ShiftingWAgg: Aggregation Method: ShiftingWAgg

In aggreCAT: Mathematically Aggregating Expert Judgments

Aggregation Method: ShiftingWAgg

Description

Weighted by judgements that shift the most after discussion

Usage

ShiftingWAgg(
  expert_judgements,
  type = "ShiftWAgg",
  name = NULL,
  placeholder = FALSE,
  percent_toggle = FALSE
)

Arguments

expert_judgements	A dataframe in the format of data_ratings.
type	One of "ShiftWAgg", "BestShiftWAgg", "IntShiftWAgg", "DistShiftWAgg", or "DistIntShiftWAgg".
name	Name for aggregation method. Defaults to type unless specified.
placeholder	Toggle the output of the aggregation method to impute placeholder data.
percent_toggle	Change the values to probabilities. Default is FALSE.

Details

When judgements are elicited using the IDEA protocol (or any other protocol that allows experts to revisit their original estimates), the second round of estimates may differ from the original first set of estimates an expert provides. Greater changes between rounds will be given greater weight.

type may be one of the following:

\loadmathjax

ShiftWAgg: Takes into account the shift in all three estimates

Considers shifts across lower, \mjeqnL_i,cascii, and upper, \mjeqnU_i,cascii, confidence limits, and the best estimate, \mjeqnB_i,cascii. More emphasis is placed on changes in the best estimate such that:

\mjdeqn

w\_Shift_i,c = |B1_i,c - B_i,c| + \frac|L1_i,c - L_i,c|+|U1_i,c - U_i,c|2,ascii

where \mjeqnL1_i,c, B1_i,c,U1_i,cascii are the first round lower, best and upper estimates (prior to discussion) and \mjeqnL_i,c, B_i,c,U1_i,cascii are the individual’s revised second round estimates (after discussion).

\mjdeqn\hat

p_c(ShiftWAgg) = \sum_i=1^N \tildew\_Shift_i,cB_i,cascii

BestShiftWAgg: Weighted according to shifts in best estimates alone

Taking into account the fact that the scales best estimates are measured on are bounded, we can calculate shifts relative to the largest possible shift.

\mjdeqn

w\_BestShift_i,c= \begincases \frac|B1_i,c - B_i,c|B1_i,c, \beginaligned \displaystyle &\ for\ (B1_i,c > 0.5\ and\ B_i,c \leq 0.5)
\displaystyle &\ or\ B_i,c < B1_i,c \leq 0.5\ or\ B1_i,c > B_i,c > 0.5 \endaligned
\frac|B1_i,c - B_i,c|1- B1_i,c, \beginaligned \displaystyle &\ for\ (B1_i,c < 0.5\ and\ B_i,c \geq 0.5)
\displaystyle &\ or\ B1_i,c < B_i,c < 0.5\ or\ B_i,c > B1_i,c > 0.5. \endaligned \endcasesascii

\mjdeqn\hat

p_c(BestShiftWAgg) = \sum_i=1^N \tildew\_BestShift_i,cB_i,cascii

IntShiftWAgg: Weighted by shifts in interval widths alone.

Individuals whose interval widths narrow between rounds are given more weight.

\mjdeqn

w\_IntShift_i,c = \frac1(U_i,c-L_i,c)-(U1_i,c-L1_i,c)+1ascii

\mjdeqn\hat

p_c(IntShiftWAgg) = \sum_i=1^N \tildew\_IntShift_i,cB_i,cascii

DistShiftWAgg: Weighted by whether best estimates become more extreme (closer to 0 or 1) between rounds.

\mjdeqn

w\_DistShift_i,c = 1 - (\min (B_i,c, 1-B_i,c) - \min (B1_i,c, 1-B1_i,c))ascii

\mjdeqn\hat

p_c(DistShiftWAgg) = \sum_i=1^N \tildew\_DistShift_i,cB_i,cascii

DistIntShiftWAgg: Rewards both narrowing of intervals and shifting towards the certainty limits between rounds.

We simply multiply the weights calculated in the "DistShiftWAgg" and "IntShiftWAgg" methods.

\mjdeqn

w\_DistIntShift_i,c = \tildew\_IntShift_i,c \cdot \tildew\_DistShift_i,cascii

\mjdeqn\hat

p_c(DistIntShiftWAgg) = \sum_i=1^N \tildew\_DistIntShift_i,cB_i,cascii

Value

A tibble of confidence scores cs for each paper_id.

Examples

ShiftingWAgg(data_ratings)

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