# Analyzing a simple experiment with heterogeneous variances using asreml, MCMCglmm and SAS

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I was working with a small experiment which includes families from two *Eucalyptus* species and thought it would be nice to code a first analysis using alternative approaches. The experiment is a randomized complete block design, with species as fixed effect and family and block as a random effects, while the response variable is growth strain (in \( \mu \epsilon\)).

When looking at the trees one can see that the residual variances will be very different. In addition, the trees were growing in plastic bags laid out in rows (the blocks) and columns. Given that trees were growing in bags siting on flat terrain, most likely the row effects are zero.

Below is the code for a first go in R (using both MCMCglmm and ASReml-R) and SAS. I had stopped using SAS for several years, mostly because I was running a mac for which there is no version. However, a few weeks ago I started accessing it via their OnDemand for Academics program via a web browser.

The R code using REML looks like:

# Options options(stringsAsFactors = FALSE) setwd('~/Dropbox/research/2013/growth-stress') # Packages require(ggplot2) require(asreml) require(MCMCglmm) # Reading data, renaming, factors, etc gs = read.csv('eucalyptus-growth-stress.csv') summary(gs) # Both argophloia and bosistoana gsboth = subset(gs, !is.na(strain)) gsboth = within(gsboth, { species = factor(species) row = factor(row) column = factor(column) fam = factor(fam) }) ma = asreml(strain ~ species, random = ~ fam + row, rcov = ~ at(species):units, data = gsboth) summary(ma)$varcomp # gamma component std.error z.ratio constraint #fam!fam.var 27809.414 27809.414 10502.036 2.6480022 Positive #row!row.var 2337.164 2337.164 3116.357 0.7499666 Positive #species_E.argopholia!variance 111940.458 111940.458 26609.673 4.2067580 Positive #species_E.bosistoana!variance 63035.256 63035.256 7226.768 8.7224681 Positive |

While using MCMC we get estimates in the ballpark by using:

# Priors bothpr = list(R = list(V = diag(c(50000, 50000)), nu = 3), G = list(G1 = list(V = 20000, nu = 0.002), G2 = list(V = 20000, nu = 0.002), G3 = list(V = 20000, nu = 0.002))) # MCMC m2 = MCMCglmm(strain ~ species, random = ~ fam + row + column, rcov = ~ idh(species):units, data = gsboth, prior = bothpr, pr = TRUE, family = 'gaussian', burnin = 10000, nitt = 40000, thin = 20, saveX = TRUE, saveZ = TRUE, verbose = FALSE) summary(m2) # Iterations = 10001:39981 # Thinning interval = 20 # Sample size = 1500 # # DIC: 3332.578 # # G-structure: ~fam # # post.mean l-95% CI u-95% CI eff.samp # fam 30315 12211 55136 1500 # # ~row # # post.mean l-95% CI u-95% CI eff.samp # row 1449 5.928 6274 589.5 # # R-structure: ~idh(species):units # # post.mean l-95% CI u-95% CI eff.samp # E.argopholia.units 112017 71152 168080 1500 # E.bosistoana.units 65006 52676 80049 1500 # # Location effects: strain ~ species # # post.mean l-95% CI u-95% CI eff.samp pMCMC # (Intercept) 502.21 319.45 690.68 1500 <7e-04 *** # speciesE.bosistoana -235.95 -449.07 -37.19 1361 0.036 * |

The SAS code is not that disimilar, except for the clear demarcation between data processing (data step, for reading files, data transformations, etc) and specific procs (procedures), in this case to summarize data, produce a boxplot and fit a mixed model.

* termstr=CRLF accounts for the windows-like line endings of the data set; data gs; infile "/home/luis/Projects/euc-strain/growthstresses.csv" dsd termstr=CRLF firstobs=2; input row column species $ family $ strain; if strain ^= .; run; proc summary data = gs print; class species; var strain; run; proc boxplot data = gs; plot strain*species; run; proc mixed data = gs; class row species family; model strain = species; random row family; repeated species / group=species; run; /* Covariance Parameter Estimates Cov Parm Group Estimate row 2336.80 family 27808 species species E.argoph 111844 species species E.bosist 63036 */ |

I like working with multiple languages and I realized that, in fact, I missed SAS a bit. It was like meeting an old friend; at the beginning felt strange but we were quickly chatting away after a few minutes.

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