Comparing Logit and Probit Coefficients Across Groups

(1999) - Paul D. Allison

Journal: Sociological Methods & Research
Link:: http://journals.sagepub.com/doi/10.1177/0049124199028002003
DOI:: 10.1177/0049124199028002003
Links::
Tags:: #paper #Methods #Logit #Probit
Cite Key:: [@allisonComparingLogitProbit1999]

Abstract

In logit and probit regression analysis, a common practice is to estimate separate models for two or more groups and then compare coefficients across groups. An equivalent method is to test for interactions between particular predictors and dummy (indicator) variables representing the groups. Both methods may lead to invalid conclusions if residual variation differs across groups. New tests are proposed that adjust for unequal residual variation.

Notes

“Unlike linear regression coefficients, coefficients in these binary regression models are confounded with residual variation (unobserved hetero-” (Allison, 1999, p. 186)

“geneity)” (Allison, 1999, p. 187)

“Hence, unmeasured variables affecting the chances of promotion may be more important for women than for men” (Allison, 1999, p. 190)

“As before, g can be either the logit link function or the probit link function. Note that the probability on the left-hand side is now a conditional probability. But since ε is not observed, what we really need is the unconditional probability. If g is the probit function and ε has a standard normal distribution, it can be shown that the unconditional probability is also given by a probit model (Finney 1971:196-97” (Allison, 1999, p. 190)

“f g is the logit function and ε has a standard logistic distribution, the result is not a logit model but something that can be very closely approximated by a logit model (Allison 1987).” (Allison, 1999, p. 190)

“Most researchers now recognize that such comparisons are potentially invalidated by differences in the standard deviations across groups” (Allison, 1999, p. 191)

“nstead, they compare unstandardized coefficients. The problem with logit and probit coefficients, however, is that they are inherently standardized because they depend on the magnitude of the disturbance variance. The coefficients representing the true causal effects cannot be directly estimated.” (Allison, 1999, p. 191)

“For purely descriptive purposes, comparison of population-averaged coefficients may be acceptable. But if the goal is to make inferences about causal relationships, a focus on subject-specific coefficients seems more appropriate.” (Allison, 1999, p. 191)

“he key to a solution is that the disturbance variance affects all the coefficients in the same way.” (Allison, 1999, p. 191)

“I suggest examining the ratios of the coefficients in the different groups as I did in Table 1. If one group has coefficients that are consistently higher or lower than those in another group, it is a good indication of a potential problem that is amenable to solution” (Allison, 1999, p. 199)