[R] Logistic and Linear Regression Libraries

[David Winsemius]

On Oct 31, 2009, at 7:29 AM, tdm wrote:

>
>
> OK, I think I've figured it out, the predict of lrm didn't seem to  
> pass it
> through the logistic function. If I do this then the value is  
> similar to
> that of lm. Is this by design?

Yes, at least for certain meanings of "this". When working with  
probabilities or propotions as the dependent variable, the estimates  
will be similar in the central regions of the data but diverge at the  
extremes, although it is linear regression that blows up when  
estimating probabilities. Logistic regression is by design constrained  
to predict a true probability even outside the range of the data,  
while the "prediction" for an ordinary least squares model has no such  
constraint.

> Why would it be so?
>
> 1 / (1 + Exp(-1 * 3.38)) =  0.967
>
>

I am guessing that you have not read the help page for predict.lrm. In  
it Harrell clearly indicates that the default output from that  
function is of type "lp" or the linear predictor. Since you were  
apparently unaware that logistic regression and simple linear  
regression were different approaches to modeling, then you are  
probably also unaware that you need to use the inverse of the logistic  
transformation on the linear predictor, which expressed on the log  
odds scale, to get back a probability estimate.


> tdm wrote:
>>
>>
>> Anyway, do you know why the lrm predict give me a values of 3.38?
>>
>>
>
==

David Winsemius, MD
Heritage Laboratories
West Hartford, CT