Contributor
Posts: 24

# Multinomial Logistic Output

Just wondering if my interpretation of the output is correct for a multinomial logistic regression. The dropped group is "no" depression (category 4), with 3 being "mild", 2 is "moderate", etc.

Would the interpretation for LOW SES (with High SES being the dropped group be): the log odds of being in mild depression versus no depression will increase by 1.709 if moving from high to low SES?

 Odds Ratio Estimates Effect DEPRESSION_CAT Point Estimate 95% WaldConfidence Limits LOW_SES 0 8.907 8.819 8.997 LOW_SES 1 5.731 5.693 5.769 LOW_SES 2 2.615 2.604 2.627 LOW_SES 3 1.709 1.704 1.713 MIDDLE_SES 0 3.563 3.537 3.589 MIDDLE_SES 1 2.275 2.265 2.285 MIDDLE_SES 2 1.599 1.594 1.604 MIDDLE_SES 3 1.478 1.476 1.481 BLACK_NH 0 0.675 0.671 0.679 BLACK_NH 1 0.653 0.650 0.656 BLACK_NH 2 0.871 0.869 0.874 BLACK_NH 3 0.929 0.927 0.931 ASIAN_NH 0 0.357 0.349 0.365 ASIAN_NH 1 0.409 0.404 0.415 ASIAN_NH 2 0.555 0.550 0.559 ASIAN_NH 3 0.814 0.811 0.817 HISPANIC 0 0.408 0.405 0.411 HISPANIC 1 0.562 0.560 0.565 HISPANIC 2 0.834 0.832 0.837 HISPANIC 3 0.849 0.847 0.851
SAS Employee
Posts: 386

## Re: Multinomial Logistic Output

Your description of the model isn't precise enough to answer with certainty. It's always best to include the procedure code you ran so that the model being fit is clear. A multinomial response can be either nominal or ordinal, so the model could treat the response as nominal with the LINK=GLOGIT option, or as ordinal if that option is not used. Since the Effect column in the Odds Ratios table does not include labels like "SES low vs high" but does include the response level, I also have to assume that you used LINK=GLOGIT (event though the response seems to be ordinal) and you created your own dummy variables LOW_SES and MIDDLE_SES which probably use a 0,1 coding and are such that the high SES level corresponds to both equaling zero. If correct, it would be better and easier if you would instead enter a single, three-level SES variable in both the MODEL statement and CLASS statement. In the CLASS statement, you can specify the reference level and type of coding:

class ses (param=ref ref='high');

Further, from the table it appears that you did not use the DESCENDING option in the PROC statement or as a response variable option resulting in modeling generalized logits that compare each response level to the last (4).

Assuming all of that, then the 1.709 odds ratio estimate means that the odds of response=3 to response=4 when SES=low is 1.709 times the odds of response=3 to response=4 when SES=high.

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