# Ordinal Logistic Regression in R - Understanding coefficients

I am creating an OLR model using R with the polr function in the MASS package. All of my predictors are also ordinal data, all of the data is the integers from 1 to 5 coming from a customer survey.

I am aware that the coefficients you obtain are log odds ratios, and I am familiar with taking the exponent to find the odds ratios. What I don't understand is the following points:

1) What do the polynomial terms actually represent? Because the coefficients are the same if I change the scale to be say from -2 to 2, so I assume the data is transformed into some standard labelling and then squares, cubics etc. are taken.

2)How do I interpret these polynomial coefficients?

• Regarding (1), you're under the proportional odds assumption, which means that slopes per ordinal variable levels will be equal. Same as in multinomial regression, every equation in your model represents odds ratio between a given ordinal level and all other levels. – Digio Aug 19 '19 at 8:55
• @Digio I am aware of the proportional odds assumption, but my question is what is the interpretation of a quadratic or cubic coefficient? I understand what it would mean for non-ordinal data, but as ordinal data does not have to even be numeric, what do these terms represent – James Aug 19 '19 at 9:00
• Are you asking for the back-transformation of a single squared regressor? I guess the first question would be, why transform the regressor in the first place. Also, maybe this answer is relevant to your question? – Digio Aug 19 '19 at 9:30
• I think the issue is on interpreting the polynomial contrasts used for the ordinal predictor, where you may have expected just a dummy coding of the contrasts (this is not specific to logistic regression). More on that in this beautiful answer to an earlier question – Dries Aug 19 '19 at 12:24
• When using an ordinal predictor, I have to choose a contrast, and by default R will use polynomial contrasts. Would polynomial contrasts be able to show me if there is a, say, quadratic relationship between the predictor and the dependant variable? I have both of the linked answers but I don't feel like either fully answer my question. Essentially, is the interpretation the same as the linear one, ie a unit increase in this amount means that you are e^coef times more likely to be in a higher level if all other predictors are kept the same? – James Aug 19 '19 at 13:21