Thank you! (In part, for such faith in my abilities:) Have to go hunt myself a programmer for dinner...)
It seems that if M-r 1 gives M-r 2 the same subsample of the middle latent variables (photoes of fields of vision, scoring them gives you the datapoints), and the x1 is compared with x2, they can see the least difference between them, which is (largely?) sample-independent. If, however, M-r 1 and M-r 2 each draw their subsamples independently, the difference between x1 and x2 should be larger due to chance, right?.. So if we look at the difference in differences between x1and x2, and it is greater for some middle latent variables (ways of staining) than for others, can we use it as a measure of 'the overall variability of the measuring method'? Say, if we have ten measurers and four measuring methods...
(I'm asking you this because it is relatively simple to do in practice, not because I think this would be the most efficient way.)
You can estimate the bias of each measurer much more efficiently if you have them measure the same sample, yes, analogous to crossover: now the differences are due less to the wide diversity of the sampled population and more to the particular measurer.
(To put it a little more mathily, when each measurer measures different samples, then the measurements will be spread very widely because it's Var(measurer-bias) + Var(population); but if we have the measurers measure the same sample, then Var(population) drops out and now there's just Var(measurer-bias). If...
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