Dear list, I'm trying to specify the appropriate random effects structure for a repeated-measure design with multiple, fully crossed within-subject factors. F1, F2 & F3 are fully crossed factors, repeated several times (> 100, but not fully balanced) for each subject (each subject saw each unique combination of F1xF2xF3 several times, order not important). Subjects are nested within sex. F1 has 4 levels, F2 10 levels, and F3 40 levels. I am interested in F1, F2, F3 and sex as fixed factors, but trying to account for the massive amount of pseudo-replication within the data set. I tried to do my homework, and, for a simple repeated measure on different subjects characterized by sex, something like meas ~ 1 + (1 | sex/subject) would be appropriate. I am having a hard time, though, extending this to my design, where a repeated measure on a few subjects was repeated for each combination of factors F1, F2, and F3. Is it simply meas ~ 1 + (1 | sex/subject) + (1 | F1) + (1 | F2) + (1 | F3)? I apologize if this is something obvious. I'm new to mixed models & lmer and wasn't able to find a similar enough example despite quite some perusing. Many thanks, Michael
Specifying a repeated-measure design with 3 fully crossed within-subject factors
2 messages · Michael Cone
7 days later
So, maybe I abstracted this a little bit too much. The following is an
example I took from
Tamhane, A. C. and Hayter, A. J. (2004) Comparing Variances of Several
Measurement Methods Using a Randomized Block Design with Repeat
Measurements: A Case Study. In Advances in Ranking and Selection,
Multiple Comparisons, and Reliability, Balakrishnan, N., Kannan, N. and
Nagaraja, H. N. (Editors), Birkhauser, Boston, 165?178.
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The insertion gain of a hearing aid is defined as the difference
between the sound pressure level (SPL) measured at the eardrum of the
wearer with the hearing aid in place and the SPL at the eardrum with no
aid in place, the stimulus being the same under both conditions.
The study measured the insertion gain of a hearing aid at different
loudspeaker locations. The standard practice was to locate the
loadspeaker in the ear-level horizontal plane of the subject. It was
claimed that loudspeaker locations above the horizontal plane would
yield more precise (less variable) results.
The study compared the following loudspeaker locations:
- Location 0: 0? azimuth, 0? elevation (Standard/Control)
- Location 1: 45? azimuth, 0? elevation (New)
- Location 2: 0? azimuth, 90? elevation (New)
- Location 3: 45? azimuth 45? elevation (new)
There were 10 subjects with five replicate measurements of insertion
gain at each of the four loudspeaker locations.
The investigator was primarily interested in comparing the
within-subject variances for different loudspeaker locations
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Imagine this study being conducted with 4 different kinds of auditory
stimuli, each presented at the same combinations of azimuth and
elevation, with replicate measurements, all presented to 5 subjects. A
minimal reproducible example:
df <- expand.grid(meas.num = seq(1, 10),
elevation = c(0, 15, 30, 45, 60, 75, 90),
azimuth = c(0, 15, 30, 45),
stimuli = c("stim1", "stim2", "stim3", "stim4"),
subject = c("subj1", "subj2", "subj3", "subj4",
"subj5",
"subj6"))
df$sex <- "m"
df[df$subject %in% c("subj1", "subj2", "subj3"), ]$sex <- "f"
df$val <- rnorm(nrow(df), mean=10, sd=5) # dummy measurement values
Here, I would be interested in comparing
(1) the overall within-subject variances for each stimulus, as well as
(2) the within-subject variances between differing combinations of
azimuth & elevation both within the same stimulus and between differing
stimuli,
both within each sex and for both sexes.
I would greatly appreciate any comments, questions, or pointers in the
right direction.
Michael