Tests for independence between categorical variables

Abstract

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. • Pearson’s independence test is numerically equivalent to the LM in regression models. • LR test is numerically identical in the non-linear regression models. • Heteroskedastic Wald test in LPM and GMM coincide with Wald in multinomial model. • All these equivalences apply to serial independence tests in discrete Markov chains.