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Compute ANRI (Adjusted Normalized Resolution Index)

Source: R/anri_functions.R
compute_anri.Rd

Computes ANRI, a bias-corrected version of NRI following Yaniv et al. (1991). ANRI adjusts NRI for the number of confidence bins and sample size, providing more accurate estimates especially when J (bins) is small relative to N.

Usage

compute_anri(
  data,
  confidence_bins,
  choosers_only = TRUE,
  lineup_size = 6,
  confidence_scale = c("auto", "0-1", "0-100"),
  innocent_suspect = "auto"
)

Arguments

data

A dataframe with the following columns:

  • target_present: Logical. TRUE if guilty suspect in lineup

  • identification: Character. "suspect", "filler", or "reject"

  • confidence: Numeric. Confidence rating

confidence_bins

Numeric vector of bin edges (required for ANRI)

choosers_only

Logical. Whether to analyze only suspect IDs (default = TRUE)

lineup_size

Integer. Lineup size (default = 6)

confidence_scale

How the confidence scale is interpreted: "auto" (default), "0-1", or "0-100". See make_calibration_data.

innocent_suspect

How innocent-suspect identifications in target-absent lineups are obtained. "designated": the lineups had a designated innocent suspect, so target-absent "suspect" rows are counted directly, and zero such rows means a false-ID rate of zero. "estimated": there was no designated innocent suspect, so the innocent-suspect count is estimated as filler IDs divided by lineup_size. "auto" (the default) chooses "designated" when any target-absent row is a suspect ID or the data have a non-missing suspect_pos column, and "estimated" otherwise, with a message.

Value

A list containing:

  • anri: Adjusted Normalized Resolution Index

  • nri: Original Normalized Resolution Index (unadjusted)

  • n_total: Total sample size

  • n_bins: Number of confidence bins

  • calibration_data: Per-bin accuracy and sample sizes

  • overall_accuracy: Mean accuracy

Details

ANRI corrects NRI for small-sample and small-bin-count bias:

$$NRI = \frac{\frac{1}{N} \sum_{j=1}^{J} n_j (a_j - \bar{a})^2}{\bar{a}(1-\bar{a})}$$

$$ANRI = \frac{N \cdot NRI - J + 1}{N - J + 1}$$

Where:

  • N = total sample size

  • J = number of bins

  • n_j = sample size in bin j

  • a_j = accuracy (proportion correct) in bin j

  • a_bar = overall accuracy

**When to use ANRI vs NRI:**

  • Use ANRI when J is small (e.g., 3-5 bins)

  • Use ANRI when N is modest (e.g., < 200)

  • Use ANRI when comparing across different numbers of bins

  • NRI is asymptotically unbiased as N approaches infinity

ANRI provides a less biased estimate of the population resolution, making it more appropriate for hypothesis testing and group comparisons. When target-absent suspect identifications are estimated from filler choices, N and the bin counts are effective (possibly fractional) counts from make_calibration_data(), so the correction is an approximation. See make_calibration_data for the designated-suspect distinction.

References

Yaniv, I., Yates, J. F., & Smith, J. E. K. (1991). Measures of discrimination skill in probabilistic judgment. Psychological Bulletin, 110(3), 611-617.

Juslin, P., Olsson, N., & Winman, A. (1996). Calibration and diagnosticity of confidence in eyewitness identification. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(5), 1304-1316.

Examples

set.seed(123)
n <- 200
data <- data.frame(
  target_present = rep(c(TRUE, FALSE), each = n / 2),
  identification = sample(c("suspect", "filler", "reject"), n,
                          replace = TRUE, prob = c(0.5, 0.25, 0.25)),
  confidence = round(runif(n, 0, 100))
)
result <- compute_anri(data, confidence_bins = seq(0, 100, 20))
result$anri
#> [1] -0.01987784