February 26, The results below are generated from an R script.

Transcription

1 February 26, 2015 The results below are generated from an R script. weights = read.table(" header = T) R functions: aov(y~a+b+a:b, data=mydata) or aov(y~a*b, data=myd interaction.plot, model.tables weights.aov = aov(gain ~ diet * supplement, data = weights) summary(weights.aov) Df Sum Sq Mean Sq F value Pr(>F) diet e-14 *** supplement e-07 *** diet:supplement Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 model.tables(weights.aov, "mean") Tables of means Grand mean diet diet barley oats wheat supplement supplement agrimore control supergain supersupp diet:supplement supplement diet agrimore control supergain supersupp barley oats wheat model.tables(weights.aov, type = "effects") Tables of effects diet diet 1

2 barley oats wheat supplement supplement agrimore control supergain supersupp diet:supplement supplement diet agrimore control supergain supersupp barley oats wheat attach(weights) The following objects are masked from weights (pos = 7): diet, gain, supplement interaction.plot(diet, supplement, gain) mean of gain supplement supersupp agrimore control supergain barley oats wheat diet plot.design(gain ~ diet * supplement, data = weights) 2

3 barley mean of gain oats agrimore supersupp control supergain wheat diet supplement Factors temp = model.tables(weights.aov, type = "means", se = T) lsms = temp[[1]]$"diet:supplement" barplot(lsms, beside = T, col = 1:3) legend(6.5, 27, c("barley", "oats", "wheat"), fill = 1:3) barley oats wheat agrimore control supergain supersupp 3

4 # or use locator to decide where to add the legend legend(locator(1), c('barley', 'oats', # 'wheat'), fill=1:3) error.bars = function(yv, se, names = NULL) { ncol = ifelse(is.matrix(yv), nrow(yv), length(yv)) names = ifelse(is.null(names), colnames(yv), names) xv = barplot(yv, beside = T, col = 1:ncol, plot = F) barplot(yv, beside = T, xlim = c(min(xv), max(xv) * 1.3), ylim = c(0, max(yv) + max(se)), names = colnames(yv), ylab = deparse(substitute(yv)), col = 1:ncol) for (i in 1:length(xv)) { arrows(xv[i], yv[i] + se[i], xv[i], yv[i], angle = 90, code = 1, length = 0.05, lwd = 2) } names = ifelse(is.matrix(yv), rownames(yv), names(yv)) legend(x = max(xv) * 1.05, y = max(yv), rownames(yv), fill = 1:ncol) } temp = model.tables(weights.aov, type = "means", se = T) lsms = temp[[1]]$"diet:supplement" sig = sqrt(sum((resid(weights.aov))^2)/weights.aov$df.residual) nrep = table(weights$diet, weights$supplement) se = sig/sqrt(nrep) error.bars(lsms, se) lsms barley oats wheat agrimore control supergain supersupp # multiple comparisons library(multcomp) has more functions TukeyHSD(weights.aov, which = "diet") Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = gain ~ diet * supplement, data = weights) 4

5 $diet diff lwr upr p adj oats-barley wheat-barley wheat-oats TukeyHSD(weights.aov, which = "supplement") Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = gain ~ diet * supplement, data = weights) $supplement diff lwr upr p adj control-agrimore supergain-agrimore supersupp-agrimore supergain-control supersupp-control supersupp-supergain TukeyHSD(weights.aov, which = "diet:supplement") Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = gain ~ diet * supplement, data = weights) $`diet:supplement` diff lwr upr p adj oats:agrimore-barley:agrimore wheat:agrimore-barley:agrimore barley:control-barley:agrimore oats:control-barley:agrimore wheat:control-barley:agrimore barley:supergain-barley:agrimore oats:supergain-barley:agrimore wheat:supergain-barley:agrimore barley:supersupp-barley:agrimore oats:supersupp-barley:agrimore wheat:supersupp-barley:agrimore wheat:agrimore-oats:agrimore barley:control-oats:agrimore oats:control-oats:agrimore wheat:control-oats:agrimore barley:supergain-oats:agrimore oats:supergain-oats:agrimore wheat:supergain-oats:agrimore barley:supersupp-oats:agrimore oats:supersupp-oats:agrimore wheat:supersupp-oats:agrimore barley:control-wheat:agrimore oats:control-wheat:agrimore wheat:control-wheat:agrimore

