significance of random effects in cross-classified model

[ginamartin]

Hello, I am running a 3 level logistic cross-classified model (neighbourhoods and schools) predicting a binary drinking outcome. I understand that it is best not to use the credibility intervals to determine significance of the random effects but the lrtest, for nested models. Does this apply to the cross-classified models? If so what is the comparison model? If not what is the best way to determine significance?

Thank you very much,
Gina

[ChrisCharlton]

As you are fitting a cross-classified model and refer to credible intervals I assume that you are using MCMC, in which case you would do the comparison using the DIC statistic (see chapter 2 of the MCMC guide: http://www.bristol.ac.uk/cmm/media/soft ... mc-web.pdf). The comparison would be between the model with or without the extra parameters, and a reduction in DIC value suggests a better model. If on the other hand you were using (R)IGLS with MLwiN then you would need to do a Wald test as MLwiN estimates binomial models using quasi-likelihood.

[ginamartin]

Thank you for your reply Chris!