Quantum Forest

One of the big changes coming from quantitative genetics is the emphasis on fixed over random effects. In genetics the idea is to partition observed variance in different effects that can be related to “causes” (additivity, dominance, etc). Now variances are mostly nuisance parameters, and the main objective is to estimate the effect of different treatments (e.g. fertilisers or silviculture) on growth. For now I am using the typical Likelihood Ratio Test for the variances and Wald’s tests for the fixed effects. This works OK under Restricted (or residual) Maximum Likelihood (REML), but the problem is how to run multiple comparisons or specific contrasts, where I need to recur to approximations. This seems to be the price to pay for the flexibility of working with unbalance and accessing many different covariance structures.

So, what are the approaches that I am using at the moment? In Splus, I use lme to fit the models and then create whatever contrast matrix I want and use the L option in anova to test that contrast. In GenStat, I use reml with vkeep to save some of the output to then use pairtest. I need to figure out how to save the level of replication for each level and then I could use allpairwise. It seems that using these approximations is not a capital sin, but just a peccadillo.