How should I deal with continuous independent variables in a regression for ordinal dependent variables?

Question

I am doing a research for which I will perform a data-analysis in SPSS.

My dependent variable is 'father involvement'. I have four different questions that have measured different forms of 'father involvement'. These questions are all ordinal on a 1-2-3 scale.

I would like to run seperate ordinal models for these different questions. My independent variables include two meanscales (gender role attitudes and relationship satisfaction), continuous variables (income and workhours) and an ordinal variable (education level). Additionally I want to see whether there is an interaction-effect between income and relationship satisfaction and whether gender role attitudes function as a mediator for education level

My problem is as follows: I am having a hard time understanding exactly how to deal with continuous independent variables in a ordinal regression. The outputs are quite chaotic since there are a lot of empty cells, which makes intepreting the estimations hard. I am wondering whether using continuous independent variables is advised, or whether it is better to categorize them.

Any suggestive readings or other forms of advice are very welcome.

Thomas

Answer 1

Semiparametric ordinal regression models such as the proportional odds model handle the ordinal nature of Y in a special way. But concerning the right hand side of the model, the handling of various types of Xs is the same as with any other regression model; you just need to know how estimates/predictions/contrasts are stated, e.g., as differences in log odds that can be anti-logged to get odds ratios. This is discussed in detail in RMS.

As with all regression models, the issue of whether you are a daredevil in assuming that a continuous predictor acts linearly is a big one. Given sufficient sample size it is not usually wise to assume linearity, and regression splines are your friend.