## Ordinal Logit Regression and Proportional Odds Assumption

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# Ordinal Logit Regression and Proportional Odds Assumption

In ordered logit models,  the test for proportional odds tests whether our one-equation model is valid. If we were to reject the null hypothesis, we would conclude that ordered logit coefficients are not equal across the levels of the outcome and we would fit a less restrictive model (i.e., multinomial logit model). If we fail to reject the null hypothesis, we conclude that the assumption holds.

I noticed that If I include the option NOINT in the model statement in Proc logistics, this test is not performed by SAS. Why is that? Does it mean that with no intercept in the model, the assumption of equality of the logit coefficients across the levels of outcomes in no longer necessary?

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‎05-02-2013 03:54 PM
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## Re: Ordinal Logit Regression and Proportional Odds Assumption

Look at the model that is fit WITH intercepts.  There is a common part (which assumes proportionality) and then there are the intercepts, which are the classes into which you are categorizing (as nearly as possible).  WITHOUT intercepts, there is only the common (linear in the predictors) part.  What I think you are seeing is an interaction between one of the predictors and the outcome variable that is not proportional.

Steve Denham

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## Re: Ordinal Logit Regression and Proportional Odds Assumption

I think it means something more like "Without intercepts, and for the cumulative (ordered) logit link, all categories are assumed to be identical."  Thus no test.  The intercepts drive the classification at first is how I think of it.

Steve Denham

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## Re: Ordinal Logit Regression and Proportional Odds Assumption

Then the question will be " How can I test my assumption about the similarity off the categories? " Or in other words, if I use the intercepts and the assumption is not rejected, then the results should be similar to the ones with no intercept?

The reason that I ask is that the results with and without the intercept are very different.

the assumption is also rejected when I use intercept.

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‎05-02-2013 03:54 PM
Posts: 2,655

## Re: Ordinal Logit Regression and Proportional Odds Assumption

Look at the model that is fit WITH intercepts.  There is a common part (which assumes proportionality) and then there are the intercepts, which are the classes into which you are categorizing (as nearly as possible).  WITHOUT intercepts, there is only the common (linear in the predictors) part.  What I think you are seeing is an interaction between one of the predictors and the outcome variable that is not proportional.

Steve Denham

Frequent Contributor
Posts: 89

## Re: Ordinal Logit Regression and  Proportional Odds Assumption

Thanks for clarification steve

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## Re: Ordinal Logit Regression and  Proportional Odds Assumption

Hi.  According to the documentation for Proc Logisti, NOINT sets only the FIRST intercept to zero, not all.  There is an example but I'm not sure of the utility.

My recollection from theory is that generally such a restricted model does not lead to a valid likelihood function, and likelihood ratio tests are distorted.  That may be why SAS suppressed the test.

I would think that if the null is rejected with intercept(s), restricting the model can't improve the situation.

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