I'm a fairly inexperienced statistician fighting a huge deadline and just need some peace of mind that I'm not making a massive error here. I'd be most grateful for pointers.

I've been playing around with different model combinations using the lmer() function, and have managed to get the AIC scores down from over 10,000 with the most basic combinations to -180 by factoring in various random effects. But I'm concerned I might be creating bias by using variables that already correlate. Is this a valid concern or does the model mitigate for this?

  • $\begingroup$ I don't really follow your question. Can you say more about your situation, your data & your goals? You may want to read our FAQ & this blog post regarding how to ask a good question. $\endgroup$ – gung - Reinstate Monica Sep 5 '12 at 2:49
  • $\begingroup$ The ultimate goal is to compare HLM with other approaches (eg. OLS regression) in the context of crime spatial modelling. The concern here is if I am introducing biases into the model by including random effects variables (such as an area's deprivation score and crime rate) that are likely to have some correlation. I wonder if this distorts the results (meaning variables need to be relatively orthogonal), or if lmer is smart to this? My apologies if vague - I'm entirely self-taught and have found it pretty tough getting into the language, so just need some guidance. $\endgroup$ – geotheory Sep 5 '12 at 9:46
  • $\begingroup$ Information criteria simply don't work with multilevel data, as they explicitly assume i.i.d. So AIC, BIC or DIC would all be bad measures of model performance in presence of nesting. Think about the sample size in BIC: should this be the number of clusters or the number of ultimate observations? The answer you would give might vary depending on whether your explanatory variable does or does not vary within the cluster. $\endgroup$ – StasK Sep 19 '12 at 4:06
  • $\begingroup$ That's interesting @StasK. I am pretty sure I have seen them recommended for the purpose of choosing among them, although I can't remember exactly where. $\endgroup$ – Peter Flom - Reinstate Monica Sep 27 '12 at 11:25
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    $\begingroup$ It's a shame that this work has not been published and publicized properly, and the reasons are totally opaque to me. The best resource that I am aware of is math.bu.edu/people/sray/talk/jsm_2007.pdf; this guy has moved on to other hotter stuff with bioinformatics computing though. James Berger mentioned the extended BIC in his Wald lectures at the 2007 JSM (amstat.org/meetings/jsm/2007/onlineprogram/…); again, I have not seen this stuff published by him. $\endgroup$ – StasK Sep 27 '12 at 17:42

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