title: A Model-Free Diagnostic for Single-Peakedness of Item Responses Using Ordered Conditional Means.
abstract: In this article we propose a model-free diagnostic for single-peakedness (unimodality) of item responses. Presuming a unidimensional unfolding scale and a given item ordering, we approximate item response functions of all items based on ordered conditional means (OCM). The proposed OCM methodology is based on Thurstone & Chave's (1929) criterion of irrelevance, which is a graphical, exploratory method for evaluating the "relevance" of dichotomous attitude items. We generalized this criterion to graded response items and quantified the relevance by fitting a unimodal smoother. The resulting goodness-of-fit was used to determine item fit and aggregated scale fit. Based on a simulation procedure, cutoff values were proposed for the measures of item fit. These cutoff values showed high power rates and acceptable Type I error rates. We present 2 applications of the OCM method. First, we apply the OCM method to personality data from the Developmental Profile; second, we analyze attitude data collected by Roberts and Laughlin (1996) concerning opinions of capital punishment.
authors.affiliation: a Institute of Psychology, Erasmus University Rotterdam.
authors.forename: Marike
authors.initials: M
authors.lastname: Polak
authors.affiliation: b Psychological Institute, Leiden University.
authors.forename: Mark
authors.initials: M
authors.lastname: de Rooij
authors.affiliation: b Psychological Institute, Leiden University.
authors.forename: Willem J
authors.initials: WJ
authors.lastname: Heiser