Testing Categorized Bivariate Normality With Two-Stage Polychoric Correlation Estimates

نویسندگان

  • Alberto Maydeu-Olivares
  • Carlos García-Forero
  • David Gallardo-Pujol
  • Jordi Renom
چکیده

Structural equation modeling (SEM) with ordinal indicators rely on an assumption of categorized normality. This assumption may be tested for pairs of variables using the likelihood ratio G or Pearson’s X statistics. For increased computational efficiency, SEM programs usually estimate polychoric correlations in two stages. However, two-stage polychoric estimates are not asymptotically efficient and G and X need not be asymptotically chi-square when the estimator is not efficient. Recently, Maydeu-Olivares and Joe (2005) have introduced a new statistic, Mn, that is asymptotically chi-square even for estimators that are not efficient. We investigate the behavior of G, X, and Mn when testing underlying bivariate normality with polychoric correlations estimated in two stages.

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تاریخ انتشار 2009