I am now working with an econometrics project, where the dataset contains lots of binary(dummy) variables. Since the linear probability model (LPM) I constructed by directly regressing independent variables on a dependent variable (which is binary also) does not violate the mathematical principle (probabilities should be within 0 and 1), I try to keep that result, as well as compare that result to Probit and Logistic models' estimators, and observe all of their significance levels.
One interaction term that I designed added is significant at 5% level in the LPM, but when I work with Probit and Logistic models it turns to be insignificant.
How could I explain this thing happening? Can I still keep that interaction term (though that is significant at 10% level in Probit/Logistic)? If not, which result should I prefer: LPM or Probit/Logistic? Why? Thanks!
Best Answer
Ordinary linear regression uses the assumption of a continuous dependent variable, and is poorly equipped for a binary dependent variable. In particular, it's liable to make absurd predictions, such as saying that the probability of the event occurring is above 100% or below 0%. Stick to your logistic model or probit model instead.