ExtremisationWAgg: Aggregation Method: ExtremisationWAgg

In aggreCAT: Mathematically Aggregating Expert Judgments

Aggregation Method: ExtremisationWAgg

Description

Calculate beta-transformed arithmetic means of best estimates.

Usage

ExtremisationWAgg(
  expert_judgements,
  type = "BetaArMean",
  name = NULL,
  alpha = 6,
  beta = 6,
  cutoff_lower = NULL,
  cutoff_upper = NULL,
  placeholder = FALSE,
  percent_toggle = FALSE,
  round_2_filter = TRUE
)

Arguments

expert_judgements	A dataframe in the format of data_ratings.
type	One of "BetaArMean" or "BetaArMean2".
name	Name for aggregation method. Defaults to type unless specified.
alpha	parameter for the 'shape1' argument in the stats::pbeta function (defaults to 6)
beta	parameter for the 'shape2' argument in the stats::pbeta function (defaults to 6)
cutoff_lower	Lower bound of middle region without extremisation in "BetaArMean2" aggregation types.
cutoff_upper	Upper bound of middle region without extremisation in "BetaArMean2" aggregation types.
placeholder	Toggle the output of the aggregation method to impute placeholder data.
percent_toggle	Change the values to probabilities. Default is FALSE.
round_2_filter	Note that the IDEA protocol results in both a Round 1 and Round 2 set of probabilities for each claim. Unless otherwise specified, we will assume that the final Round 2 responses (after discussion) are being referred to.

Details

This method takes the average of best estimates and transforms it using the cumulative distribution function of a beta distribution.

type may be one of the following:

BetaArMean: Beta transformation applied across the entire range of calculated confidence scores. \loadmathjax

\mjdeqn\hat

p_c\left( \textBetaArMean \right) = H_\alpha \beta\left(\frac1N \sum_i=1^N B_i,c \right),ascii

where \mjeqnH_\alpha \betaascii is the cumulative distribution function of the beta distribution with parameters \mjeqn\alphaascii and \mjeqn\betaascii, which default to 6 in the function.

The justification for equal parameters (the 'shape1' and 'shape2' arguments in the stats::pbeta function) are outlined in Satopää et al (2014) and the references therein (note that the method outlined in that paper is called a beta-transformed linear opinion pool). To decide on the default shape value of 6, we explored the data_ratings dataset with random subsets of 5 assessments per claim, which we expect to have for most of the claims assessed by repliCATS.

BetaArMean2: Beta transformation applied only to calculated confidence scores that are outside a specified middle range. The premise being that we don't extremise "fence-sitter" confidence scores.

\mjdeqn\hat

p_c\left( \textBetaArMean2 \right) = \begincases \displaystyle H_\alpha \beta\left(\frac1N \sum_i=1^N B_i,c \right), \text for \frac1N \sum_i=1^N B_i,c < \textitcutoff\_lower
\displaystyle \frac1N \sum_i=1^N B_i,c, \text for \textitcutoff\_lower \leq \frac1N \sum_i=1^N B_i,c \leq \textitcutoff\_upper
\displaystyle H_\alpha \beta\left(\frac1N \sum_i=1^N B_i,c \right), \text for \frac1N \sum_i=1^N B_i,c > \textitcutoff\_upper
\endcasesascii

Value

A tibble of confidence scores cs for each paper_id.

Examples

ExtremisationWAgg(data_ratings)

aggreCAT documentation built on June 8, 2025, 11:06 a.m.