lme1 <- lme(resp~fact1*fact2, random=~1|subj)
should be ok, providing that variances are homogenous both between & within subjects. The function will sort out which factors & interactions are to be compared within subjects, & which between subjects. The problem with df's arises (for lme() in nlme, but not in lme4), when random effects are crossed, I believe.
It is difficult to give a general rule on the effect of imbalance; it depends on the relative contributions of the two variances and the nature of the imbalance. There should be a rule that people who ask these sorts of questions are required to make their data available either (if the data set is small) as part of their message or (if data are extensive) on a web site. Once the results of the analysis are on display, it is often possible to make an informed guess on the likely impact. Use of simulate.lme() seems like a good idea.
John Maindonald.
On 11 Aug 2004, at 8:05 PM, [EMAIL PROTECTED] wrote:
From: Spencer Graves <[EMAIL PROTECTED]>
Date: 10 August 2004 8:44:20 PM
To: Gijs Plomp <[EMAIL PROTECTED]>
Cc: [EMAIL PROTECTED]
Subject: Re: [R] Enduring LME confusion… or Psychologists and Mixed-Effects
Have you considered trying a Monte Carlo? The significance probabilities for unbalanced anovas use approximations. Package nlme provides "simulate.lme" to facilitate this. I believe this function is also mentioned in Pinheiro and Bates (2000).
hope this helps. spencer graves
p.s. You could try the same thing in both library(nlme) and library(lme4). Package lme4 is newer and, at least for most cases, better.
Gijs Plomp wrote:
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 illuminating answer can help R spread into the psychological community.
John Maindonald email: [EMAIL PROTECTED] phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Bioinformation Science, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200.
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