Not sure the right place to ask this question but struggling with specifying the correct notation and wording for my linear mixed model.
Problem set up:
I have a set number of biological replicates (any number doesn't matter), each biological replicate has 3 technical replicates. I want to estimate random effect for the biological replicate while controlling for fixed factors: batch & lane
I've completed this using asreml by modeling the random effect to have a normal distribution with variance equal to the Ainverse:
asreml(fixed= txpt ~1 + batch + lane random = ~ ped(animal_id,var=T,init=1), ginverse=list(animal_id=ainv2),data=tip.subset, family=asreml.gaussian(link = "identity"))
How can I translate this into matrix notation? Here is my personal shot:
Y= Xb + Zu + e
where y is a vector of observations across all technical replicates X & Z are incidence matrices for the fixed and random effects respectively b & u are the fixed (batch and lane) and random (biological replicate) effects to be estimated
Any guidance is much appreciated!