Multivariate logistic regression with an odd IC

[Laura Galarza]

Hi all,
I'm running a logistic regression on Stata 14.2 using logistic
I've run first the univariate analysis and all looked fine but when I tried the multivariate analyses, this is what came back:

Logistic regression                             Number of obs     =         32
                                                LR chi2(2)        =       7.51
                                                Prob > chi2       =     0.0234
Log likelihood =  -17.85913                     Pseudo R2         =     0.1738

--------------------------------------------------------------------------------
recuperengcreg | Odds Ratio   Std. Err.       z        P>|z|          [95% Conf. Interval]
---------------+----------------------------------------------------------------
    WFNSgrupos |  7.05e-07   .0011365    -0.01   0.993            0           .
         VMdic |        8674937    1.40e+10     0.01   0.992            0           .
         _cons |        851450      1.37e+09     0.01   0.993            0           .
--------------------------------------------------------------------------------

All variables are dichotomous variables.
Any idea what is the problem?
Thanks so much

[Dirk Enzmann]

This is not your first post to this Forum -- you should have read the complete FAQ before posting. In your case #12 might be especially relevant.

It is better to show us your data before we speculate about sparsely populated cells etc.

[Laura Galarza]

Sorry about this, I though maybe enough.
Here comes my data for this variables (I'll also add the univariate analysis for the variables)

input float recuperengcreg byte WFNSgrupos float VMdic
0 2 1
. 1 1
0 2 1
. 2 1
. 2 1
1 2 1
0 2 1
0 2 1
. 1 1
0 2 1
. 2 1
0 2 1
. 2 1
0 2 1
. 2 1
0 1 1
0 2 1
0 2 1
1 2 1
. 2 1
0 2 1
. 2 1
0 2 1
0 1 1
1 2 1
. 2 1
. 2 1
. 1 0
. 1 0
0 1 0
1 1 0
. 1 0
. 1 0
0 1 0
1 1 0
1 1 0
. 1 0
. 1 0
. 1 0
1 1 0
1 1 0
. 1 0
. 1 0
. 1 0
. 1 0
1 1 0
0 1 0
0 1 0
. 1 0
1 1 0
0 1 0
1 1 0
1 1 0
0 1 0
. 1 0
1 1 0
. 1 0
end

 logistic recuperengcreg VMdic

Logistic regression                             Number of obs     =         32
                                                LR chi2(1)        =       6.62
                                                Prob > chi2       =     0.0101
Log likelihood = -18.306253                     Pseudo R2         =     0.1531

--------------------------------------------------------------------------------
recuperengcreg | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
         VMdic |   7.222222   5.942108     2.40   0.016     1.439932    36.22428
         _cons |         .6   .3098387    -0.99   0.323     .2180684    1.650858
--------------------------------------------------------------------------------

. 
. logistic recuperengcreg WFNSgrupos

Logistic regression                             Number of obs     =         32
                                                LR chi2(1)        =       3.95
                                                Prob > chi2       =     0.0468
Log likelihood = -19.639426                     Pseudo R2         =     0.0914

--------------------------------------------------------------------------------
recuperengcreg | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
    WFNSgrupos |   4.583333   3.693047     1.89   0.059     .9447586    22.23525
         _cons |   .1745455   .2008595    -1.52   0.129     .0182971    1.665079
--------------------------------------------------------------------------------

[Dirk Enzmann]

If you look at a twoway table of your variables WFNSgrupo and VMdic using only the valid cases of recuperengcreg you will see an empty cell (and a cell with 100% of the column percentages). Logit models predicting recuperengcreg by VMdic if WFNSgrupo is 2 or predicting recuperengcreg by WFNSgrupo if VMdic is 0 will automatically omit the predictor because of collinearity:

. tab2 VMdic WFNSgrupos if recuperengcreg < ., col chi2

-> tabulation of VMdic by WFNSgrupos if recuperengcreg < .

+-------------------+
| Key               |
|-------------------|
|     frequency     |
| column percentage |
+-------------------+

           |      WFNSgrupos
     VMdic |         1          2 |     Total
-----------+----------------------+----------
         0 |        16          0 |        16
           |     88.89       0.00 |     50.00
-----------+----------------------+----------
         1 |         2         14 |        16
           |     11.11     100.00 |     50.00
-----------+----------------------+----------
     Total |        18         14 |        32
           |    100.00     100.00 |    100.00

          Pearson chi2(1) =  24.8889   Pr = 0.000

. logit recuperengcreg VMdic if WFNSgrupos == 2

note: VMdic omitted because of collinearity.
Iteration 0:  Log likelihood = -7.2741177  
Iteration 1:  Log likelihood = -7.2741177  

Logistic regression                                     Number of obs =     14
                                                        LR chi2(0)    =   0.00
                                                        Prob > chi2   =      .
Log likelihood = -7.2741177                             Pseudo R2     = 0.0000

--------------------------------------------------------------------------------
recuperengcreg | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
         VMdic |          0  (omitted)
         _cons |  -1.299283   .6513389    -1.99   0.046    -2.575884   -.0226821
--------------------------------------------------------------------------------

. logit recuperengcreg WFNSgrupos if VMdic == 0

note: WFNSgrupos omitted because of collinearity.
Iteration 0:  Log likelihood = -10.585012  
Iteration 1:  Log likelihood = -10.585012  

Logistic regression                                    Number of obs =      16
                                                       LR chi2(0)    =   -0.00
                                                       Prob > chi2   =       .
Log likelihood = -10.585012                            Pseudo R2     = -0.0000

--------------------------------------------------------------------------------
recuperengcreg | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
    WFNSgrupos |          0  (omitted)
         _cons |   .5108256   .5163978     0.99   0.323    -.5012954    1.522947
--------------------------------------------------------------------------------

(see also Example 2 under the heading "Model identification" in the Manual [R] for logit). The reason is the empty cell (or the fact that you have not enough data in this situation).

[Dirk Enzmann]

Follow-up on #4:

You also can have a look at "(quasi) complete separation" (e.g. https://stats.oarc.ucla.edu/other/mu...ith-the-issue/) and the PDF-Manual entry to exlogistic.

[Laura Galarza]

Thanks so much for your answer.
I'll take a look at all the references you mentioned.