Estimating correlation from dichotomized normal variables

Given dichotomized data from a bivariate normal distribution, the tetrachoric correlation coefficient provides a reasonable estimate of Pearson's correlation between the underlying variables. Greer et al. 2003. A Monte Carlo evaluation of the tetrachoric correlation coefficient. Educ. Psychol. Meas. 63, 931–950] suggested that this may be the case also under suitable transformations of the margins. As a complement to their work, this paper considers the estimation of Pearson's correlation between variables that are normal, but not jointly. A small Monte Carlo study is used to assess whether various approximations of the tetrachoric correlation coefficient could be helpful in this context. The results are encouraging, in terms of both bias and mean-square error.