Re: [R] Appropriate regression model for categorical variables

From: Ted Harding <ted.harding_at_nessie.mcc.ac.uk>
Date: Wed, 13 Jun 2007 00:24:10 +0100 (BST)


On 12-Jun-07 17:45:44, Tirthadeep wrote:
>
> Dear users,
> In my psychometric test i have applied logistic regression
> on my data. My data consists of 50 predictors (22 continuous
> and 28 categorical) plus a binary response.
>
> Using glm(), stepAIC() i didn't get satisfactory result as
> misclassification rate is too high. I think categorical
> variables are responsible for this debacle. Some of them have
> more than 6 level (one has 10 level).
>
> Please suggest some better regression model for this situation.
> If possible you can suggest some article.

I hope you have a very large number of cases in your data!

The minimal complexity of the 28 categorical variables compatible with your description is

  1 factor at 10 levels
  2 factors at 7 levels
 25 factors at 2 levels

which corresponds to (2^25)*(7^2)*10 = 16441671680 ~= 1.6e10 distinct possible combinations of levels of the factors. Your true factors may have far more than this.

Unless you have more cases than this in your data, you are likely to fall into what is called "linear separation", in which the logistic regression will find a perfect predictor for your binary outcome. This prefect predictor may well not be unique (indeed if you have only a few hundred cases there will probably be millions of them).

Therefore your logistic reggression is likely to be meaningless.

I can only suggest that you consider very closely how to

  1. reduce the numbers of levels in some of your factors, by coalescing levels together;
  2. defining new factors in terms of the old so as to reduce the total number of factors (which may include ignoring some factors altogether)

so that you end up with new categorical variables whose total number of possible combinations is much smaller (say at most 1/5) of the number of cases in your data.

In summary: you have to many explanatory variables.

Best wishes,
Ted.



E-Mail: (Ted Harding) <Ted.Harding_at_manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 13-Jun-07                                       Time: 00:23:49
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