# Random effects, fixed effects, or perhaps nested fixed effects?

Simple question (I hope).

I have the following experimental design:

Two groups: A, B (let's say they represent the two sexes), where I randomly sampled 4 subjects from each group, and measured blood pressure of each subject 3 times (let's say in 3 random time points during the day)

Here's an R example of my data:

set.seed(1)
my.df <- data.frame(group = as.factor(c(rep("A",12),rep("B",12))),
subject = c(sapply(c("A","B"), function(x) c(sapply(1:4, function(y) rep(paste(x,y,sep="."),3))))),
measurement = c(c(sapply(rnorm(4,0,2), function(x) rnorm(3,x,1))),c(sapply(rnorm(4,0.2,1), function(x) rnorm(3,x,1)))))


What I want to test is whether the blood pressure is significantly different between the two groups, but I want to account for the random effects the subjects may have.

As far as I understand, if I had many more measurements for each subject the appropriate model would be a mixed effects model where the fixed effect is the group and the random effect is subject. For example, using the lme4 package this would be:

fit <- lmer(measurement ~ group + (1|subject), data = my.df)


But only having 3 measurements for each subject doesn't allow a powerful estimation of the random effect. So my question is what is the appropriate alternative?

1. Ignore subject and therefore use a fixed effects model.
2. Perhaps use subject as a nested fixed effect, if such a thing exists?
3. Any other alternatives

Thanks

• Use a two-stage least squares model, ie, just take the average of the three measurements (if you believe there is no within-subject temporal effect hence the measures are exchangeable). Since the number of observations you are averaging (3) is constant, you don't even need to use a weighted procedure for the second stage model. – Andrew M Jan 28 '16 at 20:43