Nonparametric Kernel Smoothing Item Response Theory Analysis of Likert Items

Abstract

Likert scales are the most common psychometric response scales in the social and behavioral sciences. Likert items are typically used to measure individuals’ attitudes, perceptions, knowledge, and behavioral changes. To analyze the psychometric properties of individual Likert-type items and overall Likert scales, mostly methods based on classical test theory (CTT) are used, including corrected item–total correlations and reliability indices. CTT methods heavily rely on the total scale scores, making it challenging to directly examine the performance of items and response options across varying levels of the trait. In this study, Kernel Smoothing Item Response Theory (KS-IRT) is introduced as a graphical nonparametric IRT approach for the evaluation of Likert items. Unlike parametric IRT models, nonparametric IRT models do not involve strong assumptions regarding the form of item response functions (IRFs). KS-IRT provides graphics for detecting peculiar patterns in items across different levels of a latent trait. Differential item functioning (DIF) can also be examined by applying KS-IRT. Using empirical data, we illustrate the application of KS-IRT to the examination of Likert items on a psychological scale.

Keywords

• Likert-type scale
• classical test theory
• parametric/nonparametric IRT models
• kernel smoothing IRT
• IRFs