(Generalized) linear mixed models in R for continous and categorical traits for animal models #R

(G)LMM - R

#### (Generalized) linear mixed models in R for continous and categorical traits for animal models ###
#
# General TasK: Fit (G)LMM in R for an animal model with hundreds 
# of thousands of observations.
# This is generally a feasable task, as the pedigree-based covariance structure of
# the main random term is very sparse (A-Inverse).
# Nevertheless, this is far from trivial directly in R and there are a lot of 
# caveats. 
#
# Problems:
# 1) Storing large (although sparse) matrices in R
#
# The problem that arises here is not memory but the way indices are stored
# in common R. Integers can only store 2^31 elements, which used to be the 
# size limitation for vectors in R before R-3.0.0. This limitation has been
# removed (indices for long vectors are now being stored differently, partly as 
# doubles), but packages like 'Matrix', 'Rcpp' and 'RcppEigen' are still restricted
# to integer indices.
#
# 2) Matrix operations using 'Matrix'-package
#
# Matrix is a great package and relies on the C-library 'cholmod'.
# Yet again we face the integer problem, but cholmod offers 'long long' versions
# for every single function - so it is not cholmod but the Matrix-package that stands in
# our way. For too long vectors it will throw an error saying something like "problem too large...".
#
# 3) Mixed Model packages
#
# 'lme4'
# The standard package for that task is 'lme4', which (out of the box) does not support defining 
# user defined covariance structures or directly passing design matrices.
# 'pedigreemm' is supposed to overcome that limitation exactly for the purpose of fitting
# animal models. It offers lightning fast computation of the cholesky and Inverse of A, which
# is right what we need. The function 'editPed' adds missing individuals to the pedigree and orders
# it according to generations. That is painfully slow implemented - install this modified package
# to overcome the problem: https://github.com/cheuerde/pedigreemm
# Unfortunately it turns out that pedigreemm is still not suitable for big animal models.
# lme4 is too big to get an idea of what is going on in every step, but my guess is that 
# a lot of overhead is generated due to verbosing and checking stuff.
#
# 'MCMCglmm'
# Probably one of the most versatile and useful packages out there. It allows you to fit any
# model that one might desire (multivariate, any distribution, covariance structeres, ...).
# It is a gibbs sampler but still reasonably fast, and it does what lme4 fails to do:
# Running big animal models (500k observations).
# It also comes with a variety on pedigree functions, but pedigreemm is very nice in that
# respect too. So it is a good idea to do the pedigree processing using pedigreemm and fit 
# the model using MCMCglmm.
#
# 'BGLR'
# Another way is to use BGLR, which was not built for that purpose but it is general enough to 
# do the job. The main problem is that is does not take sparse design matrices...

ped <- pedigree(sire = c(NA,NA,1, 1,4,5),
dam = c(NA,NA,2,NA,3,2), label= 1:6)