Description Usage Format Details Author(s) Source References Examples

*Community of European management schools* (CEMS) data as used in the
paper by Dittrich et al. (1998, 2001), re-formatted for use with
`BTm()`

1 |

A list containing three data frames, `CEMS$preferences`

,
`CEMS$students`

and `CEMS$schools`

.

The `CEMS$preferences`

data frame has `303 * 15 = 4505`

observations (15 possible comparisons, for each of 303 students) on the
following 8 variables:

- student
a factor with levels

`1:303`

- school1
a factor with levels

`c("Barcelona", "London", "Milano", "Paris", "St.Gallen", "Stockholm")`

; the first management school in a comparison- school2
a factor with the same levels as

`school1`

; the second management school in a comparison- win1
integer (value 0 or 1) indicating whether

`school1`

was preferred to`school2`

- win2
integer (value 0 or 1) indicating whether

`school2`

was preferred to`school1`

- tied
integer (value 0 or 1) indicating whether no preference was expressed

- win1.adj
numeric, equal to

`win1 + tied/2`

- win2.adj
numeric, equal to

`win2 + tied/2`

The `CEMS$students`

data frame has 303 observations (one for each
student) on the following 8 variables:

- STUD
a factor with levels

`c("other", "commerce")`

, the student's main discipline of study- ENG
a factor with levels

`c("good, poor")`

, indicating the student's knowledge of English- FRA
a factor with levels

`c("good, poor")`

, indicating the student's knowledge of French- SPA
a factor with levels

`c("good, poor")`

, indicating the student's knowledge of Spanish- ITA
a factor with levels

`c("good, poor")`

, indicating the student's knowledge of Italian- WOR
a factor with levels

`c("no", "yes")`

, whether the student was in full-time employment while studying- DEG
a factor with levels

`c("no", "yes")`

, whether the student intended to take an international degree- SEX
a factor with levels

`c("female", "male")`

The `CEMS$schools`

data frame has 6 observations (one for each
management school) on the following 7 variables:

- Barcelona
numeric (value 0 or 1)

- London
numeric (value 0 or 1)

- Milano
numeric (value 0 or 1)

- Paris
numeric (value 0 or 1)

- St.Gallen
numeric (value 0 or 1)

- Stockholm
numeric (value 0 or 1)

- LAT
numeric (value 0 or 1) indicating a 'Latin' city

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 Dittrich et al. (1998): see the examples.

David Firth

Royal Statistical Society datasets website, at https://rss.onlinelibrary.wiley.com/hub/journal/14679876/series-c-datasets/pre_2016.

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.

Dittrich, R., Hatzinger, R. and Katzenbeisser, W. (1998) Modelling the
effect of subject-specific covariates in paired comparison studies with an
application to university rankings. *Applied Statistics* **47**,
511–525.

Dittrich, R., Hatzinger, R. and Katzenbeisser, W. (2001) Corrigendum:
Modelling the effect of subject-specific covariates in paired comparison
studies with an application to university rankings. *Applied
Statistics* **50**, 247–249.

Turner, H. and Firth, D. (2012) Bradley-Terry models in R: The BradleyTerry2
package. *Journal of Statistical Software*, **48**(9), 1–21.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | ```
##
## Fit the standard Bradley-Terry model, using the simple 'add 0.5'
## method to handle ties:
##
table3.model <- BTm(outcome = cbind(win1.adj, win2.adj),
player1 = school1, player2 = school2,
formula = ~.. , refcat = "Stockholm",
data = CEMS)
## The results in Table 3 of Dittrich et al (2001) are reproduced
## approximately by a simple re-scaling of the estimates:
table3 <- summary(table3.model)$coef[, 1:2]/1.75
print(table3)
##
## Now fit the 'final model' from Table 6 of Dittrich et al.:
##
table6.model <- BTm(outcome = cbind(win1.adj, win2.adj),
player1 = school1, player2 = school2,
formula = ~ .. +
WOR[student] * Paris[..] +
WOR[student] * Milano[..] +
WOR[student] * Barcelona[..] +
DEG[student] * St.Gallen[..] +
STUD[student] * Paris[..] +
STUD[student] * St.Gallen[..] +
ENG[student] * St.Gallen[..] +
FRA[student] * London[..] +
FRA[student] * Paris[..] +
SPA[student] * Barcelona[..] +
ITA[student] * London[..] +
ITA[student] * Milano[..] +
SEX[student] * Milano[..],
refcat = "Stockholm",
data = CEMS)
##
## Again re-scale to reproduce approximately Table 6 of Dittrich et
## al. (2001):
##
table6 <- summary(table6.model)$coef[, 1:2]/1.75
print(table6)
##
## Not run:
## Now the slightly simplified model of Table 8 of Dittrich et al. (2001):
##
table8.model <- BTm(outcome = cbind(win1.adj, win2.adj),
player1 = school1, player2 = school2,
formula = ~ .. +
WOR[student] * LAT[..] +
DEG[student] * St.Gallen[..] +
STUD[student] * Paris[..] +
STUD[student] * St.Gallen[..] +
ENG[student] * St.Gallen[..] +
FRA[student] * London[..] +
FRA[student] * Paris[..] +
SPA[student] * Barcelona[..] +
ITA[student] * London[..] +
ITA[student] * Milano[..] +
SEX[student] * Milano[..],
refcat = "Stockholm",
data = CEMS)
table8 <- summary(table8.model)$coef[, 1:2]/1.75
##
## Notice some larger than expected discrepancies here (the coefficients
## named "..Barcelona", "..Milano" and "..Paris") from the results in
## Dittrich et al. (2001). Apparently a mistake was made in Table 8 of
## the published Corrigendum note (R. Dittrich personal communication,
## February 2010).
##
print(table8)
## End(Not run)
``` |

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