testInformation: Test Information from Logistic IRT Model.

In petersenlab: A Collection of R Functions by the Petersen Lab

Test Information from Logistic IRT Model.

Description

Estimate test information from logistic item response theory model.

Usage

test_info_4PL(
  theta,
  alpha,
  beta,
  gamma = rep(0, length(alpha)),
  delta = rep(1, length(alpha))
)

error_variance_4PL(
  lower = -Inf,
  upper = Inf,
  alpha,
  beta,
  gamma = rep(0, length(alpha)),
  delta = rep(1, length(alpha)),
  mean = 0,
  sd = 1,
  density_cutoff = 1e-10
)

reliability_4PL(
  alpha,
  beta,
  gamma = rep(0, length(alpha)),
  delta = rep(1, length(alpha))
)

Arguments

theta	Numeric. The respondent's level on the latent factor/construct.
alpha	Numeric. The discrimination parameter of the item, indicating how steeply the item response changes with the person's (theta).
beta	Numeric. The difficulty parameter of the item, indicating the expected count at a given level on the construct (theta).
gamma	Numeric. The lower asymptote.
delta	Numeric. The upper asymptote.
lower	Numeric. The lower range of theta, for estimating error variance or reliability.
upper	Numeric. The upper range of theta, for estimating error variance or reliability.
mean	Numeric. Mean of normal latent variable.
sd	Numeric. Standard deviation of normal latent variable.
density_cutoff	Numeric. Cut-off value for very large or very small bounds needed for numerical stability.

Details

Created by Philipp Doebler ([e-mail]) and Loreen Sabel ([e-mail]).

Value

The amount of information for a given the test as a whole at each of the values of theta specified. Based on test information, one can estimate error variance and marginal reliability using error_variance_4PL() and reliability_4PL(), respectively.

See Also

Other IRT: deriv_d_negBinom(), discriminationToFactorLoading(), fourPL(), itemInformation(), reliabilityIRT(), standardErrorIRT()

Examples

test_info_4PL(0,1,0,0,1) # 0.25
test_info_4PL(-0.849, 1.1, -1, 0.2, 0.95) # Magis, 2013, Fig. 2
optimize(function(x)- test_info_4PL(x, 1.1, -1, 0.2, 0.95), c(-3, 3))

# test
set.seed(23)
# parameters (some are totally unrealistic)
alpha <- runif(20,0.5,2.5)
beta <- runif(20,-2,2)
gamma <- runif(20,0,0.3)
delta <- runif(20,0.8,1)
error_variance_4PL(
  lower = -Inf, upper = Inf,
  alpha, beta, gamma, delta)

error_variance_4PL(
  lower= -Inf, upper= Inf,
  alpha, beta, gamma, delta,
  density_cutoff = 1e-9)

error_variance_4PL(
  lower= -Inf, upper= Inf,
  alpha, beta, gamma, delta,
  density_cutoff = 1e-8)

error_variance_4PL(
  lower = -Inf, upper= Inf,
  alpha, beta, gamma, delta,
  density_cutoff = 1e-7)

reliability_4PL(alpha, beta, gamma, delta)

theta <- seq(-4, 4, length.out = 101)

plot(theta, test_info_4PL(theta, alpha, beta, gamma, delta))

petersenlab documentation built on April 4, 2025, 12:22 a.m.