Description Usage Format Details Source References Examples
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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