turner.herbicide {agridat} | R Documentation

## Herbicide control of larkspur

### Description

Herbicide control of larkspur

### Usage

    data("turner.herbicide")

### Format

A data frame with 12 observations on the following 4 variables.

`rep`

  rep factor

`rate`

  rate of herbicide

`live`

  number of live plants before application

`dead`

  number of plants killed by herbicide

### Details

Effectiveness of the herbicide Picloram on larkspur plants at 4 doses (0, 1.1, 2.2, 4.5) in 3 reps. Experiment was done in 1986 at Manti, Utah.

### Source

David L. Turner and Michael H. Ralphs and John O. Evans (1992). Logistic Analysis for Monitoring and Assessing Herbicide Efficacy. Weed Technology, 6, 424-430. http://www.jstor.org/stable/3987312

### References

Christopher Bilder, Thomas Loughin. Analysis of Categorical Data with R.

### Examples

    data(turner.herbicide)
    dat <- turner.herbicide

    dat <- transform(dat, prop=dead/live)
    # xyplot(prop~rate,dat, pch=20, main="turner.herbicide", ylab="Proportion killed")

    m1 <- glm(prop~rate, data=dat, weights=live, family=binomial)
    coef(m1) # -3.46, 2.6567  Same as Turner eqn 3

    # Make conf int on link scale and back-transform
    p1 <- expand.grid(rate=seq(0,to=5,length=50))
    p1 <- cbind(p1, predict(m1, newdata=p1, type='link', se.fit=TRUE))
    p1 <- transform(p1, lo = plogis(fit - 2*se.fit),
                    fit = plogis(fit),
                    up = plogis(fit + 2*se.fit))

    # Figure 2 of Turner
    if(require(latticeExtra)){
      foo1 <- xyplot(prop~rate,dat, cex=1.5,
                     main="turner.herbicide (model with 2*S.E.)",
                     xlab="Herbicide rate", ylab="Proportion killed")
      foo2 <- xyplot(fit~rate, p1, type='l')
      foo3 <- xyplot(lo+up~rate, p1, type='l', lty=1, col='gray')
      print(foo1 + foo2 + foo3)
    }

    # What dose gives a LD90 percent kill rate?
    # require(MASS)
    # dose.p(m1, p=.9)
    ##             Dose       SE
    ## p = 0.9: 2.12939 0.128418

    # Alternative method
    # require(car) # logit(.9) = 2.197225
    # deltaMethod(m1, g="(log(.9/(1-.9))-b0)/(b1)", parameterNames=c('b0','b1'))
    ##                      Estimate       SE
    ## (2.197225 - b0)/(b1)  2.12939 0.128418

    # What is a 95 percent conf interval for LD90?  Bilder & Loughin page 138
    root <- function(x, prob=.9, alpha=0.05){
      co <- coef(m1)    # b0,b1
      covs <- vcov(m1)  # b00,b11,b01
      # .95 = b0 + b1*x
      # (b0+b1*x) + Z(alpha/2) * sqrt(b00 + x^2*b11 + 2*x*b01) > .95
      # (b0+b1*x) - Z(alpha/2) * sqrt(b00 + x^2*b11 + 2*x*b01) < .95
      f <- abs(co[1] + co[2]*x - log(prob/(1-prob))) /
        sqrt(covs[1,1] + x^2 * covs[2,2] + 2*x*covs[1,2])
      return( f - qnorm(1-alpha/2))
    }
    lower <- uniroot(f=root, c(0,2.13))
    upper <- uniroot(f=root, c(2.12, 5))
    c(lower$root, upper$root)
    # 1.92 2.45

[Package agridat version 1.16 Index]