Which statement is true regarding regression models with binary dependent variables?

In the context of regression models with binary dependent variables, the statement that logistic and complementary log-log functions behave similarly for negative values of z is accurate. Both the logistic function and the complementary log-log function can be used to model binary outcomes, and when evaluating their behaviors for negative values of z (the linear predictor that typically consists of the independent variables weighted by their coefficients), both functions exhibit certain similar properties.

To understand this, consider that the logistic function transforms the linear combination of predictors into a probability that approaches 0 as z decreases towards negative infinity. The complementary log-log function, while it has a different transformation, also trends towards zero as z becomes more negative, thus leading to similarities in their interpretation at these extreme values.

On the other hand, the statements that the logit function is exclusively comparable to the probit function and that the probit function is superior to logistic for all applications are misleading. While logit and probit models can be compared in their interpretations, they are not exclusively comparable as their underlying assumptions and interpretations differ. Also, it's not accurate to assert one is superior because the choice between probit and logistic models often depends on the specific nature of the data and the research question at hand.

The assertion that logistic regression does