REML mixed model

[#1]

Hello, 

I have few very general questions related to running a mixed model using REML.

1. Why is REML always recommneded ? what's the most obvious advantages of it over EMS method?

2. How do I make meaningful inferences for the given residual by predicted plot?

3. How do I generat %CV from REML?

Thank you.

[#2]

Also How do you interpret a negative value Variance component of a random factor in REML?

[#3]

I am not sure that there is a meaningful interpretation of a negative variance component.

I would first check that it is significantly non-zero: do CIs overlap with zero? The most sensible interpretation is that it is a neglible component of total variation.

If you have a large significant negative variance component that might give you cause to question the model.

I believe you can specify to bound all variance components to be positive if you would prefer. 

[#4]

There is a good explanation of REML in Peter Goos and Brad Jones' book on Optimal Design of Experiments, if you have it (I would recommend getting a copy). That is in the context of split plot DoE. I am guessing that you are using mixed models for variance components analysis, perhaps in measurement system analysis.

[#5 · Accepted solution]

1. Select Help > Books > Fitting Linear Models. Chapter 3 is devoted to fitting models with random effects using REML estimation procedure. In general, EMS only works in balanced designs. REML gives the same result in such cases so you lose nothing by always using it. The only disadvantage is that REML is more computationally expensive but that is a moot point today.
2. The Residual by Predicted Plot is not intended to be used for inference (hypothesis tests). It is a visual assessment of the estimated errors (residuals) to identify violations of the assumptions of the linear regression such as lack of fit, heteroscedasticity, and influential observations.
3. You compute the %CV from the variance components as 100*Sqrt(VC)/Mean as usual.

The negative variance is actually a negative covariance, if that interpretation helps you to accept such a result. Use the confidence interval for the estimate to decide if it is not zero. REML is more flexible than EMS. By allowing negative estimates around zero and adjusting the degrees of freedom, you get the desired coverage from the inference about the fixed effects.

[#6]

I'm not sure what version of JMP you are using, but a %CV hidden column was added to the REML Variance Components Estimates report starting with JMP 12.1.  You can see it by right clicking inside that report and selecting Columns < CV.