Comparing Mixed Model results with OLS regression

#1
Hi there. I'm an inexperienced an entirely self-taught statistician fighting a huge deadline. I'd be most grateful for advice!

Background:

I've been working on fitting an HLM model that explores the spatial relationships between crime and socio-economic factors such as deprivation scores and education indicators. The Intraclass Correlation Coefficient demonstrates a 12% attribution of variances to group factors, which I guess is relatively low(?) but then this IS a highly complex system.. But the model's evolution (using lmer in R) has seen a steady improvement of AIC scores, so I will probably present tentative results about its value.

Question:

I am now a little confused about how to demonstrate the model's effectiveness against other non-HLM techniques such as simple OLS regression. Is this purely by standard errors / residuals, or am I missing something important?! Mixed-models / HLM do not return correlations.

Thanks in advance!
 

Jake

Cookie Scientist
#3
There's not a straightforward answer because the justification is based entirely in statistical theory -- that is, there's not really any specific, tangible piece of the results that you can point to and say "look at this here, now do you see how much better the mixed model results are?" You can of course simply compare the mixed model results to the OLS results and observe that they are different from one another. However, this in itself does not give you any particular reason to believe that one set of results is more "correct" than the other. It just tells us that they are different. We simply know from statistical theory that the results from a model that makes unrealistic assumptions about the data generating process (i.e., OLS's assumption that errors are independent) are less trustworthy than the results of a model that relaxes those unrealistic assumptions (i.e., the mixed model approach of explicitly modeling nonindependence).