[R] alternative to logistic regression

[markleeds at verizon.net]

>From: Prof Brian Ripley <ripley at stats.ox.ac.uk>
>Date: 2007/11/16 Fri AM 09:44:59 CST
>To: markleeds at verizon.net
>Cc: Terry Therneau <therneau at mayo.edu>, r-help at r-project.org
>Subject: Re: Re: [R] alternative to logistic regression

Thanks Brian: I'll look at the MASS book example
for sure but I don't think I was so clear
in my last question so let me explain again.

What I meant to say was : 

Suppose Person A and Person B both have the same raw data which is categorical response ( say 3 responses ) and 1 numeric predictor.

Now, suppose person A fits a logit regression with the logit link  and family = binomal  so that it's an S curve in the  probability space and the the predictor was numeric so the x axis was numeric.

suppose person B fits a logit regression with the logit link and family = binomal  so that it's an S curve in the  probability space and the the predictor was a factor so the x axis was say deciles.

They both then predict off of their respective models
given a new value of the predictor ( Person A's
predictor is in the form of a number and Person B's
predictor is say a decile where the number fell in.

Would their forecast of the probability given that
predictor be roughly 
the same ? I'm sorry to be a pest but I'm not clear on that. Thanks and I'm sorry to bother you so much.















>On Fri, 16 Nov 2007, markleeds at verizon.net wrote:
>
>>> From: Prof Brian Ripley <ripley at stats.ox.ac.uk>
>>> Date: 2007/11/16 Fri AM 09:28:27 CST
>>> To: Terry Therneau <therneau at mayo.edu>
>>> Cc: markleeds at verizon.net, r-help at r-project.org
>>> Subject: Re: [R] alternative to logistic regression
>>
>> Thanks to both of you, Terry and Brian for your comments. I'm not sure what I am going to do yet because I don't have enough data yet to explore/
>> confirm my linear hypothesis but your comments
>> will help if I go that route.
>>
>> I just had one other question since I have you both thinking about GLM's at the moment : Suppose one
>> is doing logistic or more generally multinomial regression with one predictor. The predictor is quantitative
>> in the range of [-1,1] but, if I scale it, then
>> the range becomes whatever it becomes.
>>
>> But, there's also the possibility of making the predictor a factor say 
>> by deciling it and then say letting the deciles be the factors.
>>
>> My question is whether would one expect roughly the same probability 
>> forecasts from two models, one using the numerical predictor and one 
>> using the factors ?  I imagine that it shouldn't matter so much but I 
>> have ZERO experience in logistic regression and I'm not confident with 
>> my current intuition.  Thanks so much for talking about my problem and I 
>> really appreciate your insights.
>
>It's just as in linear regression. If there really is a linear 
>relationship the predictions will be the same.  But it is quadratic, they 
>will be very different.  Discreting a numeric explanatory variable is a 
>common way to look for non-linearity (as in the 'cpus' example studied in 
>MASS).
>
>
>-- 
>Brian D. Ripley,                  ripley at stats.ox.ac.uk
>Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
>University of Oxford,             Tel:  +44 1865 272861 (self)
>1 South Parks Road,                     +44 1865 272866 (PA)
>Oxford OX1 3TG, UK                Fax:  +44 1865 272595