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

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