Greetings

I could use some help thinking through a random effects design question.

A student came with data that is an intervention study. Quite a few
variables were collected on each of 4 weekly visits, before the
intervention. There were 2 intervention levels, A and B. After that, there
were 3 followup visits.  The research question is "does either A or B have
an effect on Y, taking into account the baseline levels established by the
4 preliminary measurements."


Visualize like that

ID  Time  Treatment  StudyTime X1 Y1 Y2
1    1         0                     0            23  44  40
1    2         0                     0            10  33  21
1    3         0                     0            33 44  50
1    4         0                     0              . . .
1    5         A                    1
1    6         A                    2
1    7         A                    3
2    1         0                     0
2    2         0                     0
2    3         0                     0
2    4         0                     0
2    5         B                    1
2    6         B                    2
2    7         B                    3

Note that in the 4 pre-treatment points, I have the value of Treatment set
at 0, as if to assume there can be no effect from a treatment which has not
yet been applied.

Plots indicate the subjects are not homogeneous (intra-individual
differences), so I'm thinking a random intercept is in order.

What lmer formula would you write out? Maybe check for coarse treatment
effect

lmer(Y1 ~ Treatment + X1 + (1 | ID), data = dat)

I was thinking of enforcing the idea that the pre-treatment scores should
be assumed to have the same expected value and estimate a bent line change

lmer(Y1 ~ Treatment * StudyTime + X1 + (1 | ID), data = dat)

I'd be grateful for any ideas you have to share, or pointers to
articles/books we should get.

I do not have the data in hand, I may get it soon, I may be able to answer
your "what happens if" questions.

Here are some bits I'm curious about, I expect you see lots of other
troubles:

1. There are 4 pre-treatment values, and 3 post-treatment values.  What
problems flow from that imbalance?

Some here suggest we take the easy road and calculate a pre-treatment mean
and a post-treatment mean and then model the difference.

2. My formula above estimate the random effect with all 7 time points. My
intuition is that it should be based on 4 scores in the baseline period,
and then applied as an estimate in the following periods.  What magic words
am I missing here?

So far, we've been playing with the monkey-business of missing observations
and how to best do multiple imputations. That turns out to be not obvious
or easy, but we make some headway.  There are 10 "complete" imputed
datasets in the long format.

pj
-- 
Paul E. Johnson
Professor, Political Science      Assoc. Director
1541 Lilac Lane, Room 504      Center for Research Methods
University of Kansas                 University of Kansas
http://pj.freefaculty.org               http://quant.ku.edu

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