R/example5.R

In RNED/agriTutorial: Tutorial Analysis of Some Agricultural Experiments

#' @name example5
#' @title  EXAMPLE 5: Transformation of treatment levels to improve model fit
#' @description
#' Mead (1988, p. 323) describes an experiment on spacing effects with turnips,
#' which was laid out in three complete blocks. Five different seed rates
#' (0.5, 2, 8, 20, 32 lb/acre) were tested in combination with four different row widths
#' (4, 8, 16, 32 inches), giving rise to a total of 20 treatments.
#' @details
#' Transformation of the dependent variable will often stabilize the variance of the observations
#' whereas transformation of the regressor variables will often simplify the fitted model. In this
#' study, the fit of a regression model based on the original seed rate and row width variables is compared
#' with the fit of a regression model based on log transformed seed rates and log transformed row widths.
#' In each case, the model lack-of-fit is examined by assessing the extra variability explained when the
#' Density and Spacing treatment factors and their interactions are added to the quadratic regression models.
#' All yields are logarithmically transformed to stabilize the variance.
#'
#' The first analysis fits a quadratic regression model of log yields on the untransformed seed rates and row
#' widths (Table 16) while the second analysis fits a quadratic regression model of log yields on the log
#' transformed seed rates and log transformed row widths (Table 17). The analysis of variance of the first model
#' shows that significant extra variability is explained by the Density and
#' Spacing factors and this shows that a quadratic regression model is inadequate for the untransformed regressor
#' variables. The analysis of variance of the second model, however, shows no significant extra variability
#' explained by the Density and Spacing factors and this shows that the quadratic regression model with the log
#' transformed regressor variables gives a good fit to the data and should be the preferred model for the
#' observed data.
#'
#' The superiority of the model with log transformed regressor variables is confirmed by an examination of
#' the diagnostic plots for the two models.
#'
#' \code{\link[agriTutorial]{agriTutorial}} : back to home page\cr
#'
#' @references
#' Mead, R. (1988). The design of experiments. Statistical principles for practical application.
#' Cambridge: Cambridge University Press.
#'
#' @examples
#'
#' \dontrun{
#'
#' ## *************************************************************************************
#' ##                            Preliminaries
#' ##**************************************************************************************
#'
#' ## sink("F:\\tutorial2\\OutputsR\\outExample5.txt") #sink file for outputs
#' ## pdf("F:\\tutorial2\\OutputsR\\outExample5_Fig_S1.pdf") #opens a graphical pdf output file
#' ## Loads turnip data
#' data(turnip)
#' ## write.table(turnip, "c:/turnip.txt", sep="\t") # export data to a text file
#' ## write.xlsx(turnip, "c:/turnip.xlsx") # export data to a spread sheet
#' ## Untransformed spacing and density polynomials
#'
#'
#' ## *************************************************************************************
#' ##   Quadratic regression models with and without transformation of regressor variables
#' ##**************************************************************************************
#'
#'
#' RowSpacing=poly(turnip$rowspacing,3,raw=TRUE)
#' colnames(RowSpacing)=c("linSpacing","quadSpacing","cubSpacing")
#' Density=poly(turnip$density,4,raw=TRUE)
#' colnames(Density)=c("linDensity","quadDensity","cubDensity","quartDensity")
#' turnip=cbind(turnip,Density,RowSpacing)
#'
#' ## Log transformed raw spacing and density polynomials
#' logRowSpacing=poly(log(turnip$rowspacing),3,raw=TRUE)
#' colnames(logRowSpacing)=c("linlogSpacing","quadlogSpacing","cublogSpacing")
#' logDensity=poly(log(turnip$density),4,raw=TRUE)
#' colnames(logDensity)=c("linlogDensity","quadlogDensity","cublogDensity","quartlogDensity")
#' turnip=cbind(turnip,logDensity,logRowSpacing)
#'
#' ## Table 16 Quadratic response surface for untransformed planting density by row spacing model
#' quad.mod  = lm(log_yield ~ Replicate + linDensity * linSpacing + quadDensity + quadSpacing +
#' Density*Spacing, turnip)
#' anova(quad.mod)
#'
#' ## Table 17 Quadratic response surface for transformed log planting density by log row spacing
#' log.quad.mod =
#' lm(log_yield ~ Replicate + linlogDensity*linlogSpacing + quadlogDensity  + quadlogSpacing +
#' Density*Spacing  ,turnip)
#' anova(log.quad.mod)
#'
#' ## graphical plots of untransformed data
#' par(mfrow=c(2,2),oma=c(0,0,2,0))
#' fit.quad.mod=lm(log_yield~Replicate+linDensity*linSpacing+quadDensity+quadSpacing,turnip)
#' plot(fit.quad.mod,sub.caption=NA)
#' title(main="Fig 12a Quadratic response for untransformed density by row spacing", outer=TRUE)
#'
#' ## graphical plots of log transformed data
#' par(mfrow=c(2,2),oma=c(0,0,2,0))
#' fit.log.quad.mod = lm(log_yield ~ Replicate + linlogDensity*linlogSpacing + quadlogDensity  +
#' quadlogSpacing, turnip)
#' plot(fit.log.quad.mod,sub.caption=NA)
#' title(main="Fig 12b Quadratic response for transformed log density by log row spacing", outer=TRUE)
#'
#'
#' ## *************************************************************************************
#' ##                                  Closure
#' ##**************************************************************************************
#'
#'
#' ## dev.off()# closes graphical device
#' ## sink() #closes sink file
#' }
#'
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