Mallows-Bradley-Terry Model

Fits a Mallows-Bradley-Terry (MBT) model by maximum likelihood.

mbt(data, bootstrap = FALSE, nsim = 1000, ...)

Arguments

data

a data frame, the first t columns containing the ranks, the (t + 1)th column containing the frequencies

bootstrap

logical. Return a parametric bootstrap p-value?

nsim

number of bootstrap replicates

...

further aguments passed to simulate

Details

mbt provides a front end for glm. See Critchlow and Fligner (1991) and Mallows (1957) for details.

Value

coefficients

a vector of parameter estimates (scale values) constrained to sum to unity

goodness.of.fit

the goodness of fit statistic including the likelihood ratio fitted vs. saturated model (-2logL), the degrees of freedom, the p-value of the corresponding chi-square distribution, and if bootstrap is TRUE the bootstrap p-value

perm.idx

the names of the non-zero frequency ranks

y

the vector of rank frequencies including zeros

mbt.glm

the output from a call to glm

Author

Florian Wickelmaier

References

Critchlow, D.E., & Fligner, M.A. (1991). Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation in GLIM. Psychometrika, 56, 517–533. doi:10.1007/bf02294488

Mallows, C.L. (1957). Non-null ranking models. I. Biometrika, 44, 114–130. doi:10.1093/biomet/44.1-2.114

See also

tartness, glm.

Examples

data(tartness)        # tartness rankings of salad dressings (Vargo, 1989)
mbt(tartness, bootstrap=TRUE, nsim=500)  # fit Mallows-Bradley-Terry model
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> 
#> Mallows-Bradely-Terry (MBT) models
#> 
#> Parameter estimates:
#>      a       b       c       d  
#> 0.0912  0.5182  0.2317  0.1588  
#> 
#> Goodness of fit (-2 log likelihood ratio):
#> 	G2(20) = 22.25, p = 0.3272, bootstrap p = 0.08
#>