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st: Negative probabilities after a margins command for a categorical variable (post logistic model)


From   "Scheetz, Marc" <mschee@midwestern.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Negative probabilities after a margins command for a categorical variable (post logistic model)
Date   Fri, 11 Oct 2013 19:19:59 +0000

Dear Listserv,
I am wondering if anyone can help explain the scenario below to me.  I am using the margins command after a multivariate-logistic model with the outcome of “died”.  I am attempting to characterize the probabilities of death according to each categorical increase of the variable “log2X”.  The referent category below is 2^0=1.

My question is that I receive 95% CIs that have negative margins in  2 of the categories (i.e. 2._at: log2X=1, 4._at:log2X= 3).

Perhaps this is  a rudimentary question, but I thought that probabilities calculated from Odds Ratios could not be negative.  Is this because it is a probability relative to the referent category?  Do you see other errors in my syntax (below)?  Many thanks in advance,
Marc


. logistic died i.log2X a2_day0 log10_days_to_pos_cx
note: 4.log2X != 0 predicts failure perfectly
      4.log2X dropped and 5 obs not used

note: 5.log2X != 0 predicts failure perfectly
      5.log2X dropped and 3 obs not used


Logistic regression                               Number of obs   =         83
                                                  LR chi2(6)      =      18.58
                                                  Prob > chi2     =     0.0049
Log likelihood = -35.358908                       Pseudo R2       =     0.2081

--------------------------------------------------------------------------------------
                died | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
         log2X       |
                  1  |   .7903086     .92746    -0.20   0.841     .0792275    7.883466
                  2  |   6.471551   5.420137     2.23   0.026     1.253427    33.41317
                  3  |   1.587899   1.492738     0.49   0.623     .2515548    10.02335
                  4  |          1  (empty)
                  5  |          1  (empty)
                  6  |   6.542207   6.159993     1.99   0.046     1.033362    41.41868
                     |
             a2_day0 |   1.075268   .0732118     1.07   0.286     .9409374    1.228775
log10_days_to_pos_cx |   4.854903   3.054503     2.51   0.012      1.41462    16.66177
               _cons |    .012261   .0189665    -2.85   0.004     .0005913    .2542394


. margins, at(log2X=(0(1)6))

Predictive margins                                Number of obs   =         83
Model VCE    : OIM

Expression   : Pr(died), predict()

1._at        : log2X     =           0

2._at        : log2X     =           1

3._at        : log2X     =           2

4._at        : log2X     =           3

5._at        : log2X     =           4

6._at        : log2X     =           5

7._at        : log2X     =           6

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1518137   .0514472     2.95   0.003     .0509791    .2526484
          2  |   .1259233   .1108515     1.14   0.256    -.0913416    .3431883
          3  |   .4764486   .1462235     3.26   0.001     .1898558    .7630413
          4  |   .2137861   .1241819     1.72   0.085    -.0296061    .4571782
          5  |          .  (not estimable)
          6  |          .  (not estimable)
          7  |   .4787175   .1765856     2.71   0.007      .132616     .824819
------------------------------------------------------------------------------

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