Linear probability models

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The linear probability specification of a binary regression model assumes that, for binary outcome Y and regressor vector X,

A drawback of this model is that, unless restrictions are placed on β, the estimated coefficients can imply probabilities outside the unit interval [0,1] . For this reason, the logit model or the probit model are more commonly used.

One situation where the linear probability model is commonly used, is when the data set is so large that maximum likelihood estimation of a logit or probit model is computationally difficult. For the linear probability model, E[Y | X] = Pr(Y = 1 | X) = x'β, so the parameter β can be estimated using least squares.