Logistic regression X^2 test with large sample size (fwd)

[M Pomati]

Does anyone know of any X^2 tests to compare the fit of logistic models
which factor out the sample size? I'm dealing with a very large sample and
I fear the significant X^2 test I get when adding a variable to the model
is simply a result of the sample size (>200,000 cases).

I'd rather use the whole dataset instead of taking (small) random samples
as it is highly skewed. I've seen things like Phi and Cramer's V for
crosstabs but I'm not sure whether they have been used before on logistic
regression, if there are better ones and if there are any packages.


Many thanks

Marco


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[Marc Schwartz-3]

On Jul 31, 2012, at 10:35 AM, M Pomati <[hidden email]> wrote:

>
>
> Does anyone know of any X^2 tests to compare the fit of logistic models
> which factor out the sample size? I'm dealing with a very large sample and
> I fear the significant X^2 test I get when adding a variable to the model
> is simply a result of the sample size (>200,000 cases).
>
> I'd rather use the whole dataset instead of taking (small) random samples
> as it is highly skewed. I've seen things like Phi and Cramer's V for
> crosstabs but I'm not sure whether they have been used before on logistic
> regression, if there are better ones and if there are any packages.
>
>
> Many thanks
>
> Marco

Sounds like you are bordering on some type of stepwise approach to including or not including covariates in the model. You can search the list archives for a myriad of discussions as to why that is a poor approach.

You have the luxury of a large sample. You also have the challenge of interpreting covariates that appear to be statistically significant, but may have a rather small *effect size* in context. That is where subject matter experts need to provide input as to interpretation of the contextual significance of the variable, as opposed to the statistical significance of that same variable.

A general approach, is to simply pre-specify your model based upon rather simple considerations. Also, you need to determine if your goal for the model is prediction or explanation.

What is the incidence of your 'event' in the sample? If it is say 10%, then you should have around 20,000 events. The rule of thumb for logistic regression is to have around 20 events per covariate degree of freedom (df) to minimize the risk of over-fitting the model to your dataset. A continuous covariate is 1 df, a k-level factor is k-1 df. So with 20,000 events, your model could feasibly have 1,000 covariate df's. I am guessing that you don't have that much independent data to begin with.

So, pre-specfy your model on the full dataset and stick with it. Interact with subject matter experts on the interpretation of the model.

BTW, this question is really about statistical modeling generally, not really R specific. Such queries are best posed to general statistical lists/forums such as Stack Exchange. I would also point you to Frank Harrell's book, Regression Modeling Strategies.

Regards,

Marc Schwartz

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[M Pomati]

Marc, thank you very much for your help.
I've posted in on

<http://math.stackexchange.com/questions/177252/x2-tests-to-compare-the-fit-of-large-samples-logistic-models>

and added details.

Many thanks

Marco

--On 31 July 2012 11:50 -0500 Marc Schwartz <[hidden email]> wrote:

> On Jul 31, 2012, at 10:35 AM, M Pomati <[hidden email]> wrote:
>
> >
> >
> > Does anyone know of any X^2 tests to compare the fit of logistic models
> > which factor out the sample size? I'm dealing with a very large sample
and
> > I fear the significant X^2 test I get when adding a variable to the
model
> > is simply a result of the sample size (>200,000 cases).
> >
> > I'd rather use the whole dataset instead of taking (small) random
samples
> > as it is highly skewed. I've seen things like Phi and Cramer's V for
> > crosstabs but I'm not sure whether they have been used before on
logistic

> > regression, if there are better ones and if there are any packages.
> >
> >
> > Many thanks
> >
> > Marco
>
>
>
> Sounds like you are bordering on some type of stepwise approach to

