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I am analyzing a multilevel model using the software HLM. I am trying to find out more about the Deviance statistic that I increasingly see being reported as a measure of the explanatory value/effect size of a model. In general, I know that HLM output reports this statistic and that the smaller it is the better. However:

  • How does one use/interpret this statistic for a given analysis?
  • How does one know if the deviance one obtains is at an acceptable level?
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The deviance is calculated as 

Deviance = -2 * LogLikelihood

For a given analysis, you can't interpret the deviance, and you can't say if it is at an acceptable level. You can use the deviance to compare two models that are nested. If you add parameters to a model, the difference in the deviance is chi-square distributed, with df equal to the number of parameters that you added to the model. It allows you to test whether the change in deviance is statistically significant. (Just as you can use the change in R^2 when you add predictors to a regression model to see if the improvement in fit is statistically significant.)

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