mbt function

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.

Returns

• 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(s)

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. tools:::Rd_expr_doi("10.1007/bf02294488")

Mallows, C.L. (1957). Non-null ranking models. I. Biometrika, 44 , 114--130. tools:::Rd_expr_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