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Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis

Published online by Cambridge University Press:  01 January 2025

Carl F. Falk  and
Li Cai
Carl F. Falk*
Affiliation:
University of California, Los Angeles (UCLA)
Li Cai
Affiliation:
CRESST/University of California, Los Angeles
*
Correspondence should be made to Carl F. Falk, Graduate School of Education & Information Studies, University of California, Los Angeles (UCLA), Los Angeles, CA 90095-1521, USA Email: cffalk@gmail.com
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Abstract

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang’s (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock–Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

Keywords

Item response theorySemi-parametric modelsMonotonic polynomialItem response function
Type
Article
Information
Psychometrika , Volume 81 , Issue 2 , June 2016 , pp. 434 - 460
Copyright
Copyright © 2014 The Psychometric Society

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