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.

1 |

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.

Pabalan, N., Davey, K. G. & Packe, L. (2000).
Escalation of Aggressive Interactions During Staged Encounters in Halictus ligatus Say (Hymenoptera: Halictidae), with a Comparison of Circle Tube Behaviors with Other Halictine Species
*Journal of Insect Behavior*,
**13**, 627-650.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
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)
}
``` |

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