A graded response model for measuring person reliability

Abstract

This paper extends Lumsden's fluctuation model to the graded response case and, from the resulting basic scaling model, develops a one-dimensional item response theory graded response model (GRM). Under some additional assumptions, it follows that the item category response functions (ICRFs) can be closely approximated by the ICRFs of the standard GRM with equal item discrimination. For fixed item locations, the item responses depend on two individual differences parameters: the person central location and the person reliability. Procedures for estimating the person parameters and for addressing the goodness of fit of the proposed model as compared to the standard GRM are discussed. The accuracy of the person estimates is assessed by means of simulation studies. Finally, all the developments are illustrated using three empirical examples in personality measurement.

A Comparison of Procedures for Estimating Person Reliability Parameters in the Graded Response Model

“…In a series of papers, Ferrando (, , ) has developed procedures for estimating person reliability parameters (PRPs) in variable‐θ IRT models. In contrast with traditional constant‐θ models, variable‐θ models allow for temporary changes in individuals’ θ when responding to self‐report items.…”

“…Historically, PRPs have been difficult to estimate. Recently, Ferrando () explicated an expected a posteriori (EAP) approach to computing PRPs for the commonly used Samejima's () graded response model (GRM). In this approach, the χ distribution was used as the prior for estimating PRPs.…”

“…In this approach, the χ distribution was used as the prior for estimating PRPs. The rationale was that the inverse χ 2 distribution is commonly used as a prior for estimating variances of normal distributions in Bayesian models (Ferrando, ). Alternatively, one could justify using the lognormal distribution as the prior because it is commonly used as a prior when estimating item discrimination parameters in IRT models (Baker & Kim, ).…”

A Practical Guide to Check the Consistency of Item Response Patterns in Clinical Research Through Person-Fit Statistics

“…Other researchers like Meijer and van Krimpen-Stoop (2001) and Woods, Oltmanns, and Turkheimer (2008) found that males produced more inconsistent responses than females. Schmitt, Chan, Sacco, McFarland, and Jennings (1999) and Ferrando (2009) found that respondents low on conscientiousness generated less consistent response patterns than test takers high in conscientiousness. Zickar and Drasgow (1996) analyzed data in which respondents were instructed to answer honestly or to fake the good answer on a personality scale.…”

Person misfit on the Inventory of Depressive Symptomatology: Low quality self‐report or true atypical symptom profile?

“…Explanatory person‐fit research, in which a person‐fit statistic is regressed on explanatory variables, provides some insight into whether person misfit in a particular sample is predominantly due to inaccurate responding or due to other causes such as true atypical profiles. For example, research showing that person misfit relates to conscientiousness, education level, verbal skills, validity indices, and response styles (Conijn et al, ; Conijn et al, ; Conijn, Sijtsma, & Emons, ; Ferrando, ; LaHuis & Copeland., ; Meijer, Egberink, Emons, & Sijtsma, ; Schmitt, Chan, Sacco, McFarland, & Jennings, ; Woods et al, ) suggests that misfitting response patterns may be due to inaccurate responding. However, explained variance in the person‐fit statistic was small in these studies and other research shows that person misfit on measures of general psychological distress or depression relates to atypical depression, atypical suicide ideation, melancholic depression, and having an uncommon disorder (Conijn et al, ; Conrad et al, ; Wanders et al, ; Wardenaar et al, ).…”