petersenlab (version 1.1.0)

test_info_4PL: 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))
)

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.

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]).

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))