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.

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.

`data(Bees)`

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`

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.

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.

# NOT RUN { data(Bees) require(car) # 3-way factorial, ignoring 0 group bees.mod <- lm(cbind(Iz,Iy) ~ caste*treat*time, data=Bees) 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, xlab="Iz: Ovarian development", ylab="Iz: Ovarian reabsorption", main="Bees: ~caste*treat*time", size="effect") # two-way design, using trtime bees.mod1 <- lm(cbind(Iz,Iy) ~ caste*trtime, data=Bees) Anova(bees.mod1) 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) } # }