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

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: Negative probabilities after a margins command for a categorical variable (post logistic model). Date Mon, 14 Oct 2013 22:37:50 -0400

```Marc:

Section 5 of the FAQ lists reasons why questions don't get answered, and
none really apply to your question. Reposting, once, after a week is
quite acceptable under the circumstances.

Of course probabilities are restricted to [0,1]. The phenomenon you
observed occurs when a CI is based on the formula: estimate +/- 1.96 SE,
but there are, in fact, bounds on the true value. The "illegal"
endpoints occur more often then you would expect.

The way around this problem is to ask -margins- to operate on the logit
scale and then to back transform the CI endpoints. (This is what -svy:
tabulate- does, by the way.)

Luckily -margins- returns the displayed table in a Stata matrix
r(table). The lower and upper CIs are in rows "ll" and "ul". Below is
code to do the work. I use Mata to simplify the calculation.
Type: "help m2_op_colon" to understand how this worked.

***********Code Begins*************
sysuse auto, clear
recode rep78 1/3= 1 4=2 5=3
logistic foreign i.rep78 turn

margins, at(rep78=(1(1)3)) predict(xb)
matrix list r(table)
matrix  A = r(table)
/* Get rows corresponding to confidence limits */
matrix  C = A["ll",1...] \ A["ul",1...]
matrix list C
mata:
L =st_matrix("C")
/* Now transform to prob scale using:
P  = 1/(1 + exp(-xb) */
CI = 1:/(1 :+exp(-L))
CI
end
**********CODE ENDS***************

Steve
sjsamuels@gmail.com

>
> On Oct 14, 2013, at 10:02 AM, Scheetz, Marc wrote:
>
> Dear Listserv,
>
> I am reposting a question from last week in hopes of receiving a response.  This is my first content post to the listserv; I appreciate your consideration.  Please let me know if I violated any rules for posting.
>
> I am wondering if anyone can help explain the scenario below to me.  I am running Stata IC v13.0.  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.  I have modeled the variable as categorical since I lose power due to uneven sample size in some of the categories.
>
> 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)?  Sincerely,
>
>
> Marc Scheetz, PharmD, MSc
>
>
> . 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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```