Hi all, 

The problem I want to solve is as follows. Suppose that we have repeated
measurements per cluster. Y is the outcome variable, x is a single binary
covariate cluster constant, id represents each cluster  and we have an
unbalanced design of the following form and arbitrary number of clusters 

Y         x     id

 

Y_11     1      1

Y_12     1      1

Y_13     1      1

Y_14     1      1

Y_21     0      2

Y_22     0      2

Y_23     0      2

Y_24     0      2

Y_25     0      2

Y_26     0      2

 ....    ....    ....

 ....    ....    ....

 ....    ....    ....

where Y_jj respresents the jth measurement I the ith cluster. The first
impression is that a simple model of the form

 

Yij=beta_0+ b_i +beta_1x_i +epsilon_ij,     bi~N(0,sigmab^2)  

 

would suffice.

 

However a special feature of the data renders this model inappropriate:
There seems to be a connection between  the cluster size and the outcome Y
which is not capture fully by the model above. So what I want to do is to
"pretend" that there are some "super clusters"  at the top level for some
groups of cluster sizes. For example :

 

cluster sizes (and clusters...)    "super cluster "

1-3
1

4-6                                                  2

7-10                                                3

 

What I want to do is to fit a model with different random effects for each
super cluster (denoted by the indicator k, so the measurements would now be
of the form Y_ijk)

The model I imagine would then be of the form

 

Yijk=beta_0+ b_ik +beta_1x_i +epsilon_ijk,     bik~N(0,sigmab_k^2)  

 

So for each super cluster include a different random effect that *could*
capture  the association above.

 

I haven't managed to fit such a model in R using lmer or lme, nor to find a
similar case in the help archives so I would be grateful if anybody could
help.

 

Thank you,

 

Menelaos Pavlou

UCL

Centre for Sexual health and HIV research

 

 


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