# Which regression to use for ordinal variables?

I have 10 independent ordinal variables, each having 5 levels, all intended to measure the same latent construct, and one ordinal dependent variable named rank with 5 levels. I have read somewhere that for using regression, it is necessary to convert categorical variables with multiple levels to dummy variables, which will be very cumbersome. Is there any way I can use them as is in regression?

• Are the 10 independent ordinal variables meant to measure the same latent construct, or different ones? – Nick Stauner Apr 29 '14 at 6:18
• @NickStauner, Same – prof_jack Apr 29 '14 at 6:19

## 1 Answer

If you have enough data, you can fit a structural equation model to a polychoric correlation matrix. You might want to begin with exploratory factor analysis of the 10 ordinal variables that are meant to measure the same construct if you're not sure they actually do. If they do all load primarily on the same general factor, you can estimate that factor and regress your dependent ordinal variable onto it.

Several ways of doing this could work, but the simplest would probably be fitting a structural equation model to a polychoric correlation matrix. Another option would be to estimate latent factor scores with a rating scale model and use those to predict the dependent variable with an ordinal regression model. I'm not sure which option is better; I have some simulation study to complete on these matters...In the meantime, I'd say either ought to be a fairly good approach, assuming you have enough data.

If your sample is rather small, you'll probably need to settle for the classical test theory (CTT) assumptions. I've reviewed these in a few other answers to:

Basically, you'd treat your ordinal data as numeric, take the sum or average of individuals' responses to items intended to measure the same latent factor, and use that as your score for the individual on that factor. You could then use those conventional index scores as your predictor in an ordinal regression model as above, skipping the more complex method of latent factor estimation.

• Well i am new to spss so pardon me if i am unable to get much of it , but what i get from the last para is to convert my ordinal IVs to scale variable and treat them as numerical value to apply ordinal regression. Also i have only 15 cases in my data so i guess that is a pretty small sample. please, Correct me if i am wrong – prof_jack Apr 29 '14 at 7:56
• Yeah, 15 cases is definitely only enough for something very basic. You may also need to treat the dependent variable as numeric and fit a linear regression model with ordinary least squares estimation. The problem with doing so is that it attenuates the relationship between your variables somewhat...but you're going to have power issues no matter what you do with only 15 cases. – Nick Stauner Apr 29 '14 at 17:44