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# Re: st: R: Interpretation of logistic regression coefficients

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: R: Interpretation of logistic regression coefficients Date Sun, 27 Jan 2013 12:34:03 -0500

```Unfortunately, starting with linear regression (page 115), Long and
Freese give the common but oversimplified and often incorrect
interpretation of regression coefficients that involves holding the
other predictors constant ("regardless of the level of the other
variables in the model").  That interpretation does not reflect how
multiple linear regression works.

The appropriate general interpretation of an estimated coefficient in
a multiple regression is that it tells how y responds (on average) to
change in that predictor after adjusting for simultaneous change in
the other predictors in the data at hand.

This interpretation also applies to logistic regression and other
regression models.  In logistic regression the linear predictor is in
the log-odds scale, so the interpretation of a coefficient (say b_j)
involves change in the log-odds associated with change in that
predictor (x_j), adjusting for the contributions of the other
predictors.  If it is appropriate to increase that predictor by 1
unit, then taking exp of the coefficient, exp(b_j), yields an adjusted
odds ratio (i.e., the ratio of the odds after increasing the predictor
by 1 unit to the odds before the increase).  For a predictor whose
only values are 0 and 1, an increase of 1 unit is the only possible
increase.  For a "continuous" predictor, exp(b_j) can be interpreted
as the adjusted odds ratio per unit increase in x_j.

David Hoaglin

On Sun, Jan 27, 2013 at 10:02 AM,  <carlo.lazzaro@tiscalinet.it> wrote:
> Carlos may want to take a look at:
>
> 1) Hilbe J. Logistic regression models. Chapman & Hall/CRC, 2009.
> 2) Scott Long J, Freese J. Regresion models for catergorical variables using
> Stata. 2nd ed. Stata Press, 2006.
>
>
> Best regards,
> Carlo
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