Estimating the Latent Trait From Likert-Type Data: A Comparison of Factor Analysis, Item Response Theory, and Multidimensional Scaling

Abstract

本研究比較三個統計模式從李克特式(Likert-Type)資料中估計單向度潛在特質的能力，這三個模式是「植基於多序類相關(polychoric correlations)的因素分析」(FA-PL)，「試題反應理論中的漸變反應模式」(IRT-GRM)，以及「加權多維展開法」(WMDU)。一般常用的方法(SSI)－－分派連續性整數給李克特式量尺中的一個反應類別（如「非常同意」），再將每一題得分加總－－則做為比較的基準線。本研究為電腦模擬研究，操弄了樣本大小、測驗長度，以及試題反應分配的偏態程度等三個自變項，依變項則為回復潛在特質的真傎的正確性，結果發現：IRT-GRM表現得最好，最不受偏態的影響；FA-PL只有在試題反應分配為常態時，才能表現與IRT-GRM一樣好，而在試題反應分配為高度偏態時，甚至表現得比SSI差；最後，WMDU只有在試題反應分配為常態或輕微偏態時，才能表現得與SSI一樣好。本文也討論了這些發現對模式選擇的涵意。

Three statistical models 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 polychoric correlations (FA-PL), the graded response model in item response theory (IRT-GRM), and the weighted multidimensional unfolding (WMDU). The common procedure of summing up successive integers assigned to response categories (SSI) served as the base- line procedure. 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-PL were competitive with IRT-GRM only when item responses were normally distributed. It performed even worse than did SSI when item responses were highly skewed.WMDU might be a rival alternative to SSI only when item responses were normally distributed or moderately skewed and sample size was large for MDU models (e.g.. N=100).