# [R] Enduring LME confusion… or Psychologists and Mixed-Effects

Gijs Plomp gplomp at brain.riken.jp
Tue Aug 10 05:40:54 CEST 2004

```Dear ExpeRts,

Suppose I have a typical psychological experiment that is a
within-subjects design with multiple crossed variables and a continuous
response variable. Subjects are considered a random effect. So I could model
> aov1 <- aov(resp~fact1*fact2+Error(subj/(fact1*fact2))

However, this only holds for orthogonal designs with equal numbers of
observation and no missing values. These assumptions are easily violated
so I seek refuge in fitting a mixed-effects model with the nlme library.
> lme1 <- lme(resp~fact1*fact2, random=~1|subj)

When testing the 'significance’ of the effects of my factors, with
anova(lme1), the degrees of freedom that lme uses in the denominator
spans all observations and is identical for all factors and their
interaction. I read in a previous post on the list ("[R] Help with lme
basics") that this is inherent to lme. I studied the instructive book of
Pinheiro & Bates and I understand why the degrees of freedom are
assigned as they are, but think it may not be appropriate in this case.
Used in this way it seems that lme is more prone to type 1 errors than aov.

To get more conservative degrees of freedom one could model
> lme2 <- lme(resp~fact1*fact2, random=~1|subj/fact1/fact2)

But this is not a correct model because it assumes the factors to be
hierarchically ordered, which they are not.

Another alternative is to model the random effect using a matrix, as
seen in "[R] lme and mixed effects" on this list.
> lme3 <- (resp~fact1*fact2, random=list(subj=pdIdent(form=~fact1-1),
subj=~1,  fact2=~1)

This provides 'correct’ degrees of freedom for fact1, but not for the
other effects and I must confess that I don't understand this use of
matrices, I’m not a statistician.

My questions thus come down to this:

1. When aov’s assumptions are violated, can lme provide the right model
for within-subjects designs where multiple fixed effects are NOT
hierarchically ordered?

2. Are the degrees of freedom in anova(lme1) the right ones to report?
If so, how do I convince a reviewer that, despite the large number of
degrees of freedom, lme does provide a conservative evaluation of the
effects? If not, how does one get the right denDf in a way that can be
easily understood?

I hope that my confusion is all due to an ignorance of statistics and
that someone on this list will kindly point that out to me. I do realize
that this type of question has been asked before, but think that an