Package {pridit}

pridit: Principal Component Analysis Applied to Ridit Scoring

Description

The pridit package provides functions for implementing the PRIDIT (Principal Component Analysis applied to RIDITs) scoring system.

A single entry-point that runs the full PRIDIT pipeline—ridit scoring, weight estimation, and composite scoring—and returns a classed object with print, summary, autoplot, and coef methods.

Usage

pridit(data, sign_correction = TRUE)

Arguments

Details

PRIDIT (Principal Component Analysis applied to RIDITs) was introduced by Brockett et al. (2002) for insurance fraud detection and applied to hospital quality measurement by Lieberthal (2008). Its key properties are:

1. No parametric assumptions about the data-generating process.

2. No prior knowledge of indicator direction is required; weight signs are determined entirely by the data.

3. Each indicator weight is interpretable as its contribution to the dominant latent factor.

Value

An object of class "pridit", a list with components:

scores

Data frame with columns id and PRIDITscore, sorted descending.

weights

Named numeric vector of PRIDIT weights.

eigenvalue

Largest eigenvalue of the ridit cross-product matrix (used for score normalisation).

eigenvalue_ratio

Ratio of the first to the second eigenvalue; large values support the single-factor interpretation.

n

Number of observations.

p

Number of indicators.

call

Matched call.

Author(s)

Maintainer: Robert D. Lieberthal rlieberthal@gmail.com

Authors:

• Robert D. Lieberthal rlieberthal@gmail.com

References

Brockett, P. L., Derrig, R. A., Golden, L. L., Levine, A., & Alpert, M. (2002). Fraud classification using principal component analysis of RIDITs. Journal of Risk and Insurance, 69(3), 341–371.

Lieberthal, R. D. (2008). Hospital quality: A PRIDIT approach. Health Services Research, 43(3), 988–1005.

Lieberthal, R. D., & Comer, D. M. (2013). What are the characteristics that explain hospital quality? A longitudinal PRIDIT approach. Risk Management and Insurance Review, 17(1), 17–35.

See Also

Useful links:

• https://github.com/rlieberthal/PRIDIT

• Report bugs at https://github.com/rlieberthal/PRIDIT/issues

pridit_boot, pridit_longitudinal, step_pridit

Examples

dat <- data.frame(
  id = letters[1:10],
  x1 = runif(10),
  x2 = runif(10),
  x3 = runif(10)
)
fit <- pridit(dat)
fit
summary(fit)

Compute PRIDIT scores

Description

Applies a vector of PRIDIT weights to a ridit-scored data frame and returns a composite score in (-1, 1) for each observation. The score is normalised by the largest eigenvalue so that the mean score is zero by construction.

Usage

PRIDITscore(ridit_data, id_vector, weight_vec)

Arguments

Value

A data frame with columns id and PRIDITscore.

See Also

ridit, PRIDITweight, pridit

Examples

dat <- data.frame(
  id = c("A", "B", "C", "D", "E"),
  x1 = c(0.90, 0.85, 0.89, 1.00, 0.89),
  x2 = c(0.99, 0.92, 0.90, 1.00, 0.93)
)
rs  <- ridit(dat)
wts <- PRIDITweight(rs)
PRIDITscore(rs, dat$id, wts)

Compute PRIDIT weights

Description

Computes the PRIDIT weight vector from a ridit-scored data frame. Weights are the loadings of the first principal component of the ridit matrix, scaled by the column norms of that matrix. The sign of the weight vector is arbitrary (a property of PCA); pass the result to pridit rather than using this function directly if automatic sign correction is desired.

Usage

PRIDITweight(ridit_data)

Arguments

Value

A named numeric vector of PRIDIT weights, one per indicator column.

See Also

ridit, PRIDITscore, pridit

Examples

dat <- data.frame(
  id = c("A", "B", "C", "D", "E"),
  x1 = c(0.90, 0.85, 0.89, 1.00, 0.89),
  x2 = c(0.99, 0.92, 0.90, 1.00, 0.93)
)
rs  <- ridit(dat)
PRIDITweight(rs)

Plot a PRIDIT model

Description

Produces a two-panel ggplot2 figure: a bar chart of the top indicator weights by magnitude (left) and a histogram of the PRIDIT score distribution (right).

