constant at their mean or at some level that is substantively interesting. To explain this method, we consider the case of a binary outcome. Further details and generalization to nominal outcomes can be found in Long (1997).
Let y be a dummy variable equal to 1 if an event occurred and 0 if not. For example, y=1 if a scientist has tenure and y=0 if not. Let x1 through x3 be the independent variables, which can be either binary or continuous. The logit model uses the x’s to predict the probability that y=1 according to the equation:
These equations describe a nonlinear relationship between the x’s and the outcome probabilities. The problem in presenting results from the logit model is that the expected change in the probability for a unit change in a variable differs depending on the current level of all variables in the model.
To summarize the effect of a variable, we examined how a unit change in a variable affected the outcome probability when all variables were held constant, usually at their mean. For a continuous variable xc, we computed:
This is simply the difference in the predicted probability when xc moves from .5 below its mean to .5 above its mean, holding all other variables at their means. In the text, we interpreted this as: when xc changes by one unit, the probability of the event changes by ∆pc. For binary independent variables, we computed the effect of a change from 0 to 1:
In some cases we focused on predicted probabilities and changes in predicted probabilities at levels of the variables other than the mean. For example, in Chapter 6 we were interested in the predicted probability of being a full professor. Given that promotion to full professor rarely occurs early in the career, we computed the predicted probability holding years of experience constant at 15 years while other variables were held constant at their mean.