Random effects caused by covariate

I have 10 machines that each gather 10 time series.
From fitting the same fixed effects model to each time series individually, I have noticed that there is both substantial within- and between machine variance of the estimated model parameters, (and the within machine variance seems to also vary between machines.)

I now want to fit a random effects model to all time series together. How can I express that the model parameters from one time series are correlated with the model parameters from the time series gathered by the same machine?

Hi Arno,

I had not seen your question. If it’s still releavnt, can you maybe describe your question in more detail? Correlation can be introduced by having a common component within a machine, but that coulld just be a normal random effect, so I’m not sure that’s what you’re asking.

Any chance you could put it in (pseudo-)math terms?