Calculate the density of ordinal comparison data based on BTL models

This function calculates the density of ordinal comparison data (e.g., complete rankings, partial rankings, pairwise comparisons, or groupwise comparisons) based on an appropriate Bradley-Terry-Luce (BTL) model with object-specific worth parameters, omega.

dBTL(Pi, omega, log = FALSE, groupwise = FALSE)

Arguments

Pi: A matrix of preference orderings ("rankings"), such that the (i,j) entry is the index of the jth-most preferred object according to judge i. If groupwise=TRUE, then the index corresponds to the jth-most preferred object among those in row i; if groupwise=FALSE, it is assumed that all unranked objects (if any) are less preferred than those which are ranked.
omega: A vector of non-negative object worth parameters.
log: A boolean to indicate whether the log density should be returned. Default to FALSE.
groupwise: A boolean to indicate whether the observed rankings are complete/partial rankings (FALSE; default) or groupwise comparisons (TRUE).

Value

A numeric joint density of the observed rankings.

Examples

Pi <- matrix(data=c(1,2,3,NA,NA,1,2,3,4,5),byrow=TRUE,nrow=2)
dBTL(Pi=Pi,omega=c(10,8,6,4,2),log=TRUE,groupwise=FALSE)
#> [1] -5.821566
dBTL(Pi=Pi,omega=c(10,8,6,4,2),log=TRUE,groupwise=TRUE)
#> [1] -4.5486