hgrmDIF: Hierarchical Graded Response Models with Differential Item...

In xiangzhou09/hIRT: Hierarchical Item Response Theory Models

Description

hgrmDIF fits a hierarchical graded response model similar to hgrm(), but person-specific covariates x are allowed to affect item responses directly (not via the latent preference). This model can be used to test for the presence of differential item functioning.

Usage

hgrmDIF(
  y,
  x = NULL,
  z = NULL,
  x0 = x[, -1, drop = FALSE],
  items_dif = 1L,
  form_dif = c("uniform", "non-uniform"),
  constr = c("latent_scale"),
  beta_set = 1L,
  sign_set = TRUE,
  init = c("naive", "glm", "irt"),
  control = list()
)

Arguments

y	A data frame or matrix of item responses.
x	An optional model matrix, including the intercept term, that predicts the mean of the latent preference. If not supplied, only the intercept term is included.
z	An optional model matrix, including the intercept term, that predicts the variance of the latent preference. If not supplied, only the intercept term is included.
x0	A matrix specifying the covariates by which differential item functioning operates. If not supplied, x0 is taken to be a matrix containing all predictors in x except the intercept.
items_dif	The indices of the items for which differential item functioning is tested.
form_dif	Form of differential item functioning being tested. Either "uniform" or "non-uniform."
constr	The type of constraints used to identify the model: "latent_scale", or "items". The default, "latent_scale" constrains the mean of latent preferences to zero and the geometric mean of prior variance to one; "items" places constraints on item parameters instead and sets the mean of item difficulty parameters to zero and the geometric mean of the discrimination parameters to one. Currently, only "latent_scale" is supported in hgrmDIF().
beta_set	The index of the item for which the discrimination parameter is restricted to be positive (or negative). It may take any integer value from 1 to ncol(y).
sign_set	Logical. Should the discrimination parameter of the corresponding item (indexed by beta_set) be positive (if TRUE) or negative (if FALSE)?
init	A character string indicating how item parameters are initialized. It can be "naive", "glm", or "irt".
control	A list of control values max_iter The maximum number of iterations of the EM algorithm. The default is 150. eps Tolerance parameter used to determine convergence of the EM algorithm. Specifically, iterations continue until the Euclidean distance between β_{n} and β_{n-1} falls under eps, where β is the vector of item discrimination parameters. eps=1e-4 by default. max_iter2 The maximum number of iterations of the conditional maximization procedures for updating γ and λ. The default is 15. eps2 Tolerance parameter used to determine convergence of the conditional maximization procedures for updating γ and λ. Specifically, iterations continue until the Euclidean distance between two consecutive log likelihoods falls under eps2. eps2=1e-3 by default. K Number of Gauss-Legendre quadrature points for the E-step. The default is 21. C [-C, C] sets the range of integral in the E-step. C=3 by default.

Value

An object of class hgrm.

coefficients	A data frame of parameter estimates, standard errors, z values and p values.
scores	A data frame of EAP estimates of latent preferences and their approximate standard errors.
vcov	Variance-covariance matrix of parameter estimates.
log_Lik	The log-likelihood value at convergence.
N	Number of units.
J	Number of items.
H	A vector denoting the number of response categories for each item.
ylevels	A list showing the levels of the factorized response categories.
p	The number of predictors for the mean equation.
q	The number of predictors for the variance equation.
p0	The number of predictors for items with DIF.
coef_item	Item coefficient estimates.
control	List of control values.
call	The matched call.

Examples

y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
nes_m2 <- hgrmDIF(y, x, items_dif = 1:2)
coef_item(nes_m2)

xiangzhou09/hIRT documentation built on Dec. 25, 2021, 5:27 a.m.