Fit Signal Detection Theory Model to ROC Data

Fits an equal-variance or unequal-variance SDT model to ROC data using z-ROC analysis. Extracts discriminability (d'), decision criteria (c), and optionally the target/lure variance ratio.

Usage

fit_sdt_roc(
  data,
  lineup_size = NULL,
  model = c("equal_variance", "unequal_variance"),
  bootstrap = TRUE,
  n_bootstrap = 1000,
  conf_level = 0.95,
  seed = NULL,
  innocent_suspect = "auto"
)

Arguments

data: A dataframe with columns: target_present, identification, confidence OR a rocdata object from make_rocdata()
lineup_size: Integer. Number of people in lineup (required if data is dataframe)
model: Character. "equal_variance" or "unequal_variance" (default = "equal_variance")
bootstrap: Logical. Compute bootstrap confidence intervals? (default = TRUE)
n_bootstrap: Integer. Number of bootstrap samples (default = 1000)
conf_level: Numeric. Confidence level for intervals (default = 0.95)
seed: Integer. Random seed for reproducibility (default = NULL)
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

An S3 object of class "sdt_roc_fit" containing:

dprime: Overall discriminability (d')
criteria: Decision criterion for each confidence level (c values)
variance_ratio: Ratio of lure SD to target SD, the z-ROC slope (if unequal_variance)
slope: Slope of z-ROC
intercept: Intercept of z-ROC
roc_data: Original ROC data with z-transforms
model_type: Type of model fit
bootstrap_ci: Confidence intervals (if bootstrap = TRUE)
fit_diagnostics: R-squared, residuals, etc.

Details

**z-ROC Analysis**:

The z-ROC is created by plotting z-transformed hit rates against z-transformed false alarm rates for each confidence level.

Under equal-variance SDT: - z-ROC should be linear with slope = 1 - d' = z(HR) - z(FAR) for any criterion - Intercept = d' in the line z(HR) = z(FAR) + d'

Under unequal-variance SDT: - Slope = SD_lure / SD_target - Slope > 1 indicates greater variability in lure distribution

**Parameter Estimation**: - d' = average distance between distributions in standard deviation units - c = decision criterion (0 = unbiased, positive = conservative, negative = liberal) - Higher d' = better discriminability

**Bootstrap Confidence Intervals**: If bootstrap = TRUE, resamples data with replacement to estimate standard errors and confidence intervals for all parameters.

References

Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user's guide (2nd ed.).

Mickes, L. (2015). Receiver operating characteristic analysis and confidence-accuracy characteristic analysis in investigations of system variables. Journal of Applied Research in Memory and Cognition, 4(2), 93-102.

Examples

# Simulate data
sim_data <- simulate_lineup_data(
  n_tp = 200, n_ta = 200,
  d_prime = 1.5,
  conf_levels = 5,
  seed = 123
)

# Fit equal-variance SDT model
sdt_fit <- fit_sdt_roc(sim_data, lineup_size = 6, bootstrap = FALSE)
print(sdt_fit)
#> 
#> === SDT Model Fit to ROC Data ===
#> 
#> Model: Equal Variance 
#> 
#> Parameters:
#>   d' (discriminability): 1.518 
#> 
#> z-ROC Line:
#>   Slope: 1 
#>   Intercept: 1.518 
#>   R-squared: 0.835 
#> 
#> Decision Criteria (c):
#>  Criterion Value
#>         c1 1.462
#>         c2 0.951
#>         c3 0.601
#>         c4 0.461
#>         c5 0.425
#> 
#> Interpretation:
#>   - Moderate discriminability (1.0 <= d' < 2.0)
#>   - Conservative bias (mean c > 0)
plot(sdt_fit)


# Get d' estimate
sdt_fit$dprime
#> [1] 1.518421

# Fit unequal-variance model
sdt_uv <- fit_sdt_roc(
  sim_data, lineup_size = 6, model = "unequal_variance", bootstrap = FALSE
)
sdt_uv$variance_ratio
#>    z_far 
#> 0.713702 

# \donttest{
# Use more replicates for publication analyses.
sdt_boot <- fit_sdt_roc(
  sim_data, lineup_size = 6, n_bootstrap = 200, seed = 123
)
# }