# Is it possible to conduct a regression if all variables are ordinal?

I would like to produce a regression analysis model. I have ordinal categorical data. I can use SPSS. I do not know what analysis to perform or what assumptions to check.

What are the statistical tests that can be performed? How can I test the accuracy of the model?

• Ordinary least squares regression is not suitable for ordinal catgeorical dependent variables. If you try searching on 'ordinal response' there are some useful questions and answers. Searching on 'ordered categorical response' finds some more, such as this Aug 15 '13 at 9:44
• Also try this. Aug 15 '13 at 9:57
• I should modify my earlier comment to say "often not suitable" - there are circumstances where it's reasonable to do so. Sep 18 '13 at 1:05

Yes, it is possible.

When your dependent variable is ordinal, you want to do ordinal logistic regression. This can be done in SPSS. UCLA's excellent statistics help website has a guide to OLR in SPSS here (with more here).

Regarding your independent variables, you have several options:

• You can represent them with a standard dummy coding scheme (such as reference cell coding, see my answer here for an explanation).
• Another approach is to use an ordinal dummy coding scheme (such as difference coding, there is an explanation here).
• Lastly, Agresti has argued that you can simply replace the ordinal rankings with continuous values that represent your best guesses about the true values. There will naturally be some measurement error associated with this approach, but if you have some knowledge on which to base your guesses they won't be too bad, and you won't use as many degrees of freedom to estimate the effect.

If you use OLR for your analysis, you can get tests of each variable with standard output. In SPSS these tests are reported in the "Parameter Estimates" table. The assumption you need to worry about / check is the proportional odds assumption, which is assessed via the "Test of Parallel Lines". SPSS can output this for you as well. UCLA's guide to OLR in SPSS (linked above) covers both of these issues.

For ordinal categorical response data, the best thing is usually to use a cumulative multinomial logit model. Those are somewhat non-trivial to implement, though I think SAS can do it and there is (I think) some R package that can do it. I would have to check on which one though. The idea is that you're modeling the probability that the response is less than or equal to each category.

For the dependent variables, you can keep those as categorical, or you can set them to be ordinal values and use a linear trend on your selected values. The latter is usually effective in practice even if the interpretation of the coefficients is challenging. For a logistic model, the Mantel-Hansel test will let you test the linear trend. For a cumulative multinomial logistic model, there might be an analog that works as well.