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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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An autoregressive growth model for longitudinal item analysis.

Minjeong Jeon1, Sophia Rabe-Hesketh2

  • 1Department of Psychology, Ohio State University, 1827 Neil Avenue, Columbus, OH, 43210, USA. jeon.117@osu.edu.

Psychometrika
|December 10, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a new autoregressive growth model for analyzing longitudinal binary data, accounting for item response dependencies over time. The model addresses initial conditions and demonstrates its utility with Korean student self-esteem data.

Keywords:
autoregressive modelsinitial conditions problemmeasurement invarianceserial dependence

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Area of Science:

  • Psychometrics
  • Longitudinal Data Analysis
  • Educational Psychology

Background:

  • Analyzing longitudinal binary data requires models that account for temporal dependencies.
  • Latent trait models are common, but often assume independence between time points.
  • Existing methods may not adequately address the initial conditions problem in dynamic models.

Purpose of the Study:

  • To propose a first-order autoregressive growth model for longitudinal binary item analysis.
  • To address the initial conditions problem in such models.
  • To investigate the performance and consequences of the proposed model.

Main Methods:

  • Developed a first-order autoregressive growth model where item response probability depends on latent traits and lagged responses.
  • Adapted solutions from dynamic panel data econometrics to handle initial conditions.
  • Conducted simulations to assess power and the impact of ignoring model assumptions.

Main Results:

  • The proposed model effectively handles conditional dependence across time in longitudinal binary data.
  • Investigated asymptotic and finite sample power for autoregressive parameters.
  • Examined the consequences of ignoring local dependence and initial conditions in simulations.

Conclusions:

  • The novel autoregressive growth model provides a robust framework for longitudinal binary item analysis.
  • The methods are validated through simulations and application to real-world data.
  • Findings highlight the importance of accounting for temporal dependencies and initial conditions.