Logistic regression: Why we often can do what we think we can do

There is increasing criticism of the ways in which the raw coefficients and odds ratios from logistic regression have been used. The argument is that logistic regression models a latent propensity of success and that the scale of that latent variable is fixed by fixing the variance of the error term. If one adds a variable to a model, the variance of the residual is likely to decrease, and the scale of the dependent variable thus changes. Comparing models with and without that additional variable thus becomes problematic. Similarly, a comparison of models in groups that are likely to have different residual variances will also be problematic. However, I will argue that logistic regression has an unusual dependent variable: a probability, which measures how certain we are that an event of interest happens. This degree of certainty is a function of how much information we have, which in case of logistic regression is captured by the variables we add to the model. If the dependent variable is interpreted in that way many of the problems with logistic regression turn out to be desirable properties of the logistic regression model.