Compare DIC

[hdilk0507]

If, when a new variable (level 2) is added to the model reduction in DIC is less than 1, should I select the minimum DIC model? I noticed that estimates of coefficients of both models are approximately equal (some are almost the same).

[cazlo]

The reduction in the DIC should be at least 10 otherwise the two models are not substantially different, i.e. the parameter you are adding is not significant. So, if by adding your level-2 variable you see a reduction of less than 1, it is not worth including in the model.

[hdilk0507]

Thank you.

[billb]

There is no theory based fixed difference e.g. 10 that should be compared when comparing the DIC of two models although 10 might have been a rule of thumb suggested by someone - in theory the model with the lowest DIC is better but of course there is stochastic noise when using MCMC so a very small difference might be due to MCSE.
One interesting point is that when you add a level 2 variable to a 2 level model with random intercepts, it will explain some of the level 2 variance i.e. reduce the differences between level 2 random effects yet the DIC is based on the level 1 Likelihood so the fit will not be better but the 'effective' number of parameters might be reduced and hence the DIC better.
Bill.

[cordoba14]

Even though this thread is a bit dated, I still have the same problem. Most of my research is based on cross-national data in which I am interested in level-2 or level-3 variables. As mentioned above, the DIC is almost always insensitive to adding higher-level variables. So I might ask the provoking question: Why should we use DIC in applied multilevel modelling? Even when I include highly signficant higher level variables, I observe a change in DIC only after the decimal. The only time when DIC is really useful in my research is when I control for cross-level interactions, as DIC tells me if such a model is to be preferred or not.

Is there any way to decide if model A with higher-level variable X is to be preferred over model B with higher-level variable Y?

Thanks for the discussion!