I am trying to find out if I can somehow assess if one model fits my data significantly better than another model? They are both ordinal regressions and we have introduced an additional interaction term in the second model. Now we want to know if the model has improved. Do I only look at the model fit indices? How do I know if the model has significantly improved?
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$\begingroup$ this is my data Sandra posted on my behalf. So basically I am interested in CHANGE (not absolute values) in model fit between the model with and the model without interaction terms. I want to see if adding the interaction terms in the model SIGNIFICANTLY improves the model fit or not. So I am interested in if this change is statistically significant. I assume I have to look at Chi square and Degrees of freedom in the Model fit SPSS output? $\endgroup$– user32517Commented Nov 8, 2013 at 14:49
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1$\begingroup$ @Andreea You will have difficulties interacting with this thread because (a) you did not post the question and (b) you do not have enough reputation to comment. A good solution would be for you to re-post this question yourself. When you do so, please flag this one or the new one for moderator attention so we can combine all the materials into one thread. $\endgroup$– whuber ♦Commented Nov 8, 2013 at 16:03
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The equivalent null hypothesis is that the coefficient for the interaction term is 0. If that hypothesis is true, then your model with the interaction effect is exactly the same as your model without the interaction effect, and adding the interaction effect has thus added nothing to the model fit.
In your output there will be next to the interaction term a test for whether or not that coefficient is 0. So that alone will be enough to answer your question. This is a Wald test. If you insist on comparing models you can do a likelihood ratio test. The Wald test and likelihood ratio test will give the same answer in large samples.
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$\begingroup$ Thanks Maarten. Just to clarify something, my outcome, predictors and moderators are all categorical and ordered (it's Ordinal Regression). Therefore in the Parameter Estimates output, I have estimates and significance and Wald for each of the combinations of the moderatorexposure, which represents the interactio term. So I have Moderator categ 1*Exposure categ 1, Moderator categ 1*Exposure categ 2, Moderator categ 2 * Exposure categ 1 (which is reference) and Moderator categ 2 Exposure categ 2 (also taken as reference caegory). In this example, only Moderator 1 categ 1*Exposure 2 is signifi $\endgroup$– user32517Commented Nov 8, 2013 at 15:27
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$\begingroup$ In that case your interaction involves more than 1 parameter, so you need to take that into account. Both the Wald and likelihood ratio test are possible. I don't know how these are implemented in SPSS. $\endgroup$ Commented Nov 8, 2013 at 16:13