Comparing the Effects of Different Smoothing Algorithms on the Assessment of Dimensionality of Ordered Categorical Items with Parallel Analysis.

Rudolf Debelak,Ulrich S Tran,Mansour Ebrahimi

doi:10.1371/journal.pone.0148143

Rudolf Debelak, Ulrich S Tran + Show 1 more

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https://doi.org/10.1371/journal.pone.0148143

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Journal: PloS one	Publication Date: Feb 4, 2016
Citations: 16	License type: CC BY 4.0

Affiliation: University of Zurich, University of Vienna

Abstract

The analysis of polychoric correlations via principal component analysis and exploratory factor analysis are well-known approaches to determine the dimensionality of ordered categorical items. However, the application of these approaches has been considered as critical due to the possible indefiniteness of the polychoric correlation matrix. A possible solution to this problem is the application of smoothing algorithms. This study compared the effects of three smoothing algorithms, based on the Frobenius norm, the adaption of the eigenvalues and eigenvectors, and on minimum-trace factor analysis, on the accuracy of various variations of parallel analysis by the means of a simulation study. We simulated different datasets which varied with respect to the size of the respondent sample, the size of the item set, the underlying factor model, the skewness of the response distributions and the number of response categories in each item. We found that a parallel analysis and principal component analysis of smoothed polychoric and Pearson correlations led to the most accurate results in detecting the number of major factors in simulated datasets when compared to the other methods we investigated. Of the methods used for smoothing polychoric correlation matrices, we recommend the algorithm based on minimum trace factor analysis.

Highlights

The assessment of dimensionality of a set of variables is a central issue in psychological and educational measurement, closely connected to theory building and psychological scale construction [1,2]
We do not recommend the application of this algorithm especially in large datasets; in small datasets, which were simulated as part of our simulation study, the application of this procedure seems to be necessary to avoid convergence problems which occur if threshold parameters which are invariant over the item pairs are calculated as part of the estimation of the polychoric correlation coefficient
We are not aware of any studies which compared the variation of the two-step estimation procedure of Olsson [30], which was used in our study, with an approach that estimates threshold parameters which are invariant for each item over all item pairs, both approaches are expected to lead to similar results if the model underlying the calculation of the polychoric correlation coefficient fits the data well

Summary

Introduction

The assessment of dimensionality of a set of variables is a central issue in psychological and educational measurement, closely connected to theory building and psychological scale construction [1,2]. In the context of EFA, an adaptation of parallel analysis [11], and, for maximum likelihood factor analysis, chi square significance tests and approaches based on information criteria like the Akaike Information Criterion [12] and the Bayesian Information Criterion [13] are among the methods which were suggested to assess the dimensionality of an item set. Among these methods, the adaptations of parallel analysis (PA) are commonly regarded to provide an accurate assessment under many conditions [2], it has been noted that there is less evidence for the accuracy of PA in the context of EFA [14]

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