[R] Coefficients of Logistic Regression from bootstrap - how to get them?

[Michal Figurski]

Frank,

"How does bootstrap improve on that?"

I don't know, but I have an idea. Since the data in my set are just a 
small sample of a big population, then if I use my whole dataset to 
obtain max likelihood estimates, these estimates may be best for this 
dataset, but far from ideal for the whole population.

I used bootstrap to virtually increase the size of my dataset, it should 
result in estimates more close to that from the population - isn't it 
the purpose of bootstrap?

When I use such median coefficients on another dataset (another sample 
from population), the predictions are better, than using max likelihood 
estimates. I have already tested that and it worked!

I am not a statistician and I don't feel what "overfitting" is, but it 
may be just another word for the same idea.

Nevertheless, I would still like to know how can I get the coeffcients 
for the model that gives the "nearly unbiased estimates". I greatly 
appreciate your help.

--
Michal J. Figurski
HUP, Pathology & Laboratory Medicine
Xenobiotics Toxicokinetics Research Laboratory
3400 Spruce St. 7 Maloney
Philadelphia, PA 19104
tel. (215) 662-3413

Frank E Harrell Jr wrote:
> Michal Figurski wrote:
>> Hello all,
>>
>> I am trying to optimize my logistic regression model by using 
>> bootstrap. I was previously using SAS for this kind of tasks, but I am 
>> now switching to R.
>>
>> My data frame consists of 5 columns and has 109 rows. Each row is a 
>> single record composed of the following values: Subject_name, 
>> numeric1, numeric2, numeric3 and outcome (yes or no). All three 
>> numerics are used to predict outcome using LR.
>>
>> In SAS I have written a macro, that was splitting the dataset, running 
>> LR on one half of data and making predictions on second half. Then it 
>> was collecting the equation coefficients from each iteration of 
>> bootstrap. Later I was just taking medians of these coefficients from 
>> all iterations, and used them as an optimal model - it really worked 
>> well!
> 
> Why not use maximum likelihood estimation, i.e., the coefficients from 
> the original fit.  How does the bootstrap improve on that?
> 
>>
>> Now I want to do the same in R. I tried to use the 'validate' or 
>> 'calibrate' functions from package "Design", and I also experimented 
>> with function 'sm.binomial.bootstrap' from package "sm". I tried also 
>> the function 'boot' from package "boot", though without success - in 
>> my case it randomly selected _columns_ from my data frame, while I 
>> wanted it to select _rows_.
> 
> validate and calibrate in Design do resampling on the rows
> 
> Resampling is mainly used to get a nearly unbiased estimate of the model 
> performance, i.e., to correct for overfitting.
> 
> Frank Harrell
> 
>>
>> Though the main point here is the optimized LR equation. I would 
>> appreciate any help on how to extract the LR equation coefficients 
>> from any of these bootstrap functions, in the same form as given by 
>> 'glm' or 'lrm'.
>>
>> Many thanks in advance!
>>
> 
>