Usage

## S3 method for class 'pridit'
autoplot(object, top_n = 20L, ...)

Arguments

Value

A ggplot object (invisibly).

Plot bootstrap confidence intervals for a PRIDIT model

Description

Produces a point-and-range plot for indicator weight CIs and, if available, a ranked-score plot with error ribbons.

Usage

## S3 method for class 'pridit_boot'
autoplot(object, top_n = 20L, ...)

Arguments

Value

A ggplot object (invisibly).

Plot a longitudinal PRIDIT analysis

Description

Produces two panels: (left) a heatmap of cross-period Spearman score correlations and (right) a line plot of per-indicator weight trajectories across periods.

Usage

## S3 method for class 'pridit_longitudinal'
autoplot(object, top_n = 10L, ...)

Arguments

Value

A ggplot object (invisibly).

Extract PRIDIT weights

Description

Extract PRIDIT weights

Usage

## S3 method for class 'pridit'
coef(object, ...)

Arguments

Value

Named numeric vector of PRIDIT weights.

Bootstrap confidence intervals for PRIDIT scores and weights

Description

Resamples observations with replacement B times, refitting the full PRIDIT pipeline on each resample. Returns percentile confidence intervals for every indicator weight and, optionally, for every observation's score.

Usage

pridit_boot(fit, data, B = 500L, conf_level = 0.95, scores = TRUE, seed = NULL)

Arguments

Details

Because PCA sign is arbitrary, each bootstrap replicate's weight vector is aligned to the original fit before aggregation: if the Pearson correlation between the replicate weights and the original weights is negative, the replicate is sign-flipped.

Value

An object of class "pridit_boot", a list with components:

weights_ci

Data frame with columns indicator, estimate, lower, upper.

scores_ci

Data frame with columns id, estimate, lower, upper (or NULL if scores = FALSE).

B

Number of replicates used.

conf_level

Coverage probability.

call

Matched call.

See Also

pridit, autoplot.pridit_boot

Examples

dat <- data.frame(
  id = letters[1:30],
  x1 = runif(30), x2 = runif(30), x3 = runif(30)
)
fit  <- pridit(dat)
boot <- pridit_boot(fit, dat, B = 100, seed = 42)
boot

Longitudinal PRIDIT analysis

Description

Fits a separate PRIDIT model for each time period in a panel data set and summarises the stability of scores and weights across periods. The analysis follows Lieberthal & Comer (2013), who demonstrated that PRIDIT weights computed on one year's Hospital Compare data predict out-of-period outcomes in the following year, with cross-year weight correlations exceeding 0.99.

Usage

pridit_longitudinal(
  data,
  id_col,
  time_col,
  indicator_cols = NULL,
  sign_correction = TRUE
)

Arguments

Details

Because the PCA sign is arbitrary, each period's weight vector is aligned to the first period before computing cross-period correlations: if the Pearson correlation between a replicate's weights and the first period's weights is negative, the replicate is sign-flipped.

Cross-period score correlations are computed only for the balanced panel (observations present in all periods).

Value

An object of class "pridit_longitudinal", a list with:

fits

Named list of "pridit" objects, one per period.

weight_cors

Symmetric matrix of Pearson correlations between period weight vectors.

score_cors

Symmetric matrix of Spearman rank correlations between period scores on the balanced panel.

scores_wide

Data frame of scores in wide format (one column per period) for the balanced panel.

weights_long

Data frame of weights in long format with columns period, indicator, weight.

periods

Sorted vector of period labels.

n_balanced

Number of observations in the balanced panel.

call

Matched call.

References

Lieberthal, R. D., & Comer, D. M. (2013). What are the characteristics that explain hospital quality? A longitudinal PRIDIT approach. Risk Management and Insurance Review, 17(1), 17–35.

