Investigating the Behaviors of M2 and RMSEA2 in Fitting a Unidimensional Model to Multidimensional Data

Jie Xu, Insu Paek, Yan Xia

Research output: Contribution to journalArticlepeer-review


It has been widely known that the Type I error rates of goodness-of-fit tests using full information test statistics, such as Pearson’s test statistic χ2 and the likelihood ratio test statistic G2, are problematic when data are sparse. Under such conditions, the limited information goodness-of-fit test statistic M2 is recommended in model fit assessment for models with binary response data. A simulation study was conducted to investigate the power and Type I error rate of M2 in fitting unidimensional models to many different types of multidimensional data. As an additional interest, the behavior of RMSEA2 was also examined, which is the root mean square error approximation (RMSEA) based on M2. Findings from the current study showed that M2 and RMSEA2 are sensitive in detecting the misfits due to varying slope parameters, the bifactor structure, and the partially (or completely) simple structure for multidimensional data, but not the misfits due to the within-item multidimensional structures.

Original languageEnglish (US)
Pages (from-to)632-644
Number of pages13
JournalApplied Psychological Measurement
Issue number8
StatePublished - Nov 1 2017
Externally publishedYes


  • M
  • item response theory
  • limited information statistic
  • multidimensional structures

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)

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