WeightLoss: Weight Loss Data
In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

Description Usage Format Details Source References Examples

Contrived data on weight loss and self esteem over three months, for three groups of individuals: Control, Diet and Diet + Exercise. The data constitute a double-multivariate design.

1	data(WeightLoss)

A data frame with 34 observations on the following 7 variables.

group: a factor with levels Control Diet DietEx.
wl1: Weight loss at 1 month
wl2: Weight loss at 2 months
wl3: Weight loss at 3 months
se1: Self esteem at 1 month
se2: Self esteem at 2 months
se3: Self esteem at 3 months

Helmert contrasts are assigned to group, comparing Control vs. (Diet DietEx) and Diet vs. DietEx.

Originally taken from http://www.csun.edu/~ata20315/psy524/main.htm, but modified slightly

Friendly, Michael (2010). HE Plots for Repeated Measures Designs. Journal of Statistical Software, 37(4), 1-40. URL http://www.jstatsoft.org/v37/i04/.

data(WeightLoss)
str(WeightLoss)
table(WeightLoss$group)

contrasts(WeightLoss$group) <- matrix(c(-2,1,1, 0, -1, 1),ncol=2)
(wl.mod<-lm(cbind(wl1,wl2,wl3,se1,se2,se3)~group, data=WeightLoss))

heplot(wl.mod, hypotheses=c("group1", "group2"))
pairs(wl.mod, variables=1:3)
pairs(wl.mod, variables=4:6)

# within-S variables
within <- data.frame(measure=rep(c("Weight loss", "Self esteem"),each=3), month=rep(ordered(1:3),2))

# doubly-multivariate analysis: requires car 2.0+
## Not run: 
if (packageDescription("car")[["Version"]] >= 2) {
imatrix <- matrix(c(
	1,0,-1, 1, 0, 0,
	1,0, 0,-2, 0, 0,
	1,0, 1, 1, 0, 0,
	0,1, 0, 0,-1, 1,
	0,1, 0, 0, 0,-2,
	0,1, 0, 0, 1, 1), 6, 6, byrow=TRUE)
# NB: for heplots the columns of imatrix should have names
colnames(imatrix) <- c("WL", "SE", "WL.L", "WL.Q", "SE.L", "SE.Q")
rownames(imatrix) <- colnames(WeightLoss)[-1]
(imatrix <- list(measure=imatrix[,1:2], month=imatrix[,3:6]))
contrasts(WeightLoss$group) <- matrix(c(-2,1,1, 0,-1,1), ncol=2) 
(wl.mod<-lm(cbind(wl1, wl2, wl3, se1, se2, se3)~group, data=WeightLoss))
(wl.aov <- Anova(wl.mod, imatrix=imatrix, test="Roy"))

heplot(wl.mod, imatrix=imatrix, iterm="group:measure")
}

## End(Not run)

# do the correct analysis 'manually'
unit <- function(n, prefix="") {
	J <-matrix(rep(1, n), ncol=1)
	rownames(J) <- paste(prefix, 1:n, sep="")
	J
}                

measure <- kronecker(diag(2), unit(3, 'M')/3, make.dimnames=TRUE)
colnames(measure)<- c('WL', 'SE')

between <- as.matrix(WeightLoss[,-1]) 

between.mod <- lm(between ~ group, data=WeightLoss)
Anova(between.mod)

heplot(between.mod, hypotheses=c("group1", "group2"), 
	xlab="Weight Loss", ylab="Self Esteem",
	col=c("red", "blue", "brown"),
	main="Weight Loss & Self Esteem: Group Effect")

month <- kronecker(diag(2), poly(1:3), make.dimnames=TRUE)
colnames(month)<- c('WL', 'SE')
trends <- as.matrix(WeightLoss[,-1]) 
within.mod <- lm(trends ~ group, data=WeightLoss)
Anova(within.mod)

heplot(within.mod)
heplot(within.mod, hypotheses=c("group1", "group2"), 
	xlab="Weight Loss", ylab="Self Esteem",
	type="III", remove.intercept=FALSE,
	term.labels=c("month", "group:month"),
	main="Weight Loss & Self Esteem: Within-S Effects")
mark.H0()

Loading required package: car
Loading required package: carData
'data.frame':	34 obs. of  7 variables:
 $ group: Factor w/ 3 levels "Control","Diet",..: 1 1 1 1 1 1 1 1 1 1 ...
  ..- attr(*, "contrasts")= num [1:3, 1:2] -2 1 1 0 -1 1
  .. ..- attr(*, "dimnames")=List of 2
  .. .. ..$ : chr  "Control" "Diet" "DietEx"
  .. .. ..$ : NULL
 $ wl1  : int  4 4 4 3 5 6 6 5 5 3 ...
 $ wl2  : int  3 4 3 2 3 5 5 4 4 3 ...
 $ wl3  : int  3 3 1 1 2 4 4 1 1 2 ...
 $ se1  : int  14 13 17 11 16 17 17 13 14 14 ...
 $ se2  : int  13 14 12 11 15 18 16 15 14 15 ...
 $ se3  : int  15 17 16 12 14 18 19 15 15 13 ...

Control    Diet  DietEx 
     12      12      10 

Call:
lm(formula = cbind(wl1, wl2, wl3, se1, se2, se3) ~ group, data = WeightLoss)

Coefficients:
             wl1       wl2       wl3       se1       se2       se3     
(Intercept)   5.34444   4.45000   2.17778  14.92778  13.79444  16.28333
group1        0.42222   0.55833   0.04722   0.08889  -0.26944   0.60000
group2        0.43333   1.09167  -0.02500   0.18333  -0.22500   0.71667


Type II MANOVA Tests: Pillai test statistic
      Df test stat approx F num Df den Df   Pr(>F)   
group  2   0.72552   2.5617     12     54 0.009243 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Type II MANOVA Tests: Pillai test statistic
      Df test stat approx F num Df den Df   Pr(>F)   
group  2   0.72552   2.5617     12     54 0.009243 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1