6 barley:supergain-wheat:agrimore oats:supergain-wheat:agrimore wheat:supergain-wheat:agrimore barley:supersupp-wheat:agrimore oats:supersupp-wheat:agrimore wheat:supersupp-wheat:agrimore oats:control-barley:control wheat:control-barley:control barley:supergain-barley:control oats:supergain-barley:control wheat:supergain-barley:control barley:supersupp-barley:control oats:supersupp-barley:control wheat:supersupp-barley:control wheat:control-oats:control barley:supergain-oats:control oats:supergain-oats:control wheat:supergain-oats:control barley:supersupp-oats:control oats:supersupp-oats:control wheat:supersupp-oats:control barley:supergain-wheat:control oats:supergain-wheat:control wheat:supergain-wheat:control barley:supersupp-wheat:control oats:supersupp-wheat:control wheat:supersupp-wheat:control oats:supergain-barley:supergain wheat:supergain-barley:supergain barley:supersupp-barley:supergain oats:supersupp-barley:supergain wheat:supersupp-barley:supergain wheat:supergain-oats:supergain barley:supersupp-oats:supergain oats:supersupp-oats:supergain wheat:supersupp-oats:supergain barley:supersupp-wheat:supergain oats:supersupp-wheat:supergain wheat:supersupp-wheat:supergain oats:supersupp-barley:supersupp wheat:supersupp-barley:supersupp wheat:supersupp-oats:supersupp With randome effects, lmer in libraries lme4 and lmertest The function aov well for unbalanced design The following data are taken from Sec 2.5 of SAS System for Mixed Models, by Little et al. It is a split-plot design with cult assigned to the whole-plots and inoc to the sub-plots. Compared it witth SAS proc mixed cultivar = read.table(" header = T) names(cultivar) = c("block", "cult", "inoc", "drywt") str(cultivar) # to check variable attributes 'data.frame': 24 obs. of 4 variables: $ block: int

7 $ cult : Factor w/ 2 levels "a","b": $ inoc : Factor w/ 3 levels "con","dea","liv": $ drywt: num cultivar$block = as.factor(cultivar$block) library(lmertest) cultivar.lmer = lmer(drywt ~ cult + inoc + cult * inoc + (1 block/cult), data = cultivar, REML = F) anova(cultivar.lmer) Analysis of Variance Table of type 3 with Satterthwaite approximation for degrees of freedom Df Sum Sq Mean Sq F value Denom Pr(>F) cult inoc e-10 *** cult:inoc Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 lsmeans(cultivar.lmer) Least Squares Means table: cult inoc Estimate Standard Error DF t-value Lower CI Upper CI p-value cult a 1.0 NA <2e-16 cult b 2.0 NA <2e-16 inoc con NA <2e-16 inoc dea NA <2e-16 inoc liv NA <2e-16 cult:inoc a con <2e-16 cult:inoc b con <2e-16 cult:inoc a dea <2e-16 cult:inoc b dea <2e-16 cult:inoc a liv <2e-16 cult:inoc b liv <2e-16 cult a *** cult b *** inoc con *** inoc dea *** inoc liv *** cult:inoc a con *** cult:inoc b con *** cult:inoc a dea *** cult:inoc b dea *** cult:inoc a liv *** cult:inoc b liv *** --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 difflsmeans(cultivar.lmer, test.effs = "inoc") Differences of LSMEANS: Estimate Standard Error DF t-value Lower CI Upper CI p-value inoc con-dea e-04 *** inoc con-liv <2e-16 *** inoc dea-liv <2e-16 *** 7

8 --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 temp = difflsmeans(cultivar.lme, test.effs = "cult:inoc")[[1]] Error: object cultivar.lme not found aov works here too because it is a balanced design, not recommended cultivar.aov = aov(drywt ~ cult + inoc + cult * inoc + Error(block/cult), data = cultivar, qr = T) summary(cultivar.aov) Error: block Df Sum Sq Mean Sq F value Pr(>F) Residuals Error: block:cult Df Sum Sq Mean Sq F value Pr(>F) cult Residuals Error: Within Df Sum Sq Mean Sq F value Pr(>F) inoc e-08 *** cult:inoc Residuals Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 table(cultivar$cult, cultivar$inoc, cultivar$block),, = 1 con dea liv a b 1 1 1,, = 2 con dea liv a b 1 1 1,, = 3 con dea liv a b 1 1 1,, = 4 8

9 con dea liv a b The R session information (including the OS info, R version and all packages used): sessioninfo() R version ( ) Platform: x86_64-w64-mingw32/x64 (64-bit) locale: [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 [3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C [5] LC_TIME=English_United States.1252 attached base packages: [1] stats graphics grdevices utils datasets methods base other attached packages: [1] lmertest_2.0-0 lme4_1.0-4 lattice_ Matrix_1.1-4 knitr_1.5 loaded via a namespace (and not attached): [1] bitops_1.0-6 catools_1.14 cluster_ evaluate_0.5.1 [5] formatr_0.9 gdata_ gplots_ grid_3.1.1 [9] gtools_3.1.0 highr_0.2.1 Hmisc_ KernSmooth_ [13] MASS_ minqa_1.2.1 nlme_ numderiv_ [17] pbkrtest_0.3-7 rpart_4.1-8 splines_3.1.1 stringr_0.6.2 [21] tools_3.1.1 Sys.time() [1] " :50:26 EST" 9