We discussed adding a "batch" variable in the individual regression to alleviate some violation of the independence assumption (hence the term pseudo). For example, a diff between sample 3 and 2 would have 3 as the batch number (rule of thumb: take the first sample id).
I thought about considering this variable as a random effect term, but the independence assumption there is not quite what we want. For instance, within the neighborhood of 3, these differences (e.g. 3-2, 3-5, 3-6) are independent. However, they may not be independent of other differences in a different neighborhood (e.g. 2-5). In short, we have within-neighborhood independence but not between-neighborhood (which a mixed model would correct for).
Maybe we should stick with the fixed model and adding the batch variable as a fixed effect term.
We discussed adding a "batch" variable in the individual regression to alleviate some violation of the independence assumption (hence the term pseudo). For example, a diff between sample 3 and 2 would have 3 as the batch number (rule of thumb: take the first sample id).
I thought about considering this variable as a random effect term, but the independence assumption there is not quite what we want. For instance, within the neighborhood of 3, these differences (e.g. 3-2, 3-5, 3-6) are independent. However, they may not be independent of other differences in a different neighborhood (e.g. 2-5). In short, we have within-neighborhood independence but not between-neighborhood (which a mixed model would correct for).
Maybe we should stick with the fixed model and adding the batch variable as a fixed effect term.