Detecting Curvilinear Relationships: A Comparison of Scoring Approaches Based on Different Item Response Models

Abstract

There is a growing use of noncognitive assessments around the world, and recent research has posited an ideal point response process underlying such measures. A critical issue is whether the typical use of dominance approaches (e.g., average scores, factor analysis, and the Samejima's graded response model) in scoring such measures is adequate. This study examined the performance of an ideal point scoring approach (e.g., the generalized graded unfolding model) as compared to the typical dominance scoring approaches in detecting curvilinear relationships between scored trait and external variable. Simulation results showed that when data followed the ideal point model, the ideal point approach generally exhibited more power and provided more accurate estimates of curvilinear effects than the dominance approaches. No substantial difference was found between ideal point and dominance scoring approaches in terms of Type I error rate and bias across different sample sizes and scale lengths, although skewness in the distribution of trait and external variable can potentially reduce statistical power. For dominance data, the ideal point scoring approach exhibited convergence problems in most conditions and failed to perform as well as the dominance scoring approaches. Practical implications for scoring responses to Likert-type surveys to examine curvilinear effects are discussed.