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Nov 19, 2011

Ordinal logistic regression plot seems upside down - why?

With JMP 10, I can request a 'logistic fit plot' for an ordinal logistic regression (either using fit y on x or fit model). The apparent 'problem' is that the plot is the inverse of what I expect. That is, it requires one to view the area above a line as the probability of an event occurring. One pretty much has to ignore the lines themselves. In other words, when I expect to see a curved line showing a 'hump' (highest y values for intermediate x values), it shows a curve that is a horseshoe. If I run the same data with OLS (showing a polynomial curve), I get a nice hump to the data. (To avoid confusion, I am requesting a polynomial or quadratic function, which is why the line is peaked in the middle - that is not the problem.)

The same issue occurs with simple logistic (binary) regression. One has to view the areas above the line rather than the lines. It gives the estimates and odds ratios for an event "not" occurring rather than occurring.

I have shown this plot to a few people who are similarly confused. We are accustomed to seeing logistic regression plots (as with OLS plots) having a line that represents the probability of an event at different 'x' values.

Can anyone tell me why JMP plots the data in this way? I can't find similar examples for other software programs. Any suggestions on what to do? What does SAS do? I don't know if I can trick JMP by reversing the numerical values - I tried to do that but am uncomfortable interpreting the product.

I will attach an output showing the horseshoe plot. The highest y values correspond to the middle x-values (shown as the bottom of the trough here).