However, each method has additionally a unique set of fixed or random effects (A,B,...), which are related to the special method and correct for bias (c.f. attached figure). The general structure of the data thus would be :

Y Method X A B C

-----------------------------------------

3 M1 2 6 NA NA

4 M1 4 4 NA NA

4 M2 1 NA 5 NA

3 M3 4 NA NA 4

...

Is it possible to analyze these pooled data simultaneously, introducing the method as a fixed or random coefficient, although we have these “exclusive variables”? I don’t know how, since each unique variable creates NA’s for two of the methods, thus we have NA’s in every row leading to an exclusion of all data from the regression analysis...

Thanks for your suggestions