sinclair.clover {agridat} | R Documentation

## Clover yields in a factorial fertilizer experiment

### Description

Clover yields in a factorial fertilizer experiment

### Usage

    data("sinclair.clover")

### Format

A data frame with 25 observations on the following 3 variables.

`yield`

  yield t/ha

`P`

  phosphorous fertilizer kg/ha

`S`

  sulfur fertilizer kg/ha

### Details

A phosphorous by sulfur factorial experiment at Dipton in Southland, New Zealand. There were 3 reps. Plots were harvested repeatedly from Dec 1992 to Mar 1994. Yields reported are the total dry matter across all cuttings.

### Source

Sinclair AG, Risk WH, Smith LC, Morrison JD & Dodds KG (1994) Sulphur and phosphorus in balanced pasture nutrition. Proc N Z Grass Assoc, 56, 13-16.

### References

Dodds, KG and Sinclair, AG and Morrison, JD. (1995). A bivariate response surface for growth data. Fertilizer research, 45, 117-122. http://doi.org/10.1007/BF00790661

### Examples

    data(sinclair.clover)
    dat <- sinclair.clover

    require(lattice)
    xyplot(yield~P|factor(S), dat, layout=c(5,1),
           main="sinclair.clover - Yield by sulfur levels",
           xlab="Phosphorous")

    # Dodds fits a two-dimensional Mitscherlich-like model:
    # z = a*(1+b*{(s+t*x)/(x+1)}^y) * (1+d*{(th+r*y)/(y+1)}^x)

    # First, re-scale the problem to a more stable part of the parameter space
    dat <- transform(dat, x=P/10, y=S/10)

    # Response value for (x=0, y=maximal), (x=maximal, y=0), (x=max, y=max)
    z0m <- 5
    zm0 <- 5
    zmm <- 10.5
    # The parameters are somewhat sensitive to starting values.
    # I had to try a couple different initial values to match the paper by Dodds
    m1 <- nls(yield ~ alpha*(1 + beta*{(sig+tau*x)/(x+1)}^y) * (1 + del*{(th+rho*y)/(y+1)}^x),
              data=dat, # trace=TRUE,
              start=list(alpha=zmm, beta=(zm0/zmm)-1, del=(z0m/zmm)-1,
                         sig=.51, tau=.6, th=.5, rho=.7))
    summary(m1) # Match Dodds Table 2
    ## Parameters:
    ##       Estimate Std. Error t value Pr(>|t|)
    ## alpha 11.15148    0.66484  16.773 1.96e-12 ***
    ## beta  -0.61223    0.03759 -16.286 3.23e-12 ***
    ## del   -0.48781    0.04046 -12.057 4.68e-10 ***
    ## sig    0.26783    0.16985   1.577  0.13224
    ## tau    0.68030    0.06333  10.741 2.94e-09 ***
    ## th     0.59656    0.16716   3.569  0.00219 **
    ## rho    0.83273    0.06204  13.421 8.16e-11 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ## Residual standard error: 0.5298 on 18 degrees of freedom

    ## Not run:

    pred <- expand.grid(x=0:17, y=0:9)
    pred$z <- predict(m1, pred)

    # 3D plot of data with fitted surface.  Matches Dodds figure 2.
    require(rgl)
    bg3d(color = "white")
    clear3d()
    spheres3d(dat$x, dat$y, dat$yield,
             radius=.2, col = rep("navy", nrow(dat)))
    surface3d(seq(0, 17, by = 1), seq(0, 9, by = 1), pred$z,
              alpha=0.9, col="wheat",
              front="fill", back="fill")
    axes3d()
    title3d("sinclair.clover - yield","", xlab="Phosphorous/10",
            ylab="Sulfur/10", zlab="", line=3, cex=1.5)
    view3d(userMatrix=matrix(c(.7,.2,-.7,0, -.7,.2,-.6,0, 0,.9,.3,0, 0,0,0,1),ncol=4))
      # snapshot3d(file, "png")
      rgl.close()

    ## End(Not run)

[Package agridat version 1.16 Index]