springall {BradleyTerry2} | R Documentation |
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.
springall
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:
row
a factor with levels 1:9
, the row number in Springall's dataset
col
a factor with levels 1:9
, the column number in Springall's dataset
win
integer, the number of wins for column treatment over row treatment
loss
integer, the number of wins for row treatment over column treatment
tie
integer, the number of ties between row and column treatments
win.adj
numeric, equal to win + tie/2
loss.adj
numeric, equal to loss + tie/2
The predictors
data frame has 9 observations (one for each treatment) on the following 5 variables:
flav
numeric, the flavour concentration
gel
numeric, the gel concentration
flav.2
numeric, equal to flav^2
gel.2
numeric, equal to gel^2
flav.gel
numeric, equal to flav * gel
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.
David Firth
Springall, A (1973) Response surface fitting using a generalization of the Bradley-Terry paired comparison method. Applied Statistics 22, 59–68.
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.
## ## 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))