# Testing Categorized Bivariate Normality with Two-Stage Polychoric Correlation Estimates

@inproceedings{MaydeuOlivares2003TestingCB, title={Testing Categorized Bivariate Normality with Two-Stage Polychoric Correlation Estimates}, author={Albert Maydeu-Olivares}, year={2003} }

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

#### 21 Citations

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It is recommended that in applications of the polychoric correlation coefficient, data is tested with goodness-of-fit of the BND, that such statistic is reported in published applications, and that the polyChoric correlation is not applied when the test is significant. Expand

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The simulation results show that the currently used method of running PCA on a set of dummy variables as proposed by Filmer & Pritchett (2001) is inferior to other methods for analyzing discrete data, both simple such as using ordinal variables, and more sophisticatedsuch as using the polychoric correlations. Expand

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