heplots (version 1.6.2)

Bees: Captive and maltreated bees

Description

Pabalan, Davey and Packe (2000) studied the effects of captivity and maltreatment on reproductive capabilities of queen and worker bees in a complex factorial design.

Format

A data frame with 246 observations on the following 6 variables.

caste

a factor with levels Queen Worker

treat

a factor with levels "" CAP MAL

time

an ordered factor: time of treatment

Iz

an index of ovarian development

Iy

an index of ovarian reabsorption

trtime

a factor with levels 0 CAP05 CAP07 CAP10 CAP12 CAP15 MAL05 MAL07 MAL10 MAL12 MAL15

Details

Bees were placed in a small tube and either held captive (CAP) or shaken periodically (MAL) for one of 5, 7.5, 10, 12.5 or 15 minutes, after which they were sacrificed and two measures: ovarian development (Iz) and ovarian reabsorption (Iy), were taken. A single control group was measured with no such treatment, i.e., at time 0; there are n=10 per group.

The design is thus nearly a three-way factorial, with factors caste (Queen, Worker), treat (CAP, MAL) and time, except that there are only 11 combinations of Treatment and Time; we call these trtime below.

Models for the three-way factorial design, using the formula cbind(Iz,Iy) ~ caste*treat*time ignore the control condition at time==0, where treat==NA.

To handle the additional control group at time==0, while separating the effects of Treatment and Time, 10 contrasts can be defined for the trtime factor in the model cbind(Iz,Iy) ~ caste*trtime See demo(bees.contrasts) for details.

In the heplot examples below, the default size="evidence" displays are too crowded to interpret, because some effects are so highly significant. The alternative effect-size scaling, size="effect", makes the relations clearer.

References

Friendly, M. (2006). Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples Journal of Statistical Software, 17, 1-42.

Examples

data(Bees)
require(car)

# 3-way factorial, ignoring 0 group
bees.mod <- lm(cbind(Iz,Iy) ~ caste*treat*time, data=Bees)
car::Anova(bees.mod)

op<-palette(c(palette()[1:4],"brown","magenta", "olivedrab","darkgray"))
heplot(bees.mod, 
    xlab="Iz: Ovarian development", 
    ylab="Iz: Ovarian reabsorption",
		main="Bees: ~caste*treat*time")

heplot(bees.mod, size="effect",
    xlab="Iz: Ovarian development", 
    ylab="Iz: Ovarian reabsorption",
    main="Bees: ~caste*treat*time", 
    )

# two-way design, using trtime
bees.mod1 <- lm(cbind(Iz,Iy) ~ caste*trtime, data=Bees)
Anova(bees.mod1)

# HE plots for this model, with both significance and effect size scaling

heplot(bees.mod1, 
    xlab="Iz: Ovarian development", 
    ylab="Iz: Ovarian reabsorption",
		main="Bees: ~caste*trtime")
heplot(bees.mod1, 
    xlab="Iz: Ovarian development", 
    ylab="Iz: Ovarian reabsorption",
    main="Bees: ~caste*trtime",
    size="effect")
palette(op)

# effect plots for separate responses
if(require(effects)) {
	bees.lm1 <-lm(Iy ~ treat*caste*time, data=Bees)
	bees.lm2 <-lm(Iz ~ treat*caste*time, data=Bees)
	
	bees.eff1 <- allEffects(bees.lm1)
	plot(bees.eff1,multiline=TRUE,ask=FALSE)
	
	bees.eff2 <- allEffects(bees.lm2)
	plot(bees.eff2,multiline=TRUE,ask=FALSE)
}