Linear probability model: Difference between revisions

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In [[statistics]], a '''linear probability model''' is a special case of a [[binomial regression]] model. Here the [[dependent and independent variables|observeddependent variable]] for each observation takes values which are either 0 or 1. The probability of observing a 0 or 1 in any one case is treated as depending on one or more [[dependent and independent variables|explanatory variables]]. For the "linear probability model", this relationship is a particularly simple one, and allows the model to be fitted by [[simple linear regression]].

The model assumes that, for a binary outcome ([[Bernoulli trial]]), <math>Y</math>, and its associated vector of explanatory variables, <math>X</math>,<ref name=Cox>{{cite book |last=Cox |first=D. R. |year=1970 |title=Analysis of Binary Data |___location=London |publisher=Methuen |isbn=0-416-10400-2 |chapter=Simple Regression |pages=33–42 }}</ref>