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An autoregressive growth model for longitudinal item analysis

Published online by Cambridge University Press:  01 January 2025

Minjeong Jeon  and
Sophia Rabe-Hesketh
Minjeong Jeon*
Affiliation:
Ohio State University
Sophia Rabe-Hesketh
Affiliation:
University of California, Berkeley
*
Correspondence should be made to Minjeong Jeon, Department of Psychology, Ohio State University, 1827 Neil Avenue, Columbus, OH 43210 USA. Email: [email protected]
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Abstract

A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students’ self-esteem.

Keywords

autoregressive modelsinitial conditions problemmeasurement invarianceserial dependence
Type
Original Paper
Information
Psychometrika , Volume 81 , Issue 3 , September 2016 , pp. 830 - 850
Copyright
Copyright © 2015 The Psychometric Society

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