Linear probability model: Difference between revisions

Revision as of 09:10, 15 July 2012

Revision as of 21:08, 11 May 2013

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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|observed 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==

The model assumes that, for a binary outcome ([[Bernoulli trial]]), ''Y'', and its associated vector of explanatory variables, ''X'',<ref name=Cox>Cox, D.R. (1970) ''Analysis of Binary Data'', Methuen. ISBN 0416-10400-2(Section 2.2)</ref>

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A drawback of this model for the parameter of the [[Bernoulli distribution]] is that, unless restrictions are placed on <math> \beta </math>, the estimated coefficients can imply probabilities outside the [[unit interval]] <math> [0,1] </math> . For this reason, models such as the [[logit model]] or the [[probit model]] are more commonly used.

==References==

{{reflist}}

{{DEFAULTSORT:Linear Probability Model}}