R: Dittrich, Hatzinger and Katzenbeisser (1998, 2001) Data on...

CEMS {BradleyTerry2} | R Documentation

## Dittrich, Hatzinger and Katzenbeisser (1998, 2001) Data on Management School Preference in Europe

### Description

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

### Usage

    CEMS

### Format

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

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

### Author(s)

David Firth

### Source

Royal Statistical Society datasets website, at http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/homepage/47_4.htm.

### 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.

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.

### Examples

    ##
    ##  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)

[Package BradleyTerry2 version 1.0-6 Index]