sound.fields {BradleyTerry2} | R Documentation |
The results of a series of factorial subjective room acoustic experiments carried out at the Technical University of Denmark by A C Gade.
sound.fields
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
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.
David Firth
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.
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.
## ## 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)))