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!