st: cloglog or logit

["Kallimanis, Bellinda" <bkallimanis@fmhi.usf.edu>]

Hi, 

I have data where my outcome is a rare event, it occurs in 0.97% of my
sample (n =11,618). So I was reading about complimentary log log
regression and thought it may be appropriate, but when I compared the
predicted probabilities of the complimentary log log model and a logit
model I get a pariwise correlation of 0.9991 which suggests to me that
the complimentary log log model isn't doing a better job of predicting
than the logit model. The coefficients are reasonably close to each
other, see output below. 

Does this mean I should stick with a logit model and perhaps just alter
the cutoff value? Also I came across the work of Gary King and his
-relogit- command found at http://gking.harvard.edu/stats.shtml#relogit
though I see this was last updated in 1999 so I'm not sure how relevant
it is. Any thoughts would be greatly appreciated.

Regards,
Bellinda


. xi:logit wander age i.psych_state delirium inapprop_beh  e1k i.b4
i.g1ea_c

i.psych_state     _Ipsych_sta_0-2    (naturally coded; _Ipsych_sta_
omitted)
i.b4              _Ib4_0-2           (naturally coded; _Ib4_0 omitted)
i.g1ea_c          _Ig1ea_c_0-2       (naturally coded; _Ig1ea_c_0
omitted)


Logistic regression                               Number of obs   =
11618
                                                  LR chi2(10)     =
237.38
                                                  Prob > chi2     =
0.0000
Log likelihood = -517.27798                       Pseudo R2       =
0.1866

------------------------------------------------------------------------
------
      wander |     Coef.   Std. Err.      z    P>|z|     [95%
ConfInterval]
-------------+----------------------------------------------------------
------
         age |  .0275566   .0087225     3.16   0.002     .0104608
.0446523
_Ipsych_st~1 |  .9608209   .2334963     4.11   0.000     .5031765
1.418465
_Ipsych_st~2 |  1.079544   .3496697     3.09   0.002      .394204
1.764884
    delirium |  .7911933   .2471891     3.20   0.001     .3067116
1.275675
  inapprop_b |  .9479077   .2576809     3.68   0.000     .4428624
1.452953
         e1k |  .6659235   .2701732     2.46   0.014     .1363938
1.195453
      _Ib4_1 |  1.374957   .2451875     5.61   0.000     .8943987
1.855516
      _Ib4_2 |  2.275775   .2786492     8.17   0.000     1.729633
2.821918
  _Ig1ea_c_1 |  .2038798   .2409538     0.85   0.397     -.268381
.6761407
  _Ig1ea_c_2 | -.7956763   .3723895    -2.14   0.033    -1.525546
.0658064
       _cons |  -7.76677   .6269897   -12.39   0.000    -8.995647
6.537892
------------------------------------------------------------------------
------

xi:cloglog wander age i.psych_state delirium inapprop_beh  e1k i.b4
i.g1ea_c

i.psych_state     _Ipsych_sta_0-2    (naturally coded; _Ipsych_sta_
omitted)
i.b4              _Ib4_0-2           (naturally coded; _Ib4_0 omitted)
i.g1ea_c          _Ig1ea_c_0-2       (naturally coded; _Ig1ea_c_0
omitted)


Complementary log-log regression                Number of obs     =
11618
                                                Zero outcomes     =
11505
                                                Nonzero outcomes  = 113

                                                LR chi2(10)       =
236.78
Log likelihood = -517.57978                     Prob > chi2       =
0.0000

------------------------------------------------------------------------
------
      wander |     Coef.   Std. Err.      z    P>|z|     [95%
ConfInterval]
-------------+----------------------------------------------------------
------
         age |  .0272044   .0084431     3.22   0.001     .0106562
.0437527
_Ipsych_st~1 |  .9297655   .2285607     4.07   0.000     .4817946
1.377736
_Ipsych_st~2 |  1.067526   .3399633     3.14   0.002     .4012106
1.733842
    delirium |      .751   .2397234     3.13   0.002     .2811507
1.220849
  inapprop_b |  .8954374   .2476817     3.62   0.000     .4099902
1.380885
         e1k |  .6169237   .2571763     2.40   0.016     .1128674
1.12098
      _Ib4_1 |  1.378481   .2420793     5.69   0.000      .904014
1.852948
      _Ib4_2 |  2.235668   .2733994     8.18   0.000     1.699815
2.771521
  _Ig1ea_c_1 |  .1869587   .2322885     0.80   0.421    -.2683184
.6422358
  _Ig1ea_c_2 | -.7917172   .3630383    -2.18   0.029    -1.503259
.0801752
       _cons | -7.717735   .6062998   -12.73   0.000    -8.906061
6.52941
------------------------------------------------------------------------
------





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