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I have an ordinal dependent variable, named D, which varies from very small, small, medium, big, to very big. This variable depends on the independent variables X, V, which are continuous variables. Could I perform an ordinal logistic regression analysis in the former data in order to obtain the relationship between D and X, V? Could I obtain in this way the D variable as percentages?

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Yes, you can do ordinal logistic regression with continuous independent variables.

But what do you mean when you write

Could I obtain in this way the D variable as percentages?

You can get the D variable as percentages without doing any regression, just simple arithmetic. That's probably not what you want. You can get the predicted proportion of D in each level from an ordinal logistic regression.

In SAS there is the output statement in PROC LOGISTIC; you would want the predprobs option. In R you could look at polr in the MASS package, and then look into predicted and profile.

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