Confidence intervals logit regression

[Liza]

Hi
I am using logit regression to model the final decision made by peers in a context for selection of researchers. To model the final decision I am using bibliometric indicators. My model is as follows:

logit FD SJRm HCD

Iteration 0: log likelihood = -65.202554
Iteration 1: log likelihood = -55.134678
Iteration 2: log likelihood = -54.125659
Iteration 3: log likelihood = -54.113256
Iteration 4: log likelihood = -54.113255

Logistic regression Number of obs = 96
LR chi2(2) = 22.18
Prob > chi2 = 0.0000
Log likelihood = -54.113255 Pseudo R2 = 0.1701

------------------------------------------------------------------------------
FD | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SJRm | 1.115742 .4755204 2.35 0.019 .1837392 2.047745
HCD | .0639919 .0228296 2.80 0.005 .0192468 .1087371
_cons | -1.880489 .6640483 -2.83 0.005 -3.182 -.5789784
------------------------------------------------------------------------------

Where FD is my dependent variable (0- applicant not selected, 1 –applicant selected) and SJRm and HCD my independent variables (bibliometric indicators).

After the model I asked stata for some margins. When I use the following command
margins, at (HCD=(0(01)100)) atmeans

I get the results in table. My problem is with the 95% confidence interval. I have probabilities that are higher than 1. In my opinion the values for the confidence interval should not be above 1. Why is this happening?

Thanks

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | .4223629 .0861346 4.90 0.000 .2535421 .5911837
2 | .5809899 .0611994 9.49 0.000 .4610413 .7009385
3 | .7244727 .064986 11.15 0.000 .5971024 .8518431
4 | .8329495 .0699913 11.90 0.000 .695769 .9701299
5 | .9043565 .0614235 14.72 0.000 .7839687 1.024744
6 | .9471758 .0463939 20.42 0.000 .8562455 1.038106
7 | .9714306 .0318804 30.47 0.000 .9089462 1.033915
8 | .9847281 .0206392 47.71 0.000 .944276 1.02518
9 | .9918881 .012853 77.17 0.000 .9666966 1.01708
10 | .9957058 .0077957 127.73 0.000 .9804266 1.010985
11 | .9977309 .0046402 215.02 0.000 .9886364 1.006825
------------------------------------------------------------------------------

[Maarten Buis]

The margins command uses an approximation for computing the standard errors, the delta method. This approximation will assume that the sampling distribution of the transformed parameters (in this case probabilities) will follow a normal distribution and are thus unbounded. As an approximation it is usually fine, and I don't see major problems in your table as the numbers aren't wildly above 1.

If you prefer you can use the predict(xb) option in margins to predict the linear predictor, and use the invlogit() function to transform the linear predictor and the lower and upper bounds of the confidence intervals towards the probability metric. This will ensure that the bounds respect the 0 and 1 limits for probabilities, and there is an argument that the delta-method approximation will work better that way: http://www.stata.com/support/faqs/st...ule/index.html .

[Richard Williams]

Welcome to Statalist Liza. A few things to add to what Maarten says:

Your output is unnecessarily hard to read. Please look at the FAQ, especially points 6 and 12, for tips on posing questions more effectively and increase your chances of getting a response.

Make sure you copy and paste exactly what you typed and how Stata responded. If you really did type

margins, at (HCD=(0(01)100)) atmeans

you should have gotten 101 predicted values, not 11.

Be careful about accidental multiple posts -- in your case, I think you have the same post at least 4 times. Unfortunately, the system does trick people into thinking they haven't posted when they really have. If it happens to you, try to go to the extraneous duplicates and include a link to one of the threads. Otherwise you can get a lot of wasted duplicated effort.

[Liza]

Many thanks, this fixed my problem. I greatly appreciate your response/help.