Linear probability model

Abstract: Many social scientists believe that dumping long lists of explanatory variables into linear regression, probit, logit, and other statistical equations will successfully “control” for the effects of...

Abstract: You may often want to model a response variable that appears as a proportion or fraction: the share of consumers’ spending on food, the fraction of the vote for a candidate, or the fraction of days when air pollution is above acceptable levels in a city. To handle these data properly, you must take account of the bounded nature of the response. Just as a linear probability model on unit record data can generate predictions outside the unit interval, using a proportion in a linear regression model will generally yield nonsensical predictions for extreme values of the regressors. One way to handle this for response variables’ values strictly within the unit interval is the logit transformation y = 1

Abstract: This paper formulates and estimates a rigorously-justified linear probability model of binary choices over alternatives characterized by unobserved attributes. The model is applied to estimate preferences of congressmen as expressed in their votes on bills. The effective dimension of the attribute space characterizing votes is larger than what has been estimated in recent influential studies of congressional voting by Poole and Rosenthal. Congressmen vote on more than ideology. Issue-specific attributes are an important determinant of congressional" voting patterns. The estimated dimension is too large for the median voter model to describe congressional voting