crowder.seeds {agridat}R Documentation

Germination of Orobanche seeds for two genotypes and two treatments.

Description

Number of Orobanche seeds tested/germinated for two genotypes and two treatments.

Format

plate

Factor for replication

gen

Factor for genotype with levels O73, O75

extract

Factor for extract from bean, cucumber

germ

Number of seeds that germinated

n

Total number of seeds tested

Details

Egyptian broomrape, orobanche aegyptiaca is a parasitic plant family. The plants have no chlorophyll and grow on the roots of other plants. The seeds remain dormant in soil until certain compounds from living plants stimulate germination.

Two genotypes were studied in the experiment, O. aegyptiaca 73 and O. aegyptiaca 75. The seeds were brushed with one of two extracts prepared from either a bean plant or cucmber plant.

The experimental design was a 2x2 factorial, each with 5 or 6 reps of plates.

Source

Crowder, M.J., 1978. Beta-binomial anova for proportions. Appl. Statist., 27, 34-37. https://doi.org/10.2307/2346223

References

N. E. Breslow and D. G. Clayton. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88:9-25. https://doi.org/10.2307/2290687

Y. Lee and J. A. Nelder. 1996. Hierarchical generalized linear models with discussion. J. R. Statist. Soc. B, 58:619-678.

Examples

## Not run: 

  library(agridat)
  data(crowder.seeds)
  dat <- crowder.seeds
  m1.glm <- m1.glmm <- m1.bb <- m1.hglm <- NA


  # ----- Graphic
  libs(lattice)
  dotplot(germ/n~gen|extract, dat, main="crowder.seeds")

 
  # ----- GLM.
  # family=binomial() fixes dispersion at 1
  # family=quasibinomial() estimates dispersion, had larger std errors
  m1.glm <- glm(cbind(germ,n-germ) ~ gen*extract,
                data=dat,
                #family="binomial",
                family=quasibinomial()
                )
  summary(m1.glm)
  
  
  # --- GLMM.  Assumes Gaussian random effects
  libs(MASS)
  m1.glmm <- glmmPQL(cbind(germ, n-germ) ~ gen*extract, random= ~1|plate,
                     family=binomial(), data=dat)
  summary(m1.glmm)
  

# ----- HGML package. Beta-binomial with beta-distributed random effects
# libs(hglm)
# m1.hglm <- hglm(fixed= germ/n ~ I(gen=="O75")*extract, weights=n, data=dat,
#                 random=~1|plate, family=binomial(), rand.family=Beta(),
#                 fix.disp=1)

# ----- INLA package. See: https://haakonbakka.bitbucket.io/btopic102.html
# libs(INLA)
# gen,extract are fixed. plate is a random effect
# Priors for hyper parameters. See: inla.doc("pc.prec")
# hyper1 = list(theta = list(prior="pc.prec", param=c(1,0.01)))
# m1.inla = inla(germ ~ gen*extract + f(plate, model="iid", hyper=hyper1),
#                data=crowder.seeds, 
#                family="binomial", Ntrials=n, 
#                control.family=list(control.link=list(model="logit")))

# Compare coefficients

## round(summary(m1.glm)$coef,2)
##                        Estimate Std. Error t value Pr(>|t|)
## (Intercept)               -0.41       0.25   -1.64     0.12
## genO75                    -0.15       0.30   -0.48     0.64
## extractcucumber            0.54       0.34    1.58     0.13
## genO75:extractcucumber     0.78       0.42    1.86     0.08

## round(summary(m1.glmm)$tTable,2)
##                        Value Std.Error DF t-value p-value
## (Intercept)            -0.44      0.25 17   -1.80    0.09
## genO75                 -0.10      0.31 17   -0.34    0.74
## extractcucumber         0.52      0.34 17    1.56    0.14
## genO75:extractcucumber  0.80      0.42 17    1.88    0.08

## round(summary(m1.bb)$BCoef,2)
##                        Estimate Std. Error z value Pr(> |z|)
## (Intercept)               -0.44       0.22   -2.04      0.04
## genO75                    -0.10       0.27   -0.36      0.72
## extractcucumber            0.52       0.30    1.76      0.08
## genO75:extractcucumber     0.80       0.38    2.11      0.03

## round(summary(m1.hglm)$FixCoefMat,2)
##                                     Estimate Std. Error t-value Pr(>|t|)
## (Intercept)                            -0.47       0.24   -1.92     0.08
## I(gen == "O75")TRUE                    -0.08       0.31   -0.25     0.81
## extractcucumber                         0.51       0.33    1.53     0.16
## I(gen == "O75")TRUE:extractcucumber     0.83       0.43    1.92     0.08

## round(m1.inla$summary.fixed,2)
##                         mean   sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)            -0.46 0.24      -0.94    -0.45      -0.01 -0.45   0
## genO75                 -0.09 0.30      -0.67    -0.10       0.52 -0.11   0
## extractcucumber         0.53 0.32      -0.12     0.53       1.17  0.53   0
## genO75:extractcucumber  0.82 0.42       0.01     0.82       1.66  0.81   0

