I am trying to perform a regression analysis with spatially repeated data, i.e., multiple samples collected from multiple sites. I have been trying to do this in the proc mixed framework so that I am calculating the appropriate standard errors and probability statistics, but I am unsure if a regression model with a random statement (the site term) is correct? I get different parameter estimates than in the straight regression analysis and this give me pause.
When you use PROC MIXED for hierarchical regression model, the parameters are estimated by using Residual Maximum Likelihood method by default. If I understood your question correctly, you are trying to use Random statement in proc mixed and the output from this model is different from individual regression model which uses OLS method for estimating the parameters. Moreover OLS method assumes errors are independent and hence there is no point in comparing the two different model outputs. For more details, you can refer SAS help & SAS documentation on PROC MIXED. I hope this would be helpful to you.
Thanks for the reply. I went back in and was looking at how the estimates are calculated in the mixed vs. fixed linear models and it makes sense, as you noted, that the parameter estimates for the model are different. I was also having a problem convincing myself that the proc mixed framework was appropriate for regression, as all of the examples and literature I've been working with (Littell et al. for mixed and linear models) have strictly dealt with ANOVA/ANCOVA type analyses. I have come around to thinking that using the mixed model is indeed best for dealing with the way these data were collected.