R/springall.R

In BradleyTerry2: Bradley-Terry Models

#' Springall (1973) Data on Subjective Evaluation of Flavour Strength
#' 
#' Data from Section 7 of the paper by Springall (1973) on Bradley-Terry
#' response surface modelling.  An experiment to assess the effects of gel and
#' flavour concentrations on the subjective assessment of flavour strength by
#' pair comparisons.
#' 
#' The variables `win.adj` and `loss.adj` are provided in order to
#' allow a simple way of handling ties (in which a tie counts as half a win and
#' half a loss), which is slightly different numerically from the Rao and
#' Kupper (1967) model that Springall (1973) uses.
#' 
#' @name springall
#' @docType data
#' @format A list containing two data frames, `springall$contests` and
#' `springall$predictors`.
#' 
#' The `springall$contests` data frame has 36 observations (one for each
#' possible pairwise comparison of the 9 treatments) on the following 7
#' variables: \describe{ 
#' \item{row}{a factor with levels `1:9`,
#' the row number in Springall's dataset} #
#' \item{col}{a factor with
#' levels `1:9`, the column number in Springall's dataset}
#' \item{win}{integer, the number of wins for column treatment over row
#' treatment} 
#' \item{loss}{integer, the number of wins for row treatment
#' over column treatment} 
#' \item{tie}{integer, the number of ties
#' between row and column treatments} 
#' \item{win.adj}{numeric, equal to
#' `win + tie/2`} 
#' \item{loss.adj}{numeric, equal to `loss + tie/2`} }
#' 
#' The `predictors` data frame has 9 observations (one for each treatment)
#' on the following 5 variables: \describe{ 
#' \item{flav}{numeric, the
#' flavour concentration} 
#' \item{gel}{numeric, the gel concentration}
#' \item{flav.2}{numeric, equal to `flav^2`}
#' \item{gel.2}{numeric, equal to `gel^2`}
#' \item{flav.gel}{numeric, equal to `flav * gel`} }
#' @author David Firth
#' @references Rao, P. V. and Kupper, L. L. (1967) Ties in paired-comparison
#' experiments: a generalization of the Bradley-Terry model.  *Journal of
#' the American Statistical Association*, **63**, 194--204.
#' @source Springall, A (1973) Response surface fitting using a generalization
#' of the Bradley-Terry paired comparison method.  *Applied Statistics*
#' **22**, 59--68.
#' @keywords datasets
#' @examples
#' 
#' ##
#' ## Fit the same response-surface model as in section 7 of 
#' ## Springall (1973).
#' ##
#' ## Differences from Springall's fit are minor, arising from the 
#' ## different treatment of ties.
#' ##
#' ## Springall's model in the paper does not include the random effect.  
#' ## In this instance, however, that makes no difference: the random-effect 
#' ## variance is estimated as zero.
#' ##
#' summary(springall.model <- BTm(cbind(win.adj, loss.adj), col, row, 
#'                                ~ flav[..] + gel[..] + 
#'                                  flav.2[..] + gel.2[..] + flav.gel[..] +
#'                                  (1 | ..),
#'                                data = springall))
#' 
"springall"