R: Springall (1973) Data on Subjective Evaluation of Flavour...

springall {BradleyTerry2} | R Documentation

## Springall (1973) Data on Subjective Evaluation of Flavour Strength

### Description

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.

### Usage

    springall

### 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:

`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`

### Details

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.

### Author(s)

David Firth

### Source

Springall, A (1973) Response surface fitting using a generalization of the Bradley-Terry paired comparison method. Applied Statistics 22, 59–68.

### 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.

### 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))

[Package BradleyTerry2 version 1.0-6 Index]