[R] Extreme AIC or BIC values in glm(), logistic regression

[Thomas Lumley]

With 30 variables and only 55 residual degrees of freedom you probably have perfect separation due to not having enough data.  Look at the coefficients -- they are infinite, implying perfect overfitting.

       -thomas

On Wed, 18 Mar 2009, Maggie Wang wrote:

> Dear R-users,
>
> I use glm() to do logistic regression and use stepAIC() to do stepwise model
> selection.
>
> The common AIC value comes out is about 100, a good fit is as low as around
> 70. But for some model, the AIC went to extreme values like 1000. When I
> check the P-values, All the independent variables (about 30 of them)
> included in the equation are very significant, which is impossible, because
> we expect some would be dropped.  This situation is not uncommon.
>
> A summary output like this:
>
> Coefficients:
>                              Estimate Std. Error   z value Pr(>|z|)
> (Intercept)                   4.883e+14  1.671e+07  29217415   <2e-16 ***
> g761                         -5.383e+14  9.897e+07  -5438529   <2e-16 ***
> g2809                        -1.945e+15  1.082e+08 -17977871   <2e-16 ***
> g3106                        -2.803e+15  9.351e+07 -29976674   <2e-16 ***
> g4373                        -9.272e+14  6.534e+07 -14190077   <2e-16 ***
> g4583                        -2.279e+15  1.223e+08 -18640563   <2e-16 ***
> g761:g2809                   -5.101e+14  4.693e+08  -1086931   <2e-16 ***
> g761:g3106                   -3.399e+16  6.923e+08 -49093218   <2e-16 ***
> g2809:g3106                   3.016e+15  6.860e+08   4397188   <2e-16 ***
> g761:g4373                    3.180e+15  4.595e+08   6920270   <2e-16 ***
> g2809:g4373                  -5.184e+15  4.436e+08 -11685382   <2e-16 ***
> g3106:g4373                   1.589e+16  2.572e+08  61788148   <2e-16 ***
> g761:g4583                   -1.419e+16  8.199e+08 -17303033   <2e-16 ***
> g2809:g4583                  -2.540e+16  8.151e+08 -31156781   <2e-16 ***
> ........
> (omit)
> ........
>
> f. codes:  0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1
>
> (Dispersion parameter for binomial family taken to be 1)
>
>   Null deviance:  120.32  on 86  degrees of freedom
> Residual deviance: 1009.22  on 55  degrees of freedom
> AIC: 1073.2
>
> Number of Fisher Scoring iterations: 25
>
> Could anyone suggest what does this mean?   How can I perform a reliable
> logistic regression?
>
> Thank you so much for the help!
>
> Best Regards,
> Maggie
>
> 	[[alternative HTML version deleted]]
>
>

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle