Exact logistic regression

[gretaolsson]

Hi, 
I want to perform exact logistic regression in SAS. I've found the following code that I want to apply to different samples of varying size.
(I use the university edition. )

PROC IMPORT DATAFILE=REFFILE
 DBMS=DBF
 OUT=WORK.IMPORT;
RUN;

proc logistic data = WORK.IMPORT desc;
 model y = x1 x2;
 exact x1 x2 / estimate = both;
run;


When I run this code I get empty tables with no estimates...
Must the data be written in a specific way, in that case, how? 

I can perform ordinary logistic regression on the samples, and my goal is to compare the results.

I have attached the three files, log, results and data - that contains 20 observations. Because the files did not have the valid extension they are all in paint, sorry for that.

I'm grateful for all the help I can get.

[gretaolsson]

Do I need to give more information to get any help?

[PeterClemmensen]

Post your data in the form of a data step, most people in here dont want to download files 🙂

[gretaolsson]

My Data:
y x1 x2
1. 1 1.489611900786800 -0.486983894512530
2. 1 0.887638190472230 -0.899961461187430
3. 1 -0.328400349680380 0.320480850960210
4. 0 -1.283346136073470 0.314729922388780
5. 1 -0.014384666024895 -1.040793737862780
6. 1 1.005337941612940 0.385444205622100
7. 1 0.403112850999760 0.797554772638080
8. 1 1.432508077938930 -0.553701810045310
9. 1 0.137341139238340 0.177313212434980
10. 0 -1.341507064615280 0.042985039337917

Logg:
1 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
61
62 PROC IMPORT DATAFILE=REFFILE
63 DBMS=DBF
64 OUT=WORK.IMPORT1;
65 RUN;

NOTE: Import cancelled. Output dataset WORK.IMPORT1 already exists. Specify REPLACE option to overwrite it.
NOTE: The SAS System stopped processing this step because of errors.
NOTE: PROCEDURE IMPORT used (Total process time):
real time 0.00 seconds
cpu time 0.00 seconds

66
67


68 proc logistic data = WORK.IMPORT1;
69 model y = x1 x2;
70 run;

NOTE: PROC LOGISTIC is modeling the probability that y=0. One way to change this to model the probability that y=1 is to specify
the response variable option EVENT='1'.
WARNING: There is a complete separation of data points. The maximum likelihood estimate does not exist.
WARNING: The LOGISTIC procedure continues in spite of the above warning. Results shown are based on the last maximum likelihood
iteration. Validity of the model fit is questionable.
NOTE: There were 10 observations read from the data set WORK.IMPORT1.
NOTE: PROCEDURE LOGISTIC used (Total process time):
real time 0.12 seconds
cpu time 0.12 seconds


71
72 proc logistic data = WORK.IMPORT1 desc;
73 model y = x1 x2;
74 exact x1 x2 /estimate=both;
75 run;

NOTE: PROC LOGISTIC is modeling the probability that y=1.
WARNING: There is a complete separation of data points. The maximum likelihood estimate does not exist.
WARNING: The LOGISTIC procedure continues in spite of the above warning. Results shown are based on the last maximum likelihood
iteration. Validity of the model fit is questionable.
NOTE: There were 10 observations read from the data set WORK.IMPORT1.
NOTE: PROCEDURE LOGISTIC used (Total process time):
real time 0.12 seconds
cpu time 0.12 seconds


76
77 OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
90

[sld]

With only 10 observations in your posted dataset, split 2 and 8 between outcomes, I don't know that you'll be able to extract much from an analysis, but....

If you plot the response against each predictor, it is clear that complete separation is due to X1. A solution can be obtained using Firth's penalized likelihood. See

https://pdfs.semanticscholar.org/4f17/1322108dff719da6aa0d354d5f73c9c474de.pdf

and

http://support.sas.com/kb/22/599.html

data have;
    input a$ y x1 x2;
    datalines;
1. 1 1.489611900786800 -0.486983894512530
2. 1 0.887638190472230 -0.899961461187430
3. 1 -0.328400349680380 0.320480850960210
4. 0 -1.283346136073470 0.314729922388780
5. 1 -0.014384666024895 -1.040793737862780
6. 1 1.005337941612940 0.385444205622100
7. 1 0.403112850999760 0.797554772638080
8. 1 1.432508077938930 -0.553701810045310
9. 1 0.137341139238340 0.177313212434980
10. 0 -1.341507064615280 0.042985039337917
;
run;

proc sgplot data=have;
    scatter x=x1 y=y;
    run;

proc sgplot data=have;
    scatter x=x2 y=y;
    run;

proc logistic data = have desc;
 model y = x1 x2 / firth;
run;