Getting Started with piiR

What is the Predictive Information Index (PII)?

The Predictive Information Index (PII) quantifies how much outcome-relevant information is retained when reducing a set of predictors (e.g., items) to a composite score.

PII is defined as:

\text{PII} = 1 - \frac{\text{Var}(\hat{Y}_{\text{Full}} - \hat{Y}_{\text{Score}})}{\text{Var}(\hat{Y}_{\text{Full}})}

Where: - \(\hat{Y}_{\text{Full}}\): predictions from a full model (e.g., all items or predictors) - \(\hat{Y}_{\text{Score}}\): predictions from a reduced score (e.g., mean or sum)

A PII of 1 means no predictive information was lost. A PII near 0 means the score loses most predictive information.

Example: Using pii()

library(piiR)

# Simulate two prediction vectors
set.seed(123)
full_model_preds <- rnorm(100)
score_based_preds <- full_model_preds + rnorm(100, sd = 0.5)

# Compute PII
pii(full_model_preds, score_based_preds)

## [1] 0.7721124