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Suppose you run a logistic regression in SAS and the results seem to be the reverse of what you expected. You might have even run the analysis in another package and found that the signs of the parameter estimates were reversed as compared to your SAS output. If your outcome variable is coded such that 1 is the event of interest, then you must remember to use the descending option on proc logistic. If you omit the descending option, then SAS will predict the event of 0, and the results will be reversed (e.g., the parameter estimates will have a negative sign instead of a positive sign, and vice versa).
Here is brief example based on the SAS Class Notes, Analyzing Data. We will take the logistic example from that page and intentionally omit the descending option.
PROC LOGISTIC DATA=hsbstat; MODEL honor = sex public read math science; RUN;Analysis of Maximum Likelihood Estimates Analysis of Maximum Likelihood Estimates Parameter Standard Wald Pr > Standardized Odds Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio INTERCPT 1 13.9945 2.1519 42.2917 0.0001 . . SEX 1 1.2467 0.4660 7.1562 0.0075 0.342144 3.479 PUBLIC 1 -0.2431 0.5684 0.1829 0.6689 -0.048480 0.784 READ 1 -0.0643 0.0284 5.1485 0.0233 -0.360667 0.938 MATH 1 -0.1221 0.0350 12.1307 0.0005 -0.618577 0.885 SCIENCE 1 -0.0553 0.0328 2.8489 0.0914 -0.300945 0.946
The results do seem odd, that higher scores on read or math would be associated with being less likely to be in honors classes (honor). If we look at the log file, we see
NOTE: Proc logistic is modeling the probability that honor=0.
One way to change this to model the probability that honor=1 is to specify the descending option on the proc statement. Refer to Technical Report P-229 or the SAS System Help Files for details.
This message is telling us that the results are reversed because we forgot the descending option. We include the descending option and the results seem more like we would expect.
PROC LOGISTIC DATA=hsbstat DESCENDING; MODEL honor = sex public read math science; RUN;Analysis of Maximum Likelihood Estimates Parameter Standard Wald Pr > Standardized Odds Variable DF Estimate Error Chi-Square Chi-Square Estimate Ratio INTERCPT 1 -13.9945 2.1519 42.2917 0.0001 . . SEX 1 -1.2467 0.4660 7.1562 0.0075 -0.342144 0.287 PUBLIC 1 0.2431 0.5684 0.1829 0.6689 0.048480 1.275 READ 1 0.0643 0.0284 5.1485 0.0233 0.360667 1.066 MATH 1 0.1221 0.0350 12.1307 0.0005 0.618577 1.130 SCIENCE 1 0.0553 0.0328 2.8489 0.0914 0.300945 1.057
As you see, the signs of the parameter estimates from these two analyses are the reverse of each other, and the odds ratios are the reciprocal of each other (e.g., 1/3.479 is .287).
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