Dear all,
A friend of mine requested me to analyze some data she has generated. I
am hoping for some advice on best way of properly analyzing the data as
I have never worked with such complicated or nested designs.
Here is the setup. She has taken material from 5 animals and each
material is subdivided into 6 plate (30 plates in total). Each plate is
then assigned as either a control or a treated with a chemical AND kept
at one of three concentrations. A sample is taken daily from each plate
for six continuous days and measured (180 measurement in total). Her
main question is whether treatment has an effect.
Here is a simulated dataset:
df <- expand.grid( animal=LETTERS[1:5], group=c("Control",
"Treated"),
conc=c("X", "Y", "Z"),
day=1:6 )
df$plate <- as.numeric(factor(apply(df[ ,1:3], 1, paste,
collapse="")))
df <- df[ order(df$plate), ]
df$plate <- as.factor(df$plate)
rownames(df) <- NULL
set.seed(1066)
df$value <- runif(90, 1, 2)*(df$group=="Control") +
c(0, -0.5, -0.20)[as.numeric(df$conc)] +
rnorm(30)[ as.numeric(df$plate) ] +
runif(180, 0.9, 1.1)*df$day + rnorm(180, sd=0.5)
df[1:10, ]
animal group conc day plate value
1 A Control X 1 1 3.3403510
2 A Control X 2 1 5.1042965
3 A Control X 3 1 5.4003462
...
...
178 E Treated Z 4 30 2.8558186
179 E Treated Z 5 30 4.4567206
180 E Treated Z 6 30 5.4542460
I have tried analyzing the data as follows:
library(lme4)
lmer( value ~ group + day + conc + (1 | animal/plate), data=df )
lmer( value ~ group + day + conc + (1 | animal), data=df )
lmer( value ~ group + day + conc + (1 | plate), data=df )
BUT I am not sure which of the models above is appropriate. Any advice
would be very useful. Many thanks in advance.
Regards, Adai