R: Kousgaard (1984) Data on Pair Comparisons of Sound Fields

sound.fields {BradleyTerry2} | R Documentation

## Kousgaard (1984) Data on Pair Comparisons of Sound Fields

### Description

The results of a series of factorial subjective room acoustic experiments carried out at the Technical University of Denmark by A C Gade.

### Usage

    sound.fields

### Format

A list containing two data frames, `sound.fields$comparisons`, and `sound.fields$design`.

The `sound.fields$comparisons` data frame has 84 observations on the following 8 variables:

`field1`

  a factor with levels `c("000", "001", "010", "011", "100", "101", "110", "111")`, the first sound field in a comparison

`field2`

  a factor with the same levels as `field1`; the second sound field in a comparison

`win1`

  integer, the number of times that `field1` was preferred to `field2`

`tie`

  integer, the number of times that no preference was expressed when comparing `field1` and `field2`

`win2`

  integer, the number of times that `field2` was preferred to `field1`

`win1.adj`

  numeric, equal to `win1 + tie/2`

`win2.adj`

  numeric, equal to `win2 + tie/2`

`instrument`

  a factor with 3 levels, `c("cello", "flute", "violin")`

The `sound.fields$design` data frame has 8 observations (one for each of the sound fields compared in the experiment) on the following 3 variables:

`a`

  a factor with levels `c("0", "1")`, the direct sound factor (0 for obstructed sight line, 1 for free sight line); contrasts are sum contrasts

`b`

  a factor with levels `c("0", "1")`, the reflection factor (0 for -26dB, 1 for -20dB); contrasts are sum contrasts

`c`

  a factor with levels `c("0", "1")`, the reverberation factor (0 for -24dB, 1 for -20dB); contrasts are sum contrasts

### Details

The variables `win1.adj` and `win2.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 Davidson (1970) method that is used by Kousgaard (1984): see the examples.

### Author(s)

David Firth

### Source

Kousgaard, N. (1984) Analysis of a Sound Field Experiment by a Model for Paired Comparisons with Explanatory Variables. Scandinavian Journal of Statistics 11, 51–57.

### References

Davidson, R. R. (1970) Extending the Bradley-Terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association 65, 317–328.

### Examples

    ##
    ##  Fit the Bradley-Terry model to data for flutes, using the simple 'add 0.5'
    ##  method to handle ties:
    ##
    flutes.model <- BTm(cbind(win1.adj, win2.adj), field1, field2, ~ field,
                        id = "field",
                        subset = (instrument == "flute"),
                        data = sound.fields)
    ##
    ##  This agrees (after re-scaling) quite closely with the estimates given
    ##  in Table 3 of Kousgaard (1984):
    ##
    table3.flutes <- c(-0.581, -1.039, 0.347, 0.205, 0.276, 0.347, 0.311, 0.135)
    plot(c(0, coef(flutes.model)), table3.flutes)
    abline(lm(table3.flutes ~ c(0, coef(flutes.model))))
    ##
    ##  Now re-parameterise that model in terms of the factorial effects, as
    ##  in Table 5 of Kousgaard (1984):
    ##
    flutes.model.reparam <- update(flutes.model,
                                   formula = ~ a[field] * b[field] * c[field]
    			       )
    table5.flutes <- c(.267, .250, -.088, -.294, .062, .009, -0.070)
    plot(coef(flutes.model.reparam), table5.flutes)
    abline(lm(table5.flutes ~ coef(flutes.model.reparam)))

[Package BradleyTerry2 version 1.0-6 Index]