A linear probability model directly models binomial probabilities. An example can be seen in this note using PROC GENMOD by specifying DIST=BINOMIAL and LINK=IDENTITY in the MODEL statement. However, it is rarely a good idea unless the observed probabilities are all in the mid-range (such as 0.25 to 0.75). Otherwise, the model typically does not fit well and very often runs into estimation problems because this model allows predicted values to fall outside of the valid [0,1] range. That is why a link function such as the LOGIT or PROBIT link is typically used as they both restrict the predictions to the valid range. If your reason for wanting to fit a linear probability model is to use the model to predict probabilities or to estimate differences on the probability scale, this can still be easily done using a logit model that can fit well. The above note shows how that can be done using the Margins macro or using PROC LOGISTIC followed by the NLMeans macro.
