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Formulating latent growth using an explanatory item response model approach.

Mark Wilson1, Xiaohui Zheng, Leah McGuire

  • 1UC Berkeley, Berkeley, CA 94720, USA. markw@berkeley.edu

Journal of Applied Measurement
|June 9, 2012
PubMed
Summary

This study introduces the Latent Growth Item Response Model (LG-IRM) to enhance growth modeling by integrating item response theory (IRT) with hierarchical linear modeling (HLM). The LG-IRM framework expands traditional HLM capabilities for richer growth analyses.

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Traditional growth modeling often relies on Hierarchical Linear Modeling (HLM).
  • Item Response Theory (IRT) offers advanced measurement models.
  • Integrating these traditions can enhance the analysis of growth studies.

Purpose of the Study:

  • To extend the Hierarchical Generalized Linear Model (HGLM) framework.
  • To incorporate Random Coefficients Multinomial Logit (MRCML) measurement models into growth modeling.
  • To introduce the Latent Growth Item Response Model (LG-IRM) as a novel approach.

Main Methods:

  • Review of HLM and Rasch measurement traditions in growth modeling.
  • Development and application of the linear Latent Growth Item Response Model (LG-IRM).
  • Incorporation of extensions such as polynomial growth, differential item functioning (DIF), polytomous responses, covariates, and multiple growth dimensions.

Main Results:

  • Demonstration of the LG-IRM's flexibility in modeling complex growth patterns.
  • Empirical examples illustrate the application of various extensions.
  • Simulations assess the performance of the estimation procedures.

Conclusions:

  • The LG-IRM approach significantly extends the capabilities of traditional HLM for growth modeling.
  • This framework allows for the integration of advanced IRT measurement models.
  • The presented methods offer a powerful tool for analyzing complex growth phenomena.