Hi.
I would like to run a mixed effects model, but there's one aspect of
the model that I don't know how to code. My goal is to analyze data
from an experiment in which I tested the swimming performance (i.e.,
Umax) of two species of fish from 4 different lakes (a sample of the
data is below). Each fish was tested when it was rested and when it
was tired, and each test was performed at the fishes' acclimation
temperature and at an elevated test temperature. So, there are four
repeated measures for each subject (i.e., fish). The effects are
hierarchical and can be listed as such:
Lake (random effect with 4 levels)
Species (fixed effect with 2 levels) nested within Lake
Subject (random effect) nested within Species
Temperature (fixed effect with 2 levels) nested within Subject,
crossed with Fatigue
Fatigue (fixed effect with 2 levels) nested within Subject, crossed
with Temperature
So, using the lme function, the model should look something like this:
z <- lme(Umaxcm ~ Species*Temp*Fatigue, random= ~ 1 | Lake/Species/Sub/
(Temp*Fatigue))
The problem is how to specify that the Temp*Fatigue factorial
treatments are nested within Subject (each subject was tested at both
temperatures at both fatigue levels). Using the above formula is not
correct (it gives the error message: Invalid formula for groups).
If I use the following formula, lme returns a df value that is three
times higher than it should be for the tests of the effect of
temperature and fatigue (i.e., it considers repeated measures on a
single individual as independent):
z <- lme(Umaxcm ~ Species*Temp*Fatigue, random= ~ 1 | Lake/Species/Sub)
If I use the following formula, lme returns a df value that is twice
as high as it should be for the test of the effect of Fatigue:
z <- lme(Umaxcm ~ Species*Temp*Fatigue, random= ~ 1 | Lake/Species/Sub/
Temp/Fatigue)
Can anyone please help me figure out how to code this model so that
the effects of Temperature and Fatigue are tested properly?
Here's the sample data:
Sub Lake Species Temp Umaxcm Fatigue
1 PWD1 PWD E acclim 41.83 rested
2 PWD1 PWD E acclim 35.08 tired
3 PWD1 PWD E test 42.00 rested
4 PWD1 PWD E test 31.75 tired
5 PWD2 PWD H acclim 39.58 rested
6 PWD2 PWD H acclim 44.92 tired
7 PWD2 PWD H test 51.00 rested
8 PWD2 PWD H test 47.08 tired
Sincerely,
Jon Mee
UBC Dept. of Zoology
Vancouver, BC
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