hgrm {hIRT}

Fitting Hierarchical Graded Response Models (for Ordinal Responses)

Description

hgrm fits a hierarchical graded response model in which both the mean and the variance of the latent preference (ability parameter) may depend on person-specific covariates (x and z). Specifically, the mean is specified as a linear combination of x and the log of the variance is specified as a linear combination of z. Nonresponses are treated as missing at random.

Usage

hgrm(
  y,
  x = NULL,
  z = NULL,
  constr = c("latent_scale", "items"),
  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.

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.

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 \beta_{n} and \beta_{n-1} falls under eps, where \beta 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 \gamma and \lambda. The default is 15.

eps2

Tolerance parameter used to determine convergence of the conditional maximization procedures for updating \gamma and \lambda. 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.

control

List of control values.

call

The matched call.

References

Zhou, Xiang. 2019. "Hierarchical Item Response Models for Analyzing Public Opinion." Political Analysis.

Examples

y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