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Is it meaningful to compare the coefficients of two different predictors in multilevel model when the two are at different levels?

Specifically I have two variables which measure the same construct at two different levels (individual and group). I am using R package nlme to fit a multilevel model and want to test the hypothesis that the individual level predictor is significantly better than the group level predictor. Does it make sense to fit the model and then examine whether the confidence intervals of the individual predictor do not overlap with the coefficient of the group level predictor? Is the fact that they have different degrees of freedom a problem? Is there a better way to test this hypothesis?

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    $\begingroup$ Have you asked this on the multilevel list? $\endgroup$ – StasK May 17 '12 at 16:33
  • $\begingroup$ No. Which list would be best to ask? $\endgroup$ – George Michaelides May 18 '12 at 7:07
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I think you could start by fitting two separate models: first a model with the predictor at the first level and then another model with the predictor at the second level. Then you can check which model leads to a better fit by looking at the value of the deviance (-2LL). The smallest the value of -2LL, the better the fit. In this way you can see which predictor fits better.

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