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?
 A: 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:


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*Correlational study or ordinal data using 5-point Likert scale

*Regression testing after dimension reduction
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.
