This paper takes another look at the derivation of the method of Y-standardization used in sociological analysis involving comparisons of coefficients across logit or probit models. It shows that the method can be derived under less restrictive assumptions than hitherto suggested. Rather than assuming that the logit or probit fixes the variance of the latent error at a known constant, it suffices to assume that the variance of the error is unknown. A further result suggests that using Y-standardization for cross-model comparisons is likely to be biased by model differences in the fit of the latent error to the assumed logistic or normal distribution. Under correct specification Y-standardization recovers an effect size metric similar to Cohen's d.
Journal of Mathematical Sociology, 2015, Vol 39, Issue 1, p. 29-38