The comparability of estimates for different groups derived from models for binary observed outcomes (e.g. logit, probit) is a topic that is periodically discussed in this forum, and at least 2 prominent members (Maarten Buis and Richard Williams) have written about it. Herewith a new paper on the topic that challenges some recent literature.
"On Group Comparisons With Logistic Regression Models" by Joni Kuha and Colin Mills, Sociological Methods and Research, 2018 online
http://journals.sagepub.com/doi/abs/...49124117747306
Abstract: It is widely believed that regression models for binary responses are problematic if we want to compare estimated coefficients from models for different groups or with different explanatory variables. This concern has two forms. The first arises if the binary model is treated as an estimate of a model for an unobserved continuous response and the second when models are compared between groups that have different distributions of other causes of the binary response. We argue that these concerns are usually misplaced. The first of them is only relevant if the unobserved continuous response is really the subject of substantive interest. If it is, the problem should be addressed through better measurement of this response. The second concern refers to a situation which is unavoidable but unproblematic, in that causal effects and descriptive associations are inherently group dependent and can be compared as long as they are correctly estimated.
It'd be interesting to know Forum members' current views on this perennial topic.
FWIW Personally, I've been persuaded by J. Scott Long's arguments and approach (not cited in Kuha & Mills paper). Further details via Scott's webpage: "Group comparisons in logit and probit using predicted probabilities.
"On Group Comparisons With Logistic Regression Models" by Joni Kuha and Colin Mills, Sociological Methods and Research, 2018 online
http://journals.sagepub.com/doi/abs/...49124117747306
Abstract: It is widely believed that regression models for binary responses are problematic if we want to compare estimated coefficients from models for different groups or with different explanatory variables. This concern has two forms. The first arises if the binary model is treated as an estimate of a model for an unobserved continuous response and the second when models are compared between groups that have different distributions of other causes of the binary response. We argue that these concerns are usually misplaced. The first of them is only relevant if the unobserved continuous response is really the subject of substantive interest. If it is, the problem should be addressed through better measurement of this response. The second concern refers to a situation which is unavoidable but unproblematic, in that causal effects and descriptive associations are inherently group dependent and can be compared as long as they are correctly estimated.
It'd be interesting to know Forum members' current views on this perennial topic.
FWIW Personally, I've been persuaded by J. Scott Long's arguments and approach (not cited in Kuha & Mills paper). Further details via Scott's webpage: "Group comparisons in logit and probit using predicted probabilities.
