How to replicate random effects in lme4 from SAS? - r

Question

I am wishing to run a linear mixed model on a dependent variable DV that is collected under two different Condition at three different Timepoint. The data is structured as follows:
## dput(head(RawData,5))
structure(list(Participant = structure(c(2L, 2L, 2L, 2L, 4L),
.Label = c("Jessie", "James", "Gus", "Hudson", "Flossy",
"Bobby", "Thomas", "Alfie", "Charles", "Will", "Mat", "Paul", "Tim",
"John", "Toby", "Blair"), class = "factor"),
xVarCondition = c(1, 1, 0, 0, 1),
Measure = structure(c(1L, 2L, 3L, 4L, 1L),
.Label = c("1", "2", "3", "4", "5", "6", "7", "8",
"9", "10", "11", "12"), class = "factor"),
Sample = structure(c(1L, 2L, 1L, 2L, 1L),
.Label = c("1", "2"), class = "factor"),
Condition = structure(c(2L, 2L, 1L, 1L, 2L),
.Label = c("AM", "PM"), class = "factor"),
Timepoint = structure(c(2L, 2L, 2L, 2L, 1L),
.Label = c("Baseline", "Mid", "Post"), class = "factor"),
DV = c(83.6381348645853, 86.9813802115179, 69.2691666620429,
71.3949807856125, 87.8931998204771)),
.Names = c("Participant", "xVarCondition", "Measure",
"Sample", "Condition", "Timepoint", "DV"),
row.names = c(NA, 5L), class = "data.frame")
Each Participant performs two trials per Condition across three Timepoints as depicted by Measure; however, there are missing data so not necessarily 12 levels per participant. The column xVarCondition is simply a dummy variable that includes a 1 for each entry of AM in Condition. The column Sample refers to the 2 trials for each Condition at each Timepoint.
I am an R user but the statistician is a SAS user who believes the code for the model should be:
proc mixed data=RawData covtest cl alpha=α
class Participant Condition Timepoint Measure Sample;
model &dep=Condition Timepoint/s ddfm=sat outp=pred residual noint;
random int xVarCondition xVarCondition*TimePoint*Sample
TimePoint/subject=Participant s;
The above SAS code gives sensible answers and is working perfectly. We believe the resulting lme4 syntax for the above model to be:
TestModel = lmer(DV ~ Condition + Timepoint +
(1 | Participant/Timepoint) +
(0 + xVarCondition | Participant) +
(1 | Participant:xVarCondition:Measure), data = RawData)
However, I get the following error when running this model:
Error: number of levels of each grouping factor must be < number of observations
Are the random effects specified correctly?

Answer 1

I can't quite tell from your description, but most likely your Participant:xVarCondition:Measure term constructs a grouping variable that has no more than one more observation in each level of classification, which will make the (1|Participant:xVarCondition:Measure) term redundant with the residual error term which is always included in an lmer model. You can override the error if you really want to by including
control=lmerControl(check.nobs.vs.nlev = "ignore")
in your function call, but (if I've diagnosed the problem correctly) this will lead to the residual variance and the Participant:xVarCondition:Measure variance being jointly unidentifiable. Such unidentifiability usually doesn't cause any problems with the rest of the model, but I am more comfortable with an identifiable model (there's always the possibility that such unidentifiability will lead to numerical issues).
There's a similar example here.
You can check my conjecture as follows:
ifac <- with(RawData,
interaction(Participant,xVarCondition,Measure,drop=TRUE))
length(levels(ifac)) == nrow(RawData)