Estimating the Nominal Response Model Under Nonnormal Conditions

Kathleen Suzanne Johnson Preston,Steven Paul Reise

doi:10.1177/0013164413507063

Abstract

The nominal response model (NRM), a much understudied polytomous item response theory (IRT) model, provides researchers the unique opportunity to evaluate within-item category distinctions. Polytomous IRT models, such as the NRM, are frequently applied to psychological assessments representing constructs that are unlikely to be normally distributed in the population. Unfortunately, models estimated using estimation software with the MML/EM algorithm frequently employs a set of normal quadrature points, effectively ignoring the true shape of the latent trait distribution. To address this problem, the current research implements an alternative estimation approach, Ramsay Curve Item Response Theory (RC-IRT), to provide more accurate item parameter estimates modeled under the NRM under normal, skewed, and bimodal latent trait distributions for ordered polytomous items. Based on the results of improved item parameter recovery under RC-IRT, it is recommended that RC-IRT estimation be implemented whenever a researcher considers the construct being measured has the potential of being nonnormally distributed.

Highlights

Unidimensional item response theory (IRT) models are most frequently fitted with marginal maximum likelihood (MML; Bock & Lieberman, 1970) estimation, which
Scale constructors have the opportunity to evaluate the functioning of each withinitem category distinction by using a largely understudied polytomous IRT model, the nominal response model (NRM; Bock, 1972, 1997)
The first four rows of each table provide results for conditions estimated using order 2 and 2 knots, specifying a normal distribution under Ramsay curve item response theory (RC-IRT) estimation, which produces results equivalent to those obtained without implementing RC-IRT estimation

Summary

Introduction

Unidimensional item response theory (IRT) models are most frequently fitted with marginal maximum likelihood (MML; Bock & Lieberman, 1970) estimation, which. Further advancements in user-accessible IRT software, such as EQSIRT, permit easy and accurate IRT model estimation of nonnormal data It remains undetermined whether analyzing nonnormal data under the NRM with EQSIRT using RCIRT estimation produces more accurate item parameter estimates. It is, the purpose of this study to evaluate the recovery of category boundary discrimination (CBD) parameters using RC-IRT as estimated using EQSIRT for ordered categorical data under the NRM. MML estimates of item parameters increase in bias as the distribution deviates further from normality (Boulet, 1996; Stone, 1992; Woods, 2006, 2007a, 2007b, 2008; Woods & Lin, 2009; Woods & Thissen, 2006)

Methods

Results

Conclusion