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My colleague has an experiment with a 2x2 all between subjects design with categorical variables predicting a three-level categorical dependent variable (choise between A, B, C/ coded as -1 0 1). Is this coding correct? Can a dependent variable have three levels? What kind of analysis can he best conduct?

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    $\begingroup$ ANOVA (as initially tagged) won't be of any help, while log-linear models or techniques that consider multinomial outcomes might be appropriate here. Could say more on your design, sample size, etc.? $\endgroup$ – chl May 14 '12 at 10:30
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A dependent variable can definitely be categorical and have multiple levels. These levels may be ordinal or not (briefly, it is ordinal if the levels have a definite order - e.g. none, some, a lot). If the dependent variable is ordinal, one choice is ordinal logistic regression. If it is not ordinal one choice is multinomial logistic regression. If you are using SAS, I made a presentation on this topic (actually, the start of the talk is not SAS-specific, so it may be helpful, regardless of what software you are using).

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  • $\begingroup$ I've often found that the proportional odds assumption is not tenable - in that case, how would you model ordinal data in a way that takes the ordinal structure into account? I'm asking because I've seen you recommend ordinal logistic frequently and thought you may have some ideas here $\endgroup$ – Macro May 14 '12 at 12:14
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    $\begingroup$ One method is the "partial proportional odds" method, which relaxes part of the assumption. An old article is by Peterson and Harrell (@FrankHarrell posts here a lot). It's also covered in Agresti's book on ordinal data. An interesting topic. Worthy of more that a comment here. $\endgroup$ – Peter Flom - Reinstate Monica May 14 '12 at 15:54
  • $\begingroup$ Another method I sometimes use is to do both multinomial and ordinal, and compare the predicted probabilities. If they are close (for some substantively sensible meaning of close) then the violation of the assumption appears not to matter much, so I then use the simpler (ordinal) model. $\endgroup$ – Peter Flom - Reinstate Monica May 14 '12 at 15:59
  • $\begingroup$ Thanks for the info - I'd never heard of "partial proportional odds". Your heuristic on comparing the proportion odds model to the "saturdated" multinomial model is what I would usually do, but I've recently become interested in formulating more general ordinal models, so this discussion helps. $\endgroup$ – Macro May 17 '12 at 0:33
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    $\begingroup$ If you are interested in general ordinal models, the Agresti book is a must. Another good book (but old, unless there's a new edition) Statistical Models for Ordinal Variables. $\endgroup$ – Peter Flom - Reinstate Monica May 17 '12 at 0:40

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