The primary goal of this study was to investigate whether the structure of data generated by the most commonly used multidimensional item response theory (MIRT) models could be identified by frequently used multivariate methods. In item response theory (IRT) applications, a multivariate analysis procedure typically is recommended prior to estimating a given IRT model to ensure that the proper type of model (unidimensional vs. multidimensional) is used. Therefore, if IRT models are to be applied in testing practice, it is important to demonstrate that these dimensionality identifying procedures succeed.
This study employed a 2 (models for the multidimensional cases) × 3 (number of dimensions) × 4 (situations where the average discrimination parameters varied) × 2 (test lengths) model with 34 total cells. Seventy-five data sets were generated within each cell. Data sets were analyzed with four different methods—exploratory iterated principal factor analysis (IPFA), exploratory nonlinear factor analysis (NLFA), exploratory full-information factor analysis (FIFA), and nonmetric multidimensional scaling (MDS). Recovery of structure was determined using two sets of criteria: (1) “fit” statistics commonly used for each particular method and a statistic that was computed across methods (root mean square residual; RMSR) and (2) a comparison of relative magnitude of estimated and true item parameters using Spearman rank-order correlations.
Overall, the data generation model, true dimensionality, and the method of analysis were the most important factors for determining recovery. None of the methods recovered dimensionality well for all circumstances. Based on dimensionality recovery, NLFA best recovered unidimensional data, IPFA best recovered two-dimensional data, and MDS using the RMSR statistic best recovered three-dimensional data. With regard to structure, the NLFA and FIFA estimated values recovered the true parameters best.
|Adviser||David J. Weiss|
|School||UNIVERSITY OF MINNESOTA|
|Subjects||Quantitative psychology and psychometrics|
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