Re: st: logistic regr followed by lowess

["stata_user stata_user" <stata_dofile@hotmail.co.uk>]

Thanks a lot to Nick and Joseph for their useful comments

I would like to have your opinions about the following syntax

sysuse auto, clear
logit foreign mpg
predict p
sort mpg
line p  mpg || lowess  foreign mpg

What the lowess does here, nonparametric regression of the p and mpg?

Thanks a lot

S.

> From: Joseph Coveney <jcoveney@bigplanet.com>
> Reply-To: statalist@hsphsun2.harvard.edu
> To: Statalist <statalist@hsphsun2.harvard.edu>
> Subject: Re: st: logistic regr followed by lowess
> Date: Sat, 02 Sep 2006 11:31:10 +0900
>
> Sami wrote:
>
> I have an outcome y dichotomous (0/1) and a continuous predictor X1
>
> I use
> logit y X1
> I predict
> p
> and then I use the lowess smooth curve
>
> I have a confusion about the lowess.
>
> I am not sure if the lowess fits smooth successive non paramteric 
> regression
> (Y X1) for successive small intervals of X1 (starting with the smallest
> values of X1), and then produces a smooth option of the predicted
> probabilities
>
> Or if it fits successive logistic regression models followed by a smooth
> graph of these probabilities of these models
>
> Please can you advise on this question?
>
> --------------------------------------------------------------------------------
>
> Are you asking about the -logit- option to -lowess-?  It just affects the
> display scale of the y-axis and omits the scatterplot of the observed
> values.  -lowess- does LOWESS (LOESS) smoothing  and doesn't perform
> logistic regression to my knowledge.
>
> If you're looking to create a logistic regression calibration plot as
> advocated in Frank E. Harrell Jr, _Regression Modeling Strategies_ (N.Y.:
> Springer, 2001), then you can overlay a -twoway function- (for the logistic
> regression fit) and -lowess-.  That's shown below; it follows the lead of
> Nick's post in this thread.  Professor Harrell plots these on the
> probability scale.  If you want to show the calibration plot on the logit
> scale, then follow the second syntax below.  Note that you'll lose the
> scatterplot of the observed values when plotting on the logit scale.  The
> latter highlights discrepancies at the extremes, which are not always 
> greatest of interest.
>
> Joseph Coveney
>
> sysuse auto, clear
> logit foreign mpg
> predict probability
> graph twoway ///
>  ( function y = invlogit(_b[_cons] + _b[mpg] * x) , ///
>    range(mpg) lcolor(black) ) ///
>  ( lowess foreign mpg, ///
>    lcolor(black) lpattern(dash) ) ///
>  ( scatter foreign mpg, ///
>    msymbol(circle) mcolor(black) ///
>    ytitle(Probability That Car Manufacturer is Foreign) ///
>    ylabel( , format(%02.1f) angle(horizontal) nogrid) ///
>    xtitle(Miles per Gallon) legend(off) name(Probability) )
> predict logits, xb
> lowess foreign mpg, logit lineopts(lcolor(black) lpattern(dash)) ///
>  addplot(line logits mpg, lcolor(black) ///
>  legend(off) ///
>  ytitle(Log Odds That Manufacturer is Foreign) ///
>  ylabel( , angle(horizontal) nogrid) title("") ///
>  subtitle("") note("") name(Logit) )
> exit
>
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