Ordered Logit - Probabilities and quadratic term

Hi everyone,

I'm running into a problem interpreting a quadratic (curvilinear) relationship using an ordered logit model.

the d.v. is self reported health, 5 categories from poor(low) to excellent(high). The quadratic term is age-squared. The original age variable is in 5 year age groups starting with 45-49 (8 groups overall - with the coding being 8-15).

I've used the equation AgeCoeffecient-Age2Coeffiecient*AgeGroup (e.g. 8). This gives me different coefficients for each group with the numbers declining from group 8 (45-9) to group 15 (80+). I'm not entirely sure that equation is correct though, and then not sure where I go from here to get the odds-ratios and then the predicted probabilities. Instead of asking for the coefficient I can ask for odds-ratio in Stata12 with the ",or", and then the "margins" command for predicted probabilities but not sure if that works with a quadratic.

For the linear terms in the model, including age, I ran odd-ratios and then the "margins" command to give me the predicted probabilities that each category would report "poor health"..then the next etc etc. But am really lost when it comes to the quadratic.

Any assistance is very appreciated!