Logistic Regression Using SAS®: Theory and Application

3.11. Unobserved Heterogeneity

In Section 3.9, I explained how the logit model could be derived from a dichotomized linear model with a disturbance term that has a logistic distribution. There we saw that the logit coefficients were related to the coefficients in the underlying linear model by the formula β_j=α_j/σ, where β_j is the logit coefficient for x_j, α_j is the corresponding coefficient in the linear model, and σ is the coefficient of the disturbance term ε. This random disturbance term can be seen as representing all omitted explanatory variables that are independent of the measured x variables, commonly referred to as unobserved heterogeneity. Because σ controls the variance of the disturbance, we conclude that greater unobserved heterogeneity ...