Abstract
The last series of Raven’s standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization for RLCMs is proposed. For polytomous item responses, different alternative fused regularization penalties are presented. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes. In total, three out of five latent classes are ordered for all items. For the remaining two classes, violations for two and three items were found, respectively, which can be interpreted as a kind of latent differential item functioning.
Highlights
There has been recent interest in assessing the usefulness of short versions of the Raven’s ProgressiveMatrices. Myszkowski and Storme (2018) composed the last 12 matrices of the Standard ProgressiveMatrices (SPM-LS) and argued that it could be regarded as a valid indicator of general intelligence g.As part of this special issue, the SPM-LS dataset that was analyzed in Myszkowski and Storme (2018) was reanalyzed in a series of papers applying a wide range of psychometric approaches.Previous reanalyses of the SPM-LS dataset have in common that quantitative latent variable models were utilized
While the decision based on the Akaike information criterion (AIC) was ambiguous and selected the incorrect number of classes, the Bayesian information criterion (BIC) correctly selected model with C = 4 latent classes
This observation is consistent with the literature that argues that model selection in latent class model (LCM) should be based on the BIC instead of the AIC (Collins and Lanza 2009; Keribin 2000)
Summary
There has been recent interest in assessing the usefulness of short versions of the Raven’s ProgressiveMatrices. Myszkowski and Storme (2018) composed the last 12 matrices of the Standard ProgressiveMatrices (SPM-LS) and argued that it could be regarded as a valid indicator of general intelligence g.As part of this special issue, the SPM-LS dataset that was analyzed in Myszkowski and Storme (2018) was reanalyzed in a series of papers applying a wide range of psychometric approaches.Previous reanalyses of the SPM-LS dataset have in common that quantitative latent variable models were utilized. Matrices (SPM-LS) and argued that it could be regarded as a valid indicator of general intelligence g. As part of this special issue, the SPM-LS dataset that was analyzed in Myszkowski and Storme (2018) was reanalyzed in a series of papers applying a wide range of psychometric approaches. Discrete latent variable models (i.e., latent class models) are applied for analyzing the SPM-LS dataset. A disadvantage of discrete latent variable models is that they often have a large number of parameters to estimate. Even with only a few classes, the number of estimated parameters is typically larger than parametric models with quantitative latent variables. -called regularization approaches automatically reduce the number of parameters to estimate (see Huang et al (2017) or Jacobucci et al (2016)) for the use of regularization in structural equation modeling and Tutz and Schauberger (2015) or Battauz (2019)
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