Odds-ratio interpretation

[buder]

Does anyone know why when I am getting the same coefficient (with the opposite signs) depending on which class variable is the "dropped" variable - the odds-ratio outcomes are different? 

For example, below I have 3 class variables for one of the independent variable. If I re-classify the dropped group, it gives me different odds ratios. 

Column1	Column2	Column3	Column4	Column5
		Estimate	Odds Ratio	Change in Odds
0	1	0.2022	1.224	0.224
0	2	0.4438	1.559	0.559
1	2	0.2416	1.273	0.273
		Estimate	Odds Ratio
0	1	-0.4438	0.642	0.358
0	2	-0.2416	0.785	0.215
1	2	0.2022	1.224	0.224

How would one know which one is the correct group to drop? Shouldn't the odds-ratios be the same?

[Reeza]

Is there a good reason for coding the groups in the way that you have in the first place? Usually it's better to keep it continuous if possible, and if not, to use groupings that are either:

1. Commonly used in the field,
2. Used in business and can help support your current business decisions,
3. Looking at the distribution to see if there's a natural break point, especially when considered in correlation with the dependent variable. 

Those are actually listed in the reverse order of how I'd approach the problem. 

Based on what you've posted I don't think we can answer your question, except that you should look into Simpson's Paradox as well.

https://en.wikipedia.org/wiki/Simpson%27s_paradox

[sld]

When you change the reference class, you are specifying a different parameterization for the same model. Hence, neither is wrong, both are correct, you just need to understand how the coding system determines the definitions of the odds ratios. By studying this SAS documentation, you will be able to sort it out

 https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_logistic_se...

This might also help

https://stats.idre.ucla.edu/sas/faq/in-proc-logistic-why-arent-the-coefficients-consistent-with-the-...