The graphical display of a paired-comparison dependence effect, the counterpart of the DIF characteristic curve. For every comparison the departure of the observed response from what the object locations alone predict is taken, and the contribution of the other dependence effect is removed (a partial-residual display); these departures are then averaged in bins of the effect's own history covariate and plotted against it, with the model's fitted contribution overlaid. Observed points that rise with the covariate along the fitted line are the effect the coefficient summarises; a flat, scattered cloud means the estimate rests on little. Only the informative comparisons (a non-zero covariate: the two objects' histories differ) carry the effect, and the count in each bin is printed so a thin exposure tail is visible.
Usage
plot_btl_dependence(fit, effect = c("exposure", "carry_over"), bins = 6)Arguments
- fit
An object from
btlfitted with anordercolumn, sofit$dependence_datais present.- effect
Which effect to display:
"exposure"(the seen-before advantage, the default) or"carry_over"(response dependence).- bins
Number of covariate bins for the continuous carry-over display; exposure takes its three natural levels (-1, 0, +1).
Value
Called for its plotting side effect; invisibly a data frame of the binned covariate value, observed and fitted departure, and bin count.
References
Davidson, R. R., & Beaver, R. J. (1977). On extending the Bradley-Terry model to incorporate within-pair order effects. Biometrics, 33(4), 693-702.
Examples
set.seed(1)
beta <- c(A = -0.8, B = -0.2, C = 0.4, D = 0.9)
pr <- t(combn(names(beta), 2))
d <- data.frame(a = rep(pr[, 1], each = 40), b = rep(pr[, 2], each = 40))
d$judge <- sample(sprintf("J%02d", 1:8), nrow(d), TRUE)
d <- d[order(d$judge), ]; d$t <- ave(seq_len(nrow(d)), d$judge, FUN = seq_along)
d$win <- ifelse(runif(nrow(d)) < plogis(beta[d$a] - beta[d$b]), d$a, d$b)
f <- btl(d, "a", "b", winner = "win", judge = "judge", order = "t")
plot_btl_dependence(f, "carry_over")