including or not including covariates in the model. You can search the list
archives for a myriad of discussions as to why that is a poor approach.
>
> You have the luxury of a large sample. You also have the challenge of
interpreting covariates that appear to be statistically significant, but
may have a rather small *effect size* in context. That is where subject
matter experts need to provide input as to interpretation of the contextual
significance of the variable, as opposed to the statistical significance of
that same variable.
>
> A general approach, is to simply pre-specify your model based upon rather
simple considerations. Also, you need to determine if your goal for the
model is prediction or explanation.
>
> What is the incidence of your 'event' in the sample? If it is say 10%,
then you should have around 20,000 events. The rule of thumb for logistic
regression is to have around 20 events per covariate degree of freedom (df)
to minimize the risk of over-fitting the model to your dataset. A
continuous covariate is 1 df, a k-level factor is k-1 df. So with 20,000
events, your model could feasibly have 1,000 covariate df's. I am guessing
that you don't have that much independent data to begin with.
>
> So, pre-specfy your model on the full dataset and stick with it. Interact
with subject matter experts on the interpretation of the model.
>
> BTW, this question is really about statistical modeling generally, not
really R specific. Such queries are best posed to general statistical
lists/forums such as Stack Exchange. I would also point you to Frank
Harrell's book, Regression Modeling Strategies.
>
> Regards,
>
> Marc Schwartz
>
>




----------------------
M Pomati
University of Bristol
School for Policy Studies
8 Priory Road
Office:10B
Bristol BS8 1TZ, UK
http://www.bristol.ac.uk/sps/research/centres/poverty

 
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[David Winsemius]

On Jul 31, 2012, at 10:25 AM, M Pomati wrote:

> Marc, thank you very much for your help.
> I've posted in on
>
> <http://math.stackexchange.com/questions/177252/x2-tests-to-compare-the-fit-of-large-samples-logistic-models 
> >
>
> and added details.

I think you might have gotten a more statistically knowledgeable  
audience at:

http://stats.stackexchange.com/

(And I suggested to the moderators at math-SE that it be migrated.)

--
David.

>
> Many thanks
>
> Marco
>
> --On 31 July 2012 11:50 -0500 Marc Schwartz <[hidden email]>  
> wrote:
>
>> On Jul 31, 2012, at 10:35 AM, M Pomati <[hidden email]>  
>> wrote:
>>
>>> Does anyone know of any X^2 tests to compare the fit of logistic  
>>> models
>>> which factor out the sample size? I'm dealing with a very large  
>>> sample and
>>> I fear the significant X^2 test I get when adding a variable to  
>>> the model
>>> is simply a result of the sample size (>200,000 cases).
>>>
>>> I'd rather use the whole dataset instead of taking (small) random  
>>> samples
>>> as it is highly skewed. I've seen things like Phi and Cramer's V for
>>> crosstabs but I'm not sure whether they have been used before on  
>>> logistic
>>> regression, if there are better ones and if there are any packages.
>>>
>>>
>>> Many thanks
>>>
>>> Marco
>>
>>
>> Sounds like you are bordering on some type of stepwise approach to
> including or not including covariates in the model. You can search  
> the list
> archives for a myriad of discussions as to why that is a poor  
> approach.
>>
>> You have the luxury of a large sample. You also have the challenge of
> interpreting covariates that appear to be statistically significant,  
> but
> may have a rather small *effect size* in context. That is where  
> subject
> matter experts need to provide input as to interpretation of the  
> contextual
> significance of the variable, as opposed to the statistical  
> significance of
> that same variable.
>>
>> A general approach, is to simply pre-specify your model based upon  
>> rather
> simple considerations. Also, you need to determine if your goal for  
> the
> model is prediction or explanation.
>>
>> What is the incidence of your 'event' in the sample? If it is say  
>> 10%,
> then you should have around 20,000 events. The rule of thumb for  
> logistic
> regression is to have around 20 events per covariate degree of  
> freedom (df)
> to minimize the risk of over-fitting the model to your dataset. A
> continuous covariate is 1 df, a k-level factor is k-1 df. So with  
> 20,000
> events, your model could feasibly have 1,000 covariate df's. I am  
> guessing
> that you don't have that much independent data to begin with.
>>
>> So, pre-specfy your model on the full dataset and stick with it.  
>> Interact
> with subject matter experts on the interpretation of the model.
>>
>> BTW, this question is really about statistical modeling generally,  
>> not
> really R specific. Such queries are best posed to general statistical
> lists/forums such as Stack Exchange. I would also point you to Frank
> Harrell's book, Regression Modeling Strategies.
>>
>> Regards,
>>
>> Marc Schwartz
>>
> ----------------------
> M Pomati
> University of Bristol
>

David Winsemius, MD
Alameda, CA, USA

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