## Predicted probabilities and odds ratio from a multinomial logit regression

Frequent Contributor
Posts: 113

# Predicted probabilities and odds ratio from a multinomial logit regression

Hello,

I perform a multinomial logistic regression using proc logistic and glogit, which results with those parameters:

 Table1 Cat1 Cat2 Cat3 Car4 Cat6 Cat7 Cat8 Intercept -3.09960 -2.27930 -5.15200 -4.33730 -0.30360 -1.70810 -0.87280 Age65_69 (ref) Age70-74 -0.15780 -0.13040 -0.40460 -0.48680 0.10860 -0.04320 0.31830 Age75-79 -0.82400 -0.62110 -0.39450 -0.53650 0.23330 -0.29800 0.82200 Age80_84 -0.60620 -0.78130 -0.65530 -0.60930 0.28750 -0.25480 1.29840 Age85 -0.79490 -0.04920 -0.04200 0.12350 0.27580 -0.23910 1.33200

The odds ratios are thus:

 Table2 Cat1 Cat2 Cat3 Car4 Cat6 Cat7 Cat8 Age70-74 0.85402 0.87774 0.66724 0.61459 1.11472 0.95772 1.37479 Age75-79 0.43867 0.53735 0.67402 0.58479 1.26276 0.74230 2.27505 Age80_84 0.54542 0.45781 0.51929 0.54373 1.33309 0.77507 3.66343 Age85 0.45163 0.95199 0.95887 1.13145 1.31758 0.78734 3.78861

There are more independent variables, but for my problem, I don’t think they are relevant.

When I convert parameters to get the predicted probabilities, I have this:

 Table3 Cat1 Cat2 Cat3 Car4 Cat6 Cat7 Cat8 Age65_69 (ref) 0.01800 0.04164 0.00246 0.00556 0.31584 0.11333 0.29467 Age70-74 0.01420 0.03362 0.00150 0.00312 0.32008 0.09929 0.36482 Age75-79 0.00637 0.01784 0.00129 0.00253 0.30894 0.06451 0.48730 Age80_84 0.00658 0.01262 0.00082 0.00194 0.26923 0.05258 0.60482 Age85 0.00531 0.02554 0.00149 0.00398 0.26300 0.05235 0.61282

My problem is the following: when I take those probabilities and try to calculate the odds ratios, the results are not the same than those computed by SAS. For example, the odds ratio for Age60-74, cat1: (0.0142/(1-0.0142))/(0.018/(1-0.018))=0.7856, while the one indicated in table 2 is 0.85402.

I guess I made a mistake somewhere, but I don’t know where. Or maybe it’s just something I don’t understand yet. Moreover, I’m not totally sure the the proc logistic with glogit is the right method to perform a multinomial logistic regression. I’m on that problem since 3 days, so if you have the answer, it would be much appreciated.

Thanks

Discussion stats
• 0 replies
• 215 views
• 0 likes
• 1 in conversation