I have following data from a cross-over trial where subjects were given 2 types of treatments separated by a washout period. For each treatment measurement was made in pre and post treatment period. I want to determine if one treatment produced a greater change than other while correcting for pre level and taking into account repeat subject participation. Sample data is as follows:
id tt pre post change
1 1 5 9 4
2 1 6 8 2
3 1 2 7 5
1 2 4 6 2
2 2 5 8 3
3 2 6 9 3
How can I analyze this? I thought of following possibilities:
aov(change ~ tt * pre + Error(id), data=mydata)
aov(change ~ tt * pre + Error(id/(tt*pre)), data=mydata)
lm(change ~ tt * pre + id, data=mydata)
lmer(change ~ 1 + tt * pre + (1 | id), data=mydata)
lmer(change ~ 1 + tt * pre + (tt * pre | id), data=mydata)
Which of the above (or something else) is the correct approach?
