[R] logistic regression with 50 varaibales

[Joris Meys]

Hi,

Marcs explanation is valid to a certain extent, but I don't agree with
his conclusion. I'd like to point out "the curse of
dimensionality"(Hughes effect) which starts to play rather quickly.

The curse of dimensionality is easily demonstrated looking at the
proximity between your datapoints. Say we scale the interval in one
dimension to be 1 unit. If you have 20 evenly-spaced observations, the
distance between the observations is 0.05 units. To have a proximity
like that in a 2-dimensional space, you need 20^2=400 observations. in
a 10 dimensional space this becomes 20^10 ~ 10^13 datapoints. The
distance between your observations is important, as a sparse dataset
will definitely make your model misbehave.

Even with about 35 samples per variable, using 50 independent
variables will render a highly unstable model, as your dataspace is
about as sparse as it can get. On top of that, interpreting a model
with 50 variables is close to impossible, and then I didn't even start
on interactions. No point in trying I'd say. If you really need all
that information, you might want to take a look at some dimension
reduction methods first.

Cheers
Joris

On Mon, Jun 14, 2010 at 2:55 PM, Marc Schwartz <marc_schwartz at me.com> wrote:
> On Jun 13, 2010, at 10:20 PM, array chip wrote:
>
>> Hi, this is not R technical question per se. I know there are many excellent statisticians in this list, so here my questions: I have dataset with ~1800 observations and 50 independent variables, so there are about 35 samples per variable. Is it wise to build a stable multiple logistic model with 50 independent variables? Any problem with this approach? Thanks
>>
>> John
>
>
> The general rule of thumb is to have 10-20 'events' per covariate degree of freedom. Frank has suggested that in some cases that number should be as high as 25.
>
> The number of events is the smaller of the two possible outcomes for your binary dependent variable.
>
> Covariate degrees of freedom refers to the number of columns in the model matrix. Continuous variables are 1, binary factors are 1, K-level factors are K - 1.
>
> So if out of your 1800 records, you have at least 500 to 1000 events, depending upon how many of your 50 variables are K-level factors and whether or not you need to consider interactions, you may be OK. Better if towards the high end of that range, especially if the model is for prediction versus explanation.
>
> Two excellent references would be Frank's book:
>
>  http://www.amazon.com/Regression-Modeling-Strategies-Frank-Harrell/dp/0387952322/
>
> and Steyerberg's book:
>
>  http://www.amazon.com/Clinical-Prediction-Models-Development-Validation/dp/038777243X/
>
> to assist in providing guidance for model building/validation techniques.
>
> HTH,
>
> Marc Schwartz
>
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-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
Joris.Meys at Ugent.be
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