Estimating the latent trait from Likert-type data : a comparison of factor analysis, item response theory, and multidimensional scaling




Chan, Chihyu, 1959-

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Seven statistical procedures were compared with one another in terms of the ability to recover a unidimensional latent trait from Likert-type data. They are factor analysis based on either Pearson correlations (FA-PR) or polychoric correlations (FAPL), the graded response model in item response theory (IRT-GRM), internal unfolding (IMDU), external unfolding (EMDU), weighted unfolding (WMDU), and the common procedure of summing up successive integers assigned to response categories (SSI). Sample size, test length, and skewness of item response distributions were manipulated in this simulation study. Generally speaking, IRT-GRM performed the best and was most robust against skewness. FA-PR and FA-PL performed equally well across almost all conditions but were competitive with IRT-GRM only when item responses were normally distributed. SSI practice might be slightly worse than the two FA procedures when item responses were normally distributed, but it was better than them when item responses were highly skewed. WMDU performed as well as did SSI only when item responses were normally distributed or moderately skewed and sample size was large for MDS models (e.g., N=100). IMDU and EMDU were even worse than WMDU and appeared not appropriate for Likert-type data