Case Diagnostics for Factor Analysis of Ordered Categorical Data With Applications to Person-Fit Measurement

Maxwell Mansolf*, Steven P. Reise

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Mahalanobis distance (M-distance) case diagnostics are a useful tool for assessing response pattern inconsistency in factor analysis; however, the derivations of these statistics assume continuous variables, which limits their utility in ordinal self- or rater-report data. This research generalizes M-distance diagnostics to categorical factor analysis. We prove that the residual-based M-distance dr is equivalent to the person-fit index lco, which motivates the use of the new categorical M-distance dr* as a person-fit index. dr* is compared and contrasted with zh, a commonly used item response theory person-fit index. A simulation study is used to show that a simple transformation of dr* satisfies established criteria for person-fit measures. A sample of responses to the Rosenberg Self-Esteem Scale is used to determine parameters for a simulation study, and real data are analyzed to contrast the use of dr and dr* as indexes of person-fit in continuous and categorical factor analysis.

Original languageEnglish (US)
Pages (from-to)86-100
Number of pages15
JournalStructural Equation Modeling
Volume25
Issue number1
DOIs
StatePublished - Jan 2 2018
Externally publishedYes

Keywords

  • categorical factor analysis
  • item response theory
  • outliers
  • person-fit

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Modeling and Simulation
  • Sociology and Political Science
  • Economics, Econometrics and Finance(all)

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