See Also

pridit, autoplot.pridit_longitudinal

Examples

set.seed(1)
dat <- data.frame(
  id   = rep(letters[1:20], times = 3),
  year = rep(2020:2022, each = 20),
  x1   = runif(60),
  x2   = runif(60),
  x3   = runif(60)
)
fit_long <- pridit_longitudinal(dat, id_col = "id", time_col = "year")
fit_long

Compute ridit scores

Description

Transforms a data frame of numeric indicators into ridit scores on the interval (-1, 1) using the empirical cumulative distribution of each column across the reference population. A score of zero indicates a value exactly at the median; positive scores indicate above-median values.

Usage

ridit(data)

Arguments

Details

The ridit score for observation i on indicator j is

B_{ij} = F_j(x_{ij} - \varepsilon) - [1 - F_j(x_{ij})]

where F_j is the empirical CDF of column j and \varepsilon is a small constant that makes the lower CDF strictly left-continuous. This formulation is robust to ties and requires no parametric assumptions.

Categorical indicators should be expanded into binary dummy columns before calling ridit(); each dummy then receives its own ridit transformation and PRIDIT weight, with sign determined by the data rather than by the analyst.

Value

A data frame of the same shape as data with numeric columns replaced by their ridit scores. The ID column is preserved as-is.

References

Bross, I. D. J. (1958). How to use ridit analysis. Biometrics, 14(1), 18–38.

Brockett, P. L., Derrig, R. A., Golden, L. L., Levine, A., & Alpert, M. (2002). Fraud classification using principal component analysis of RIDITs. Journal of Risk and Insurance, 69(3), 341–371.

Examples

dat <- data.frame(
  id = c("A", "B", "C", "D", "E"),
  x1 = c(0.90, 0.85, 0.89, 1.00, 0.89),
  x2 = c(0.99, 0.92, 0.90, 1.00, 0.93)
)
ridit(dat)

recipes step: PRIDIT composite score

Description

Creates a recipes preprocessing step that fits a PRIDIT model on the training data and appends a single composite score column to any data set passed to bake(). This enables genuine out-of-sample scoring: the empirical CDFs used for ridit transformation and the PCA weights are estimated on the training fold only and then applied to the test fold without re-fitting.

Usage

step_pridit(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  score_name = "PRIDIT_score",
  sign_correction = TRUE,
  ecdfs = NULL,
  weights = NULL,
  max_eigval = NULL,
  col_norms = NULL,
  skip = FALSE,
  id = recipes::rand_id("pridit")
)

Arguments

Details

All selected columns must be numeric. The step does not remove the original columns; use step_rm() afterwards if a clean feature set is required.

Value

An updated recipe.

Examples

## Not run: 
library(recipes)

dat <- data.frame(
  id = letters[1:50],
  x1 = runif(50), x2 = runif(50), x3 = runif(50)
)

rec <- recipe(~ ., data = dat) |>
  update_role(id, new_role = "id") |>
  step_pridit(x1, x2, x3)

prepped <- prep(rec, training = dat)
bake(prepped, new_data = dat)

## End(Not run)

Test dataset for PRIDIT analysis

Description

A sample dataset containing health quality metrics for 5 healthcare providers, used to demonstrate the PRIDIT scoring methodology.

Usage

test

Format

A data frame with 5 rows and 4 variables:

ID

Character. Unique identifier for each healthcare provider (A through E)

Smoking_cessation

Numeric. Smoking cessation counseling rate (0.85-1.0)

ACE_Inhibitor

Numeric. ACE inhibitor prescription rate (0.90-1.0)

Proper_Antibiotic

Numeric. Proper antibiotic usage rate (0.98-1.0)

Source

Synthetic data created for package examples

Examples

data(test)
head(test)

# Calculate PRIDIT scores
ridit_scores <- ridit(test)
weights <- PRIDITweight(ridit_scores)
final_scores <- PRIDITscore(ridit_scores, test$ID, weights)