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I have two different dependent variables (Y1 and Y2). Both of them are ordered variables, but for Y1, it has 7 categories, while for Y2, it has 6 categories.

Now, I am using probit model to analyze the two dependent variable, employing the same set of independent variables. I am just wondering if it is possible to compare the two models?

Thanks in advance.

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    $\begingroup$ What aspects would you like to compare? What are you hoping the comparison means? $\endgroup$ – whuber Aug 19 '16 at 17:42
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    $\begingroup$ What we usually call "model comparison" is about comparing models for the same dependent variable. Hence, @whuber's question. $\endgroup$ – Kodiologist Aug 19 '16 at 18:17
  • $\begingroup$ Thanks! As for the comparisons, I am just trying to compare the model quality. $\endgroup$ – Yuan Aug 19 '16 at 19:20
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If Y1 and Y2 are just two different categories tiering of the exact same ultimate dependent variable Y; then I suspect some comparison of the two models may make some sense. If on the other hand Y1 and Y2 are two entirely different dependent variables (not only differentiated by the number of categories), then your question does not make sense. And, the straight answer is that those two models are simply not comparable.

Assuming that Y1 and Y2 are essentially derived from the exact same variable, you could compare the quality and the fit of the models using standard Goodness-of-fit measures for Probit model, and observe which categorie segmentation gave you better result. Or for the purpose of model parsimony, did increasing your number of categories from 6 to 7 was materially worth it from both an explanatory and statistical significance standpoint. This can be an interesting process, and you could test additional segmentation cuts of this same model structure using for instance fewer categories (like 4 or 5) and more categories (8, 9, etc.). Selecting the proper number of categories is based on both art and science (statistical significance of the difference between the various categories, etc.).

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