Summed Score Likelihood–Based Indices for Testing Latent Variable Distribution Fit in Item Response Theory

Author:

Li Zhen1,Cai Li2

Affiliation:

1. eMetric, San Antonio, TX, USA

2. University of California, Los Angeles, CA, USA

Abstract

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood–based statistics may be useful for testing latent variable distribution fit. We develop Satorra–Bentler type moment adjustments to approximate the test statistics’ tail-area probability. A simulation study was conducted to examine the calibration and power of the unadjusted and adjusted statistics in various simulation conditions. Results show that the proposed indices have tail-area probabilities that can be closely approximated by central chi-squared random variables under the null hypothesis. Furthermore, the test statistics are focused. They are powerful for detecting latent variable distributional assumption violations, and not sensitive (correctly) to other forms of model misspecification such as multidimensionality. As a comparison, the goodness-of-fit statistic M2 has considerably lower power against latent variable nonnormality than the proposed indices. Empirical data from a patient-reported health outcomes study are used as illustration.

Funder

Institute of Education Sciences

Publisher

SAGE Publications

Subject

Applied Mathematics,Applied Psychology,Developmental and Educational Psychology,Education

Reference40 articles.

1. The Goodness of Fit of Latent Trait Models in Attitude Measurement

2. Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

3. Fitting a response model forn dichotomously scored items

4. Cai L. (2013). flexMIRT® version 2: Flexible multilevel item factor analysis and test scoring [Computer software]. Chapel Hill, NC: Vector Psychometric Group.

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