[R] How to specify the hierarchical structure of a split plot using lmer ??

[Douglas Bates]

Søren Højsgaard 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øren

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.)