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Compute WLE and EAP Reliability Using TAM

compute_reliability_tam.Rd

Fits a Rasch or 2PL model using TAM and computes WLE and EAP reliability using TAM::WLErel() and TAM::EAPrel(). This helper does not fit or score a 3PL model.

Usage

compute_reliability_tam(resp, model = c("rasch", "2pl"), verbose = FALSE, ...)

Arguments

resp

Matrix or data.frame of item responses (0/1).

model

Character. "rasch" or "2pl". A 3PL value is deliberately unsupported because the package's validated TAM contract requires both WLE and EAP reliability, while the tested TAM 3PL path does not provide the required WLE workflow.

verbose

Logical. If TRUE, print fitting messages.

...

Additional arguments passed to TAM fitting functions.

Value

A list with components:

rel_wle

WLE reliability.

rel_eap

EAP reliability.

mod

Fitted TAM model object.

wle

Output from TAM::tam.wle().

Details

WLE vs EAP Reliability

TAM defines these reliability coefficients differently:

  • WLE reliability: \(1 - \bar{s}^2 / V_{WLE}\), based on design effect

  • EAP reliability: \(V_{EAP} / (V_{EAP} + \bar{\sigma}^2)\), based on posterior variance

WLE and EAP use different estimators and variance bases, so neither is a universal upper or lower bound for the other. EAP is the closer external analogue to the MSEM-based population estimand, but it is not identical to the information-based EQC estimand.

3PL limitation

compute_reliability_tam() intentionally rejects model = "3pl". The package's Phase 7 external 3PL oracle used a direct TAM EAP-only fit; TAM 3PL WLE was unavailable in that validated path. That oracle is evidence about the probability/information implementation, not a public 3PL WLE API.

See also

simulate_response_data for generating test data, eqc_calibrate for calibration.

Examples

if (FALSE) { # \dontrun{
# Simulate response data from calibration results
eqc_result <- eqc_calibrate(
  target_rho = 0.80,
  n_items = 25,
  model = "rasch",
  seed = 42
)
sim_data <- simulate_response_data(result = eqc_result, n_persons = 500)

# Compute TAM reliability if TAM is installed
if (requireNamespace("TAM", quietly = TRUE)) {
  tam_rel <- compute_reliability_tam(sim_data$response_matrix, model = "rasch")
  cat(sprintf("WLE reliability: %.4f\n", tam_rel$rel_wle))
  cat(sprintf("EAP reliability: %.4f\n", tam_rel$rel_eap))
}
} # }