% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/btl-targeting.R
\name{btl_information}
\alias{btl_information}
\title{Information and targeting of a paired-comparison design}
\usage{
btl_information(fit)
}
\arguments{
\item{fit}{A paired-comparison fit from \code{\link{btl}}.}
}
\value{
A list of class \code{"rasch_btl_info"}: \code{objects} (per
  object: \code{location}, the fit's \code{se}, \code{n_comparisons},
  the design \code{information}, and \code{se_naive}); \code{pairs} (per
  observed pair: \code{n}, the mean location \code{gap}, and the pair's
  \code{information}); \code{comparisons} (per comparison: the signed
  \code{gap}, \code{weight}, and the single-comparison \code{information});
  the scalar \code{total} information; \code{m}; the \code{clustered}
  flag; and \code{notes}.
}
\description{
The paired-comparison analogue of the test-information function. The
Fisher information a single comparison carries about the location
difference \code{d = beta_a - beta_b} is, in this exponential family, the
variance of its score -- \code{P(1 - P)} for the dichotomous choice and
the graded response variance \code{V} for the ordinal extension (the
score is the sufficient statistic for \code{d}, so its variance is the
information). Weighted by each comparison's replication count and summed
over the comparisons the design actually contains, this gives a
\emph{design information} for every object: how much the observed
comparisons pin its location down, the counterpart of an item's
contribution to test information. Because the information peaks at gap
zero and falls away with the location gap, near-neighbour contests are
the informative ones.
}
\details{
The design information inverts to \code{se_naive = 1 / sqrt(information)}:
the error the object's comparisons would give if its location were the
ONLY free parameter -- a single-parameter lower bound, useful for reading
which objects the design serves well. It is not the model's standard
error even with independent comparisons (every location is estimated
jointly with the others, and the fit's own \code{se} is additionally the
judge-clustered Godambe sandwich), so \code{se} sits above
\code{se_naive} as a rule; treat their ratio as descriptive, not as a
clustering test.
}
\examples{
set.seed(1)
beta <- c(A = -1, B = -0.3, C = 0.4, D = 0.9)
pr <- t(combn(names(beta), 2))
d <- data.frame(a = rep(pr[, 1], each = 30), b = rep(pr[, 2], each = 30))
d$win <- ifelse(runif(nrow(d)) < plogis(beta[d$a] - beta[d$b]), d$a, d$b)
btl_information(btl(d, "a", "b", "win"))
}
\references{
Pollitt, A. (2012). The method of adaptive comparative
  judgement. \emph{Assessment in Education}, 19(3), 281-300.
}
\seealso{
\code{\link{plot_btl_targeting}}, \code{\link{btl_next_pairs}}
}
