Using a Multilevel model when the residuals are not autocorrelated I have a dataset which includes data about US citizens nested within states. At first glance it seems appropriate to conduct a multilevel analysis, since allegedly there's supposed to be autocorrelation between the residuals of citizens from each state. I'm pretty new to this method so this is why I'm asking:
First, I run an OLS model and then the Durbin-Watson test, which indicated that there's no autocorrelation in my data (the Durbin-Watson result was 2.019). If I understand correctly, it means that a Multilevel model is not needed here and I can use a simple OLS model (?).
Then, However, I run a multilevel model, and the LR-test indicated that this model is significantly better then an OLS model.
Aren't this two results contradict? on one hand, the Durbin-Watson test indicates that there's no autocorrelation, but on the other the LR-test tells me the ML model is better.
I'm pretty sure I'm missing something here. It would be great if someone could explain what is happening here and what is the better option for my data.
Thanks a Lot!
 A: To my understanding, autocorrelation can be present in serial data, i.e. data that are collected in a series such as a time series of day-to-day measurements of mean temperature or something. The Durbin-Watson test is used to evaluate the presence of autocorrelation at lag 1, which means that observation n in the series is correlated with observation n+1. Another situation of autocorrelation might be when you have daily measures of something that has an irregular pattern over a week. Then you might often find autocorrelation at lag 7, because each given weekday has a particular pattern. I don't think autocorrelation is typically used to describe the type of intra-class correlation that might be present among people in a certain state, nested within a country.
Because you're doing OLS regression, I assume that you have a continuous dependent variable. In that case, it might be helpful to think of the different states as having different base values, different intercepts. This is modeled in a multilevel model as random intercepts. Alternatively or additionally, you could model the effect of states as an interaction effect between another independent variable and state on the dependent variable - this is called random slopes.
So my advice is that unless your data is serial in some way, you should ditch the idea about autocorrelation and stick with the multilevel regression model.
I hope this helps,
J
