Multivariate analysis of variance (MANOVA)
TODO
- link to multLDA, anovaSStypes
Install required packages
wants <- c("car", "mvtnorm")
has <- wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])One-way MANOVA
set.seed(123)
P <- 3
Nj <- c(15, 25, 20)
Sigma <- matrix(c(16,-2, -2,9), byrow=TRUE, ncol=2)
mu11 <- c(-4, 4)
mu21 <- c( 3, 3)
mu31 <- c( 1, -1)
library(mvtnorm)
Y11 <- round(rmvnorm(Nj[1], mean=mu11, sigma=Sigma))
Y21 <- round(rmvnorm(Nj[2], mean=mu21, sigma=Sigma))
Y31 <- round(rmvnorm(Nj[3], mean=mu31, sigma=Sigma))
dfMan1 <- data.frame(Y =rbind(Y11, Y21, Y31),
IV=factor(rep(1:P, Nj))) Df Wilks approx F num Df den Df Pr(>F)
IV 2 0.38675 17.024 4 112 6.222e-11 ***
Residuals 57
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(manRes1, test="Roy")
summary(manRes1, test="Pillai")
summary(manRes1, test="Hotelling-Lawley")Two-way MANOVA
Q <- 2
mu12 <- c(-1, 4)
mu22 <- c( 4, 8)
mu32 <- c( 4, 0)
library(mvtnorm)
Y12 <- round(rmvnorm(Nj[1], mean=mu12, sigma=Sigma))
Y22 <- round(rmvnorm(Nj[2], mean=mu22, sigma=Sigma))
Y32 <- round(rmvnorm(Nj[3], mean=mu32, sigma=Sigma))
dfMan2 <- data.frame(Y =rbind(Y11, Y21, Y31, Y12, Y22, Y32),
IV1=factor(rep(rep(1:P, Nj), Q)),
IV2=factor(rep(1:Q, each=sum(Nj))))Type I sum of squares
Df Pillai approx F num Df den Df Pr(>F)
IV1 2 0.81891 39.521 4 228 < 2.2e-16 ***
IV2 1 0.24055 17.896 2 113 1.771e-07 ***
IV1:IV2 2 0.14550 4.472 4 228 0.001693 **
Residuals 114
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(manRes2, test="Wilks")
summary(manRes2, test="Roy")
summary(manRes2, test="Hotelling-Lawley")Type II/III sum of squares
library(car)
fitIII <- lm(cbind(Y.1, Y.2) ~ IV1*IV2, data=dfMan2,
contrasts=list(IV1=contr.sum, IV2=contr.sum))
ManRes <- Manova(fitIII, type="III")
summary(ManRes, multivariate=TRUE)
Type III MANOVA Tests:
Sum of squares and products for error:
Y.1 Y.2
Y.1 1657.963 -349.19
Y.2 -349.190 982.94
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
Y.1 Y.2
Y.1 188.0783 412.0900
Y.2 412.0900 902.9119
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.5664167 73.80943 2 113 < 2.22e-16 ***
Wilks 1 0.4335833 73.80943 2 113 < 2.22e-16 ***
Hotelling-Lawley 1 1.3063616 73.80943 2 113 < 2.22e-16 ***
Roy 1 1.3063616 73.80943 2 113 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: IV1
Sum of squares and products for the hypothesis:
Y.1 Y.2
Y.1 782.9783 62.5900
Y.2 62.5900 891.4717
Multivariate Tests: IV1
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.8189128 39.52124 4 228 < 2.22e-16 ***
Wilks 2 0.3355622 41.03532 4 226 < 2.22e-16 ***
Hotelling-Lawley 2 1.5197264 42.55234 4 224 < 2.22e-16 ***
Roy 2 1.1019821 62.81298 2 114 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: IV2
Sum of squares and products for the hypothesis:
Y.1 Y.2
Y.1 193.3413 116.25319
Y.2 116.2532 69.90128
Multivariate Tests: IV2
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.2043019 14.50683 2 113 2.4676e-06 ***
Wilks 1 0.7956981 14.50683 2 113 2.4676e-06 ***
Hotelling-Lawley 1 0.2567580 14.50683 2 113 2.4676e-06 ***
Roy 1 0.2567580 14.50683 2 113 2.4676e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: IV1:IV2
Sum of squares and products for the hypothesis:
Y.1 Y.2
Y.1 39.72500 -69.36667
Y.2 -69.36667 158.57167
Multivariate Tests: IV1:IV2
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.1455029 4.472193 4 228 0.00169258 **
Wilks 2 0.8553409 4.591223 4 226 0.00139073 **
Hotelling-Lawley 2 0.1681379 4.707860 4 224 0.00114750 **
Roy 2 0.1620497 9.236832 2 114 0.00019151 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Detach (automatically) loaded packages (if possible)
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