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Compute PPV by Confidence with Lineup Size Correction

Source: R/ppv_range_functions.R
ppv_by_confidence.Rd

Calculates Positive Predictive Value (PPV) for each confidence level, using a specified method to correct for lineup size when estimating innocent-suspect identification rates.

Usage

ppv_by_confidence(
  data,
  lineup_size = 6,
  confidence_bins = NULL,
  correction = c("nominal", "effective", "none"),
  effective_size_data = NULL,
  quiet = FALSE,
  innocent_suspect = "auto",
  base_rate = NULL
)

Arguments

data

A dataframe with columns:

  • target_present: Logical. TRUE if guilty suspect in lineup

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

  • confidence: Numeric. Confidence rating

lineup_size

Integer. Nominal number of people in lineup (default = 6)

confidence_bins

Numeric vector of bin edges for grouping confidence (e.g., c(0, 60, 80, 100)). If NULL, uses individual confidence levels.

correction

Character. Method for estimating innocent-suspect IDs: "nominal" (best-case, assumes fair lineup), "effective" (accounts for bias), "none" (worst-case, no correction). Default = "nominal".

effective_size_data

Optional dataframe with pre-computed effective sizes per confidence bin (must have columns: conf_level, effective_size). If NULL and correction="effective", computes from data.

quiet

Logical. Suppress the note issued when correction is not applied because the data designate an innocent suspect, and the note issued when the two arms differ in size. Default FALSE.

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.

base_rate

Prior probability that the suspect is guilty. NULL (default) computes PPV from counts, as below. A number strictly between 0 and 1 computes it from the guilty-ID rate (per target-present trial) and the innocent-suspect-ID rate (per target-absent trial) at that prior, so the result does not depend on the TP:TA split.

Value

A list containing:

  • ppv_data: Dataframe with PPV by confidence level

  • overall_ppv: Overall PPV across all confidence levels

  • correction_method: The correction method requested

  • innocent_suspect_method: "designated" when target-absent trials identify an innocent suspect directly, otherwise the estimation route

  • lineup_size: Nominal lineup size

Details

PPV (Positive Predictive Value) is the probability that a suspect is guilty given an identification. The formula is:

PPV = guilty_suspect_IDs / (guilty_suspect_IDs + innocent_suspect_IDs)

Different correction methods estimate innocent_suspect_IDs differently:

  • "nominal": assumes perfect lineup fairness (error_rate / lineup_size)

  • "effective": uses effective size to account for bias (error_rate / effective_size)

  • "none": assumes all errors are innocent-suspect IDs (error_rate)

Note on the base rate: by default PPV is computed from raw target-present and target-absent counts, so the prior probability of guilt is implicitly the experiment's TP:TA ratio (e.g., 0.5 for the usual balanced design), and a message is issued when the two arms differ in size. Set base_rate to compute \(\pi g(c) / (\pi g(c) + (1 - \pi) i(c))\) from the guilty-ID rate \(g(c)\) and innocent-suspect-ID rate \(i(c)\) instead; base_rate = 0.5 reproduces the balanced-design value at any sample sizes. PPV is not base-rate-free: at different real-world base rates the PPV of the same procedure will differ. When target-absent lineups have no designated innocent suspect, the correction also relies on the pseudo-distribution assumption of spreading filler choices over lineup members, which is a modeling approximation.

When the correction is ignored

Lineup-size corrections exist to estimate how many of the observed target-absent identifications fell on an innocent suspect, in data where no innocent suspect was designated. When the data do designate one, that count is observed rather than estimated, and correction has no work to do: all three methods return the same PPV. This is correct, not a fault, but it is easy to mistake for one, so a message is issued unless quiet = TRUE. lineup_example is data of this kind.

References

Fitzgerald, R. J., Tredoux, C. G., & Juncu, S. (2023). Estimation of eyewitness error rates in fair and biased lineups. Law and Human Behavior.

Examples

data(lineup_example)
# Nominal correction (assumes fair lineup)
ppv_result <- ppv_by_confidence(lineup_example,
                                correction = "nominal",
                                confidence_bins = c(0, 60, 80, 100))
#> Target-absent lineups contain a designated innocent suspect, so innocent-suspect IDs are counted directly and the 'nominal' correction is not applied. All correction methods return the same PPV for these data. Lineup-size corrections apply only when no innocent suspect is designated.

# Effective size correction (accounts for bias)
ppv_result <- ppv_by_confidence(lineup_example,
                                correction = "effective",
                                confidence_bins = c(0, 60, 80, 100))
#> Target-absent lineups contain a designated innocent suspect, so innocent-suspect IDs are counted directly and the 'effective' correction is not applied. All correction methods return the same PPV for these data. Lineup-size corrections apply only when no innocent suspect is designated.