania State University, PA, USA. loken@psu.edu
authors.forename: Eric
authors.initials: E
authors.lastname: Loken
authors.forename: Kelly L
authors.initials: KL
authors.lastname: Rulison
mesh_terms: D000293:Adolescent; D001499:Bayes Theorem; D003198:Computer Simulation; D003625:Data Collection / Q000706:statistics & numerical data* / Q000639:trends; D005260:Female; D005544:Forecasting; D006801:Humans; D007604:Juvenile Delinquency / Q000523:psychology / Q000706:statistics & numerical data* / Q000639:trends; D008297:Male; D008432:Mathematical Computing; D015233:Models, Statistical; D012942:Social Sciences / Q000706:statistics & numerical data*; D012984:Software; D011795:Surveys and Questionnaires