  
  # ----- Stan using pre-built models from rstanarm
  ## libs(tidyverse, rstan, rstanarm)
  ## m1.stan <- stan_glm(
  ##   cbind(germ,n-germ) ~ gen*extract,
  ##   data=dat,
  ##   family = binomial(link="logit")  )
  ## round(posterior_interval(m1.stan, prob=.90),3)
  ## #                            5
  ## # (Intercept)            -0.715 -0.111
  ## # genO75                 -0.512  0.228
  ## # extractcucumber         0.123  0.977
  ## # genO75:extractcucumber  0.248  1.284


if(0) {

  # --- rjags version ---

# JAGS/BUGS.  See https://mathstat.helsinki.fi/openbugs/Examples/Seeds.html
# Germination rate depends on p, which is a logit of a linear predictor
# based on genotype and extract, plus random deviation to intercept

# To match the output on the BUGS web page, use: dat$gen=="O73".
# We use dat$gen=="O75" to compare with the parameterization above.
jdat =list(germ = dat$germ, n = dat$n,
           root = as.numeric(dat$extract=="cucumber"),
           gen = as.numeric(dat$gen=="O75"),
           nobs = nrow(dat))

jinit = list(int = 0, genO75 = 0, extcuke = 0, g75ecuke = 0, tau = 10)

# Use logical names (unlike BUGS documentation)
mod.bug =
"model {
  for(i in 1:nobs) {
    germ[i] ~ dbin(p[i], n[i])
    b[i] ~ dnorm(0.0, tau)
    logit(p[i]) <- int + genO75 * gen[i] + extcuke * root[i] +
                   g75ecuke * gen[i] * root[i] + b[i]
  }
  int ~ dnorm(0.0, 1.0E-6)
  genO75 ~ dnorm(0.0, 1.0E-6)
  extcuke ~ dnorm(0.0, 1.0E-6)
  g75ecuke ~ dnorm(0.0, 1.0E-6)
  tau ~ dgamma(0.001, 0.001)
  sigma <- 1 / sqrt(tau)
}"

libs(rjags)
oo <- textConnection(mod.bug)
j1 <- jags.model(oo, data=jdat, inits=jinit, n.chains=1)
close(oo)

c1 <- coda.samples(j1, c("int","genO75","g75ecuke","extcuke","sigma"),
                   n.iter=20000)
summary(c1) # Medians are very similar to estimates from hglm
# libs(lucid)
# print(vc(c1),3)
##             Mean    SD    2.5
## extcuke   0.543  0.331 -0.118   0.542   1.2   
## g75ecuke  0.807  0.436 -0.0586  0.802   1.7   
## genO75   -0.0715 0.309 -0.665  -0.0806  0.581 
## int      -0.479  0.241 -0.984  -0.473  -0.0299
## sigma     0.289  0.142  0.0505  0.279   0.596 

# Plot observed data with HPD intervals for germination probability
c2 <- coda.samples(j1, c("p"), n.iter=20000)
hpd <- HPDinterval(c2)[[1]]
med <- summary(c2, quantiles=.5)$quantiles
fit <- data.frame(med, hpd)

libs(latticeExtra)
obs <- dotplot(1:21 ~ germ/n, dat,
               main="crowder.seeds", ylab="plate",
               col=as.numeric(dat$gen), pch=substring(dat$extract,1))
obs + segplot(1:21 ~ lower + upper, data=fit, centers=med)


## --- R2jags version ---

libs("agridat")
libs("R2jags")
dat <- crowder.seeds

# To match the output on the BUGS web page, use: dat$gen=="O73".
# We use dat$gen=="O75" to compare with the parameterization above.
jdat =list(germ = dat$germ, n = dat$n,
           root = as.numeric(dat$extract=="cucumber"),
           gen = as.numeric(dat$gen=="O75"),
           nobs = nrow(dat))

jinit = list(list(int = 0, genO75 = 0, extcuke = 0, g75ecuke = 0, tau = 10))

mod.bug = function() {
  for(i in 1:nobs) {
    germ[i] ~ dbin(p[i], n[i])
    b[i] ~ dnorm(0.0, tau)
    logit(p[i]) <- int + genO75 * gen[i] + extcuke * root[i] +
      g75ecuke * gen[i] * root[i] + b[i]
  }
  int ~ dnorm(0.0, 1.0E-6)
  genO75 ~ dnorm(0.0, 1.0E-6)
  extcuke ~ dnorm(0.0, 1.0E-6)
  g75ecuke ~ dnorm(0.0, 1.0E-6)
  tau ~ dgamma(0.001, 0.001)
  sigma <- 1 / sqrt(tau)
}

parms <- c("int","genO75","g75ecuke","extcuke","sigma")

j1 <- jags(data=jdat, inits=jinit, parms, model.file=mod.bug,
           n.iter=20000, n.chains=1)
print(j1)
##          mu.vect sd.vect   2.5
## extcuke    0.519   0.325 -0.140  0.325   0.531   0.728   1.158
## g75ecuke   0.834   0.429 -0.019  0.552   0.821   1.101   1.710
## genO75    -0.096   0.305 -0.670 -0.295  -0.115   0.089   0.552
## int       -0.461   0.236 -0.965 -0.603  -0.455  -0.312   0.016
## sigma      0.255   0.148  0.033  0.140   0.240   0.352   0.572
## deviance 103.319   7.489 90.019 98.010 102.770 108.689 117.288

traceplot(as.mcmc(j1))
densityplot(as.mcmc(j1))
HPDinterval(as.mcmc(j1))

}


## End(Not run)

[Package agridat version 1.18 Index]