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RE: st: linear probability model


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: linear probability model
Date   Wed, 23 Jun 2010 18:11:47 +0100

I think this is far from the central issue. With continuous responses it
can be just as important as with binary responses to ensure that
predictions stay within the bounds of 0 and 1. 

Conversely a linear model might seem justifiable if predictions outside
those bounds only occurred way beyond the range of the data and if
linear, logit and probit give similar predictions. 

This is like anything else. I often argue, especially to students, that
choosing a qualitatively correct model precedes estimating the
parameters and focusing on quantitative fit. But little in this
territory seems absolute. I wouldn't turn down a Gaussian fit to human
heights if it fitted well merely because it predicts a positive
probability of negative heights, even though that is completely
unbiological. 

Nick 
n.j.cox@durham.ac.uk 

Scott Millis

The fundamental issue is the type of response variable that you have.
If it is binary, you would want to use a logit or probit model---not a
linear model.  If your response variable is continuous, you would use a
linear model.

--- On Wed, 6/23/10, dk <statad27@googlemail.com> wrote:

> What are the advantages of linear
> probability model over probit and
> logit. i have read some where that linear probability model
> fits best
> for very large sample, where maximum likelihood with probit
> and logit
> does not work can any one explain this.

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