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Linear Trend in Conditional Residual vs. Predicted Plot using REML

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cwillden

Frequent Contributor

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May 1, 2017

I've noticed that BLUPs from REML variance component estimates will systematically result in an upward trend in a conditional residual vs. conditional predicted plot.  EMS random effect predictions are always just the mean of each random effect level, so the plots always appear as expected.  I'm scratching my head a bit about why REML does this.

Here's an example where I randomly generate 100 groups of size 2 with a group variance component.  The model is just the group random effect, no fixed effects.  If I save the conditional predicteds and residuals, I make the following plot.REML Plot.PNG

 Doing the same with EMS instead of REML, I get this plot:EMS Plot.PNG

 This plot is equivalent to treating Group as a fixed effect instead of random, and is exactly what I would expect it to look like.

 So, it looks like REML BLUPs are overestimating the lower group means and underestimating the group means that are higher.  Any explanation for this behavior?

Data table with scripts is attached.  Any insight would be greatly appreciated!

-- Cameron Willden