Dear all,

I know this had been discussed in the past, but will appreciate some help
in setting a simple multiple membership model for my data, to get me
started...

Data comes from a production line that work in shifts. The response
variable is a measure of productivity (basically a the amount of material
that was processed, with some normalization. This seems to have near normal
distribution). In each shift there are 4 workers out of a pool of about 12.
the combination of workers is not determined randomly, but it has no
seeming order or simple selection rule. Basically all possible combinations
of workers are possible, and many of them actually occur. I assume that
productivity determined by the workload (a shift level variable) and by the
skill/motivation/mood/whatever of the workers of the shift. I assume that
each worker has a basic "ability" and their contribution in each shift is
normally distributed around that skill level.

so the equation I'm looking at looks like that:

productivity_i = workload_i + sigma{ j in workers(i)} (skill_j + u_j) + e_i

where u_j is normally distributed with mean 0 and s.d. sigma_j (that needs
to be estimated)
I can assume sigma_j are all equal (an initially unknow), but prefer they'd
be estimated, and can probably supply some distribution from which they are
sampled)

since every shift has exactly 4 members with similar roles, I see no reason
to add explicit weights, but I can create variable w_ij whose value is 0.25
if worker_j participates in shift_i and 0 otherwise. under this notation:
productivity_i = workload_i +sigma{all j}(skill_j*w_ij) + sigma{all
j}(u_j*w_ij) + e_i

can you help me write the right syntax for estimating this model using
MCMCglmm? lmer? (which is better?)

is there any recommended references/material on the web that discuss such
models in more depth without assuming much prior knowledge?

Thanks in advance,

Amit

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