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I am working with some survey data that uses probability weights. A number of sources explain that likelihood-based tests and fit statistics like likelihood-ratio, AIC, and BIC are not valid in the context of the weighted MLE.

Are there other tests, statistics, or graphics that one can use in this context to get an idea of how one model performs relative to another model?

Macro
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    Be careful, note that survey weights may often be doing things other than just dealing with a complex survey design. There may also be non-response and post-stratification adjustments in the weights. Remember, the weights are for *estimation of population totals*, not just the inverted sampling probabilities. Also, did you read the paper in the link? – probabilityislogic Sep 28 '13 at 21:35
  • What kind of sampling scheme do you have? I am familiar with methods for Case-cohort and Nested case control sampling. I believe any kind of independent (with replacement) sampling can also be easily dealt with, because the weights are conditionally independent given the data, hence standard empirical likelihood theory can be used to justify e.g. score tests based on the weighted likelihood ratio. – guest47 Apr 01 '13 at 04:25

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