In most mixed linear model packages (e.g. asreml, lme4, nlme, etc) one needs to specify only the model equation (the bit that looks like y ~ factors...) when fitting simple models. We explicitly say nothing about the covariances that complete the model specification. This is because most linear mixed model packages assume that, in absence of any additional information, the covariance structure is the product of a scalar (a variance component) by a design matrix. For example, the residual covariance matrix in simple models is R = I σe2, or the additive genetic variance matrix is G = A σa2 (where A is the numerator relationship matrix), or the covariance matrix for a random effect f with incidence matrix Z is Z‘ Z σf2.
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Month: October 2011 (Page 1 of 5)
Back to posting after a long weekend and more than enough rugby coverage to last a few years. Anyway, back to linear models, where we usually assume normality, independence and homogeneous variances. In most statistics courses we live in a fantasy world where we meet all of the assumptions, but in real life—and trees and forests are no exceptions—there are plenty of occasions when we can badly deviate from one or more assumptions. In this post I present a simple example, where we have a number of clones (genetically identical copies of a tree), which had between 2 and 4 cores extracted, and each core was assessed for acoustic velocity (we care about it because it is inversely related to longitudinal shrinkage and its square is proportional to wood stiffness) every two millimeters. This small dataset is only a pilot for a much larger study currently underway.
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There are several blog posts, websites (and even books) explaining the transition from using another statistical system (e.g. SAS, SPSS, Stata, etc) to relying on R. Most of that material treats the topic from the point of view of i- an individual user and ii- a researcher. This post explains some of the issues involved in, first, moving several users and, second, with an emphasis in teaching.
I have made part of this information available before, but I wanted to update it and keep it together with all the other posts in Quantum Forest. The process started in March 2009.
Last Wednesday I had a meeting with the folks of the New Zealand Drylands Forest Initiative in Blenheim. In addition to sitting in a conference room and having nice sandwiches we went to visit one of our progeny trials at Cravens. Plantation forestry trials are usually laid out following a rectangular lattice defined by rows and columns. The trial follows an incomplete block design with 148 blocks and is testing 60 Eucalyptus bosistoana families. A quick look at survival shows an interesting trend: the bottom of the trial was much more affected by frost than the top.
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Yesterday morning at 7 am I was outside walking the dog before getting a taxi to go to the airport to catch a plane to travel from Christchurch to Blenheim (now I can breath after reading without a pause). It was raining cats and dogs while I was walking doggyo, thinking of a post idea for Quantum Forest; something that I could work on without a computer. Then I remembered that I told Tal Galili that I would ‘mention r-bloggers’ in a future post. Well, Tal, this is it.