If I was building a linear mixed-effects model and I changed the variance structure (let's say to a power function) to represent an increasing variance over time points, would the assumption of homogeneous variance still need to be checked? The phrase "relaxing the assumption" comes up a lot in the text I'm reading, but wasn't sure if that means that we can completely throw that assumption out the window or not.
Usually there's a reason why you would incorporate increasing variance in your model - that's because you would have looked at the plot of the residuals for the model with homogenous variance versus time and would have found evidence of violation of the homogeneous variance assumption.
You can't "relax" an assumption unless you know from diagnostic plots that it's not supported by the data.
If you "relax" an assumption, it usually means that you are replacing it with another assumption which is supported by the data. So it doesn't really make sense to still check the original assumption for your updated model, since that model was modified to reflect the "relaxed" assumption.
1$\begingroup$ Thanks. I did see increasing variance across time in some initial plots and the residuals vs. fitted plot in my original model, which made me add in the new variance structure to account for it. I didn't see any change in the residuals vs. fitted plot after updating the model, though. Would that make sense, or indicate I should look at different variance structures? $\endgroup$– internMay 18, 2018 at 15:10
1$\begingroup$ I guess you want to look at plots of the normalized residuals versus time - it's there where you don't want to see any pattern if the increasing variance model fits your data well. You can also try different variance structures and look at the AIC values for different models. $\endgroup$ May 18, 2018 at 15:14