Testing Categorized Bivariate Normality with Two-Stage Polychoric Correlation Estimates

  title={Testing Categorized Bivariate Normality with Two-Stage Polychoric Correlation Estimates},
  author={Albert Maydeu-Olivares},
We show that when the thresholds and the polychoric correlation are estimated in two stages, neither Pearson's X^2 nor the likelihood ratio G^2 goodness of fit test statistics are asymptotically chi-square. We propose a new test statistic, Mn, that is asymptotically chi-square in this situation. Mn, may have a wide range of applications beyond the one considered here as it is asymptotically chi-square for a broad class of consistent and asymptotically normal estimators. Mn equals X^2 with an… Expand

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