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Lets say I have age as the independent variable; education (1=college; 2=masters; 3=phd) and employment (1=unemployed; 2=part-time; 3=full-time) are the dependent variables.

If I was trying to check for a non-linear relationship between this single continuous independent variable and multiple ordinal dependent variables, what might be the best options?

What if I added additional independent variables into this model, such as height and age predicting education and employment?

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  • $\begingroup$ These are bizarre variables and model specifications. You don't state how age is scaled, e.g., is it an integer or bucketed? Education may be ordinal, your grouping starts with college without clarifying whether that is a college bachelors level degree, an associates degree, some college without any degree, etc. Then, too, it eliminates the possibility that some people may have only a high school diploma and, quite possibly, not even a GED. Employment cannot be made ordinal even with the most generous of assumptions. Finally, testing height as being related to any of these is nonsense. $\endgroup$
    – user78229
    Commented Oct 16, 2017 at 14:10
  • $\begingroup$ @DJohnson - Thanks, you're right. This example has nothing to do with the real study. It's just meant to give a reasonable parallel to allow others to comment on a direction for modeling techniques that could be used. $\endgroup$
    – user01923
    Commented Oct 16, 2017 at 23:10

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You should should take a look at splines or fractional polynomials. A link that could help you : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2477199/

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