Root counts for propagated columnar apple shoots.

Usage

data("ridout.appleshoots")

Format

A data frame with 270 observations on the following 4 variables.

roots: number of roots per shoot
trtn: number of shoots per treatment combination
photo: photoperiod, 8 or 16
bap: BAP concentration, numeric

Details

There were 270 micropropagated shoots from the columnar apple cultivar Trajan. During the rooting period, shoot tips of length 1.0-1.5 cm were cultured on media with different concentrations of the cytokinin BAP in two growth chambers with 8 or 16 hour photoperiod.

The response variable is the number of roots after 4 weeks at 22 degrees C.

Almost all of the shoots in the 8 hour photoperiod rooted. Under the 16 hour photoperiod only about half rooted.

High BAP concentrations often inhibit root formation of apples, but perhaps not for columnar varieties.

Used with permission of Martin Ridout.

Source

Ridout, M. S., Hinde, J. P., and Demetrio, C. G. B. (1998). Models for Count Data with Many Zeros. Proceedings of the 19th International Biometric Conference, 179-192.

References

SAS. Fitting Zero-Inflated Count Data Models by Using PROC GENMOD. support.sas.com/rnd/app/examples/stat/GENMODZIP/roots.pdf

Examples

if (FALSE) { # \dontrun{
  
library(agridat)
data(ridout.appleshoots)
dat <- ridout.appleshoots

# Change photo and bap to factors
dat <- transform(dat, photo=factor(photo), bap=factor(bap))

libs(lattice)
# histogram(~roots, dat, breaks=0:18-0.5)

# For photo=8, Poisson distribution looks reasonable.
# For photo=16, half of the shoots had no roots
# Also, photo=8 has very roughly 1/45 as many zeros as photo=8,
# so we anticipate prob(zero) is about 1/45=0.22 for photo=8.
histogram(~roots|photo, dat, breaks=0:18-0.5, main="ridout.appleshoots")

  libs(latticeExtra)
  foo.obs <- histogram(~roots|photo*bap, dat, breaks=0:18-0.5, type="density",
                       xlab="Number of roots for photoperiod 8, 16",
                       ylab="Density for BAP levels",
                       main="ridout.appleshoots")
  useOuterStrips(foo.obs)

  # Ordinary (non-ZIP) Poisson GLM
  m1 <- glm(roots ~ bap + photo + bap:photo, data=dat,
            family="poisson")
  summary(m1) # Appears to have overdispersion


# ----- Fit a Zero-Inflated Poisson model -----

libs(pscl)

# Use SAS contrasts to match SAS output
oo <- options(contrasts=c('contr.SAS','contr.poly'))

# There are unequal counts for each trt combination, which obviously affects
# the distribution of counts, so use log(trtn) as an offset.
dat$ltrtn <- log(dat$trtn)

# Ordinary Poisson GLM: 1 + bap*photo.
# Zero inflated probability depends only on photoperiod: 1 + photo

m2 <- zeroinfl(roots ~ 1 + bap*photo | 1 + photo, data=dat,
          dist="poisson", offset=ltrtn)
logLik(m2)      # -622.2283 matches SAS Output 1
-2 * logLik(m2) # 1244.457 Matches Ridout Table 2, ZIP, H*P, P
summary(m2)     # Coefficients match SAS Output 3.

exp(coef(m2, "zero")) # Photo=8 has .015 times as many zeros as photo=16

# Get predicted _probabilities_

# Prediction data
newdat <- expand.grid(photo=c(8,16), bap=c(2.2, 4.4, 8.8, 17.6))
newdat <- aggregate(trtn~bap+photo, dat, FUN=mean)
newdat$ltrtn <- log(newdat$trtn)

# The predicted (Poisson + Zero) probabilities
d2 <- cbind(newdat[,c('bap','photo')], predict(m2, newdata=newdat, type="prob"))
libs(reshape2)
d2 <- melt(d2, id.var = c('bap','photo')) # wide to tall
d2$xpos <- as.numeric(as.character(d2$variable))
foo.poi <- xyplot(value~xpos|photo*bap, d2, col="black", pch=20, cex=1.5)

# Plot data and model
foo.obs <- update(foo.obs, main="ridout.appleshoots: observed (bars) & predicted (dots)")
useOuterStrips(foo.obs + foo.poi)
  
# Restore contrasts
options(oo)

} # }