yield.saemix {saemix}

Wheat yield in crops treated with fertiliser, in SAEM format

Description

Theyield.saemix contains data from winter wheat experiments.

Usage

yield.saemix

Format

This data frame contains the following columns:

site

the site number

dose

dose of nitrogen fertiliser (kg/ha)

yield

grain yield (kg/ha)

soil.nitrogen

end-of-winter mineral soil nitrogen (NO3- plus NH4+) in the 0 to 90 cm layer was measured on each site/year (kg/ha)

Details

The data in the yield.saemix comes from 37 winter wheat experiments carried out between 1990 and 1996 on commercial farms near Paris, France. Each experiment was from a different site. Two soil types were represented, a loam soil and a chalky soil. Common winter wheat varieties were used. Each experiment consisted of five to eight different nitrogen fertiliser rates, for a total of 224 nitrogen treatments. Nitrogen fertilizer was applied in two applications during the growing season. For each nitrogen treatment, grain yield (adjusted to 150 g.kg-1 grain moisture content) was measured. In addition, end-of-winter mineral soil nitrogen (NO3- plus NH4+) in the 0 to 90 cm layer was measured on each site-year during February when the crops were tillering. Yield and end-of-winter mineral soil nitrogen measurements were in the ranges 3.44-11.54 t.ha-1 , and 40-180 kg.ha-1 respectively.

Source

Makowski, D., Wallach, D., and Meynard, J.-M (1999). Models of yield, grain protein, and residual mineral nitrogen responses to applied nitrogen for winter wheat. Agronomy Journal 91: 377-385.

Examples

data(yield.saemix)
saemix.data<-saemixData(name.data=yield.saemix,header=TRUE,name.group=c("site"),
      name.predictors=c("dose"),name.response=c("yield"),
      name.covariates=c("soil.nitrogen"),units=list(x="kg/ha",y="t/ha",covariates=c("kg/ha")))

#  Model: linear + plateau
yield.LP<-function(psi,id,xidep) {
  x<-xidep[,1]
  ymax<-psi[id,1]
  xmax<-psi[id,2]
  slope<-psi[id,3]
  f<-ymax+slope*(x-xmax)
  #'  cat(length(f),"  ",length(ymax),"\n")
  f[x>xmax]<-ymax[x>xmax]
  return(f)
}
saemix.model<-saemixModel(model=yield.LP,description="Linear plus plateau model",   
        psi0=matrix(c(8,100,0.2,0,0,0),ncol=3,byrow=TRUE,dimnames=list(NULL,   
            c("Ymax","Xmax","slope"))),covariate.model=matrix(c(0,0,0),ncol=3,byrow=TRUE), 
        transform.par=c(0,0,0),covariance.model=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3, 
            byrow=TRUE),error.model="constant")

saemix.options<-list(algorithms=c(1,1,1),nb.chains=1,seed=666, 
       save=FALSE,save.graphs=FALSE,displayProgress=FALSE)

# Plotting the data
plot(saemix.data,xlab="Fertiliser dose (kg/ha)", ylab="Wheat yield (t/ha)")


saemix.fit<-saemix(saemix.model,saemix.data,saemix.options)

# Comparing the likelihoods obtained by linearisation and importance sampling 
# to the likelihood obtained by Gaussian Quadrature
saemix.fit<-llgq.saemix(saemix.fit)
{
   cat("LL by Importance sampling, LL_IS=",saemix.fit["results"]["ll.is"],"\n")
   cat("LL by linearisation, LL_lin=",saemix.fit["results"]["ll.lin"],"\n")
   cat("LL by Gaussian Quadrature, LL_GQ=",saemix.fit["results"]["ll.gq"],"\n")
}

# Testing for an effect of covariate soil.nitrogen on Xmax
saemix.model2<-saemixModel(model=yield.LP,description="Linear plus plateau model", 
         psi0=matrix(c(8,100,0.2,0,0,0),ncol=3,byrow=TRUE,dimnames=list(NULL, 
            c("Ymax","Xmax","slope"))),covariate.model=matrix(c(0,1,0),ncol=3,byrow=TRUE), 
         transform.par=c(0,0,0),covariance.model=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3, 
             byrow=TRUE),error.model="constant")

saemix.fit2<-saemix(saemix.model2,saemix.data,saemix.options)
# BIC for the two models
{
  cat("Model without covariate, BIC=",saemix.fit["results"]["bic.is"],"\n")
  cat("Model with covariate, BIC=",saemix.fit2["results"]["bic.is"],"\n")
  pval<-1-pchisq(-2*saemix.fit["results"]["ll.is"]+2*saemix.fit2["results"]["ll.is"],1)
  cat("        LRT: p=",pval,"\n")
}

#' @keywords datasets