Tests for independence between categorical variables

Abstract

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I prove the numerical equivalence between Pearson’s independence test statistic for categorical variables and the Lagrange Multiplier and overidentifying restrictions test statistics in several popular linear and non-linear regression models. I also show that its asymptotically equivalent Likelihood Ratio test is numerically identical in the non-linear regression models, and that the heteroskedasticity-robust Wald test statistic in the multivariate linear probability model and the moment condition model coincide with the Wald test statistic in the conditional multinomial model. Finally, I show that all these equivalences also apply to serial independence tests in discrete Markov chains.