, Volume 76, Issue 2, pp 318–336

Measuring Growth in a Longitudinal Large-Scale Assessment with a General Latent Variable Model

  • Matthias von Davier
  • Xueli Xu
  • Claus H. Carstensen

DOI: 10.1007/s11336-011-9202-z

Cite this article as:
von Davier, M., Xu, X. & Carstensen, C.H. Psychometrika (2011) 76: 318. doi:10.1007/s11336-011-9202-z


The aim of the research presented here is the use of extensions of longitudinal item response theory (IRT) models in the analysis and comparison of group-specific growth in large-scale assessments of educational outcomes.

A general discrete latent variable model was used to specify and compare two types of multidimensional item-response-theory (MIRT) models for longitudinal data: (a) a model that handles repeated measurements as multiple, correlated variables over time and (b) a model that assumes one common variable over time and additional variables that quantify the change. Using extensions of these MIRT models, we approach the issue of modeling and comparing group-specific growth in observed and unobserved subpopulations. The analyses presented in this paper aim at answering the question whether academic growth is homogeneous across types of schools defined by academic demands and curricular differences. In order to facilitate answering this research question, (a) a model with a single two-dimensional ability distribution was compared to (b) a model assuming multiple populations with potentially different two-dimensional ability distributions based on type of school and to (c) a model that assumes that the observations are sampled from a discrete mixture of (unobserved) populations, allowing for differences across schools with respect to mixing proportions. For this purpose, we specified a hierarchical-mixture distribution variant of the two MIRT models. The latter model, (c), is a growth-mixture MIRT model that allows for variation of the mixing proportions across clusters in a hierarchically organized sample. We applied the proposed models to the PISA-I-Plus data for assessing learning and change across multiple subpopulations. The results of this study support the hypothesis of differential growth.


item response theory growth models multidimensional IRT longitudinal models diagnostic models large-scale assessments 

Copyright information

© The Psychometric Society 2011

Authors and Affiliations

  • Matthias von Davier
    • 1
  • Xueli Xu
    • 1
  • Claus H. Carstensen
    • 2
  1. 1.ETSPrincetonUSA
  2. 2.Bamberg UniversityBambergGermany

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