How to specify the hierarchical structure of a split plot using lmer ??
S??ren H??jsgaard wrote:
I have a problem getting the lmer function of the lme4 package to use the
appropriate degrees of freedom for testing. Consider the Semiconductor data
from the SASmixed package:
library(SASmixed)
Semi.lme <- lme(resistance ~ ET * position, random=~1|Grp, data=Semiconductor)
anova(Semi.lme)
numDF denDF F-value p-value
(Intercept) 1 24 3237.261 <.0001
ET 3 8 1.942 0.2015
position 3 24 3.385 0.0345
ET:position 9 24 0.809 0.6125
Here, the ET effect is (correctly) tested on 8 denominator degrees of freedom.
In the example in the SASmixed package, the following code is presented:
(fm1Semi <- lmer(resistance ~ ET * position + (1|Grp), Semiconductor))
anova(fm1Semi)
Analysis of Variance Table
Df Sum Sq Mean Sq Denom F value Pr(>F)
ET 3 0.647 0.216 32.000 1.9415 0.14273
position 3 1.129 0.376 32.000 3.3855 0.02991 *
ET:position 9 0.809 0.090 32.000 0.8092 0.61127
So here, all effects are tested with 32 denominator degrees of freedom.
I have looked at the help page for lmer but have been unable to figure out
how to specify the hierarchical structure of a split plot experiment. Also,
I have Googled but without any luck. Any help will be appreciated.
S??ren
Unfortunately the answer is quite simple. The current version of the lme4 package does not attempt to get the degrees of freedom "right" - it just gives an upper bound. The reason is more than simple laziness on my part. The lmer function can fit models with non-nested grouping factors and it is not easy to define sensible values for the degrees of freedom in such cases. Hence I have put that problem aside while dealing with other issues. (Also - as long time readers of this list may know - the topic of denominator degrees of freedom is one of my least favorite topics.)