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Latent path models within an IRT framework
  • Eveline Gebhardt
In this thesis a new method is described that includes latent path models within an item response theory (IRT) framework. That is, the latent variables in a path model are estimated in combination with IRT measurement models. Thus far, researchers using IRT modelling had to produce individual person latent trait estimates with IRT software, and subsequently import these into other software packages to link them to other data sources and to perform secondary analysis such as path model analysis. Besides the impracticality of this method, different types of individual person ability estimates often lead to different—and therefore sometimes biased—results in secondary analysis. The approach that is presented in this thesis overcomes both limitations. A multi-step method is introduced in which the IRT model is estimated first. Subsequently, a full sums of squares and cross products (SSCP) matrix is constructed for all the latent variables from the population distribution parameter estimates of the first step (regression coefficients and conditional variance and covariance estimates) and of the observed variables included in the path model. Finally, the SSCP matrix is used to perform two-stage least squares for the estimation of the path model parameters. A simulation study shows that the parameter estimates are practically unbiased and that the standard errors are not worse than standard errors produced by methods employed to estimate latent path models within a structural equation modelling framework, but that their estimation can be improved in future. Another improvement would be to add the computation of fit statistics of the model. The thesis concludes with two examples in which the multi-step method is applied to test hypothetical models using real data.
  • Item response theory,
  • Latent path models,
  • ACER ConQuest,
  • Latent variable modelling,
  • IRT framework
Publication Date
Field of study
Melbourne Graduate School of Education
Citation Information
Eveline Gebhardt. "Latent path models within an IRT framework" (2016)
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