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Predicted probabilities and odds ratio from a multinomial logit regression

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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:

Table1Cat1Cat2Cat3Car4Cat6Cat7Cat8
Intercept-3.09960-2.27930-5.15200-4.33730-0.30360-1.70810-0.87280
Age65_69 (ref)
Age70-74-0.15780-0.13040-0.40460-0.486800.10860-0.043200.31830
Age75-79-0.82400-0.62110-0.39450-0.536500.23330-0.298000.82200
Age80_84-0.60620-0.78130-0.65530-0.609300.28750-0.254801.29840
Age85-0.79490-0.04920-0.042000.123500.27580-0.239101.33200

The odds ratios are thus:

Table2Cat1Cat2Cat3Car4Cat6Cat7Cat8
Age70-740.854020.877740.667240.614591.114720.957721.37479
Age75-790.438670.537350.674020.584791.262760.742302.27505
Age80_840.545420.457810.519290.543731.333090.775073.66343
Age850.451630.951990.958871.131451.317580.787343.78861

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:

Table3Cat1Cat2Cat3Car4Cat6Cat7Cat8
Age65_69 (ref)0.018000.041640.002460.005560.315840.113330.29467
Age70-740.014200.033620.001500.003120.320080.099290.36482
Age75-790.006370.017840.001290.002530.308940.064510.48730
Age80_840.006580.012620.000820.001940.269230.052580.60482
Age850.005310.025540.001490.003980.263000.052350.61282

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

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