Captive and maltreated bees — Bees • heplots

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

Source

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.

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)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>                  Df test stat approx F num Df den Df    Pr(>F)    
#> caste             1   0.72792  240.787      2    180 < 2.2e-16 ***
#> treat             1   0.19313   21.542      2    180 4.098e-09 ***
#> time              4   0.75684   27.548      8    362 < 2.2e-16 ***
#> caste:treat       1   0.02506    2.313      2    180    0.1019    
#> caste:time        4   0.28670    7.572      8    362 2.288e-09 ***
#> treat:time        4   0.01941    0.443      8    362    0.8945    
#> caste:treat:time  4   0.06796    1.592      8    362    0.1257    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>              Df test stat approx F num Df den Df    Pr(>F)    
#> caste         1   0.67976  236.673      2    223 < 2.2e-16 ***
#> trtime       10   0.82851   15.842     20    448 < 2.2e-16 ***
#> caste:trtime 10   0.32173    4.294     20    448 3.746e-09 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 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)
}
#> Loading required package: effects
#> lattice theme set by effectsTheme()
#> See ?effectsTheme for details.