Counts of webworms in a beet field, with insecticide treatments.

data("beall.webworms")

Format

A data frame with 1300 observations on the following 7 variables.

row: row
col: column
y: count of webworms
block: block
trt: treatment
spray: spray treatment yes/no
lead: lead treatment yes/no

Details

The beet webworm lays egg masses as small as 1 egg, seldom exceeding 5 eggs. The larvae can move freely, but usually mature on the plant on which they hatch.

Each plot contained 25 unit areas, each 1 row by 3 feet long. The row width is 22 inches. The arrangement of plots within the blocks seems certain, but the arrangement of the blocks/treatments is not certain, since the authors say "since the plots were 5 units long and 5 wide it is only practicable to combine them into groups of 5 in one direction or the other".

Treatment 1 = None. Treatment 2 = Contact spray. Treatment 3 = Lead arsenate. Treatment 4 = Both spray, lead arsenate.

Source

Beall, Geoffrey (1940). The fit and significance of contagious distributions when applied to observations on larval insects. Ecology, 21, 460-474. Table 6. https://doi.org/10.2307/1930285

References

Michal Kosma et al. (2019). Over-dispersed count data in crop and agronomy research. Journal of Agronomy and Crop Science. https://doi.org/10.1111/jac.12333

Examples

# \dontrun{

library(agridat)
data(beall.webworms)
dat <- beall.webworms

# Match Beall table 1
# with(dat, table(y,trt))

libs(lattice)
histogram(~y|trt, data=dat, layout=c(1,4), as.table=TRUE,
          main="beall.webworms")

# Visualize Beall table 6.  Block effects may exist, but barely.
libs(desplot)
grays <- colorRampPalette(c("white","#252525"))
desplot(dat, y ~ col*row,
        col.regions=grays(10),
        at=0:10-0.5,
        out1=block, out2=trt, num=trt, flip=TRUE, # aspect unknown
        main="beall.webworms (count of worms)")

# Following plot suggests interaction is needed
# with(dat, interaction.plot(spray, lead, y))

# Try the models of Kosma et al, Table 1.

# Poisson model
m1 <- glm(y ~ block + spray*lead, data=dat, family="poisson")
logLik(m1) # -1497.719 (df=16)
#> 'log Lik.' -1497.719 (df=16)

# Negative binomial model
# libs(MASS)
# m2 <- glm.nb(y ~ block + spray*lead, data=dat)
# logLik(m2) # -1478.341 (df=17)

# # Conway=Maxwell-Poisson model (takes several minutes)
# libs(spaMM)
# # estimate nu parameter
# m3 <- fitme(y ~ block + spray*lead, data=dat, family = COMPoisson())
# logLik(m3) # -1475.999 
# # Kosma logLik(m3)=-1717 seems too big. Typo? Different model?

# }