sound.fields {BradleyTerry2}

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)))