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I have two datasets that are very similar (such as two survey dataset that contains common variables and from a common period of time). How do I compare the result of the same model from two different data in order to see whether two datasets provide similar results?

I used this model for both data sets:

basic ordered logit regression such as "Obama's approval rating ~ democrat + republican + age + income + education + latino + black"

My first idea was to subtract Data A from Data B, compute the model with new data C(=$data_B$-$data_A$), and see if the coefficients are zero ($\beta_{B-A}$=0). But I don't think this is a proper approach.

Anther post "Comparing two datasets with same variable" asks similar question, but it is different from my question since I would like to compare the same model result from two different dataset.

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If these data are similar in nature and truly representative, then the models produced should be similar as well. I would suggest that you combine the data and test the results of different models using k-fold cross-validation (on k out-of-sample data). If the results vary drastically, then your model would have high variance. On the other hand, if your results barely change at all, then you would have high bias. You need to find the best balance between bias/variance. Here is a link on bias/variance: http://scott.fortmann-roe.com/docs/BiasVariance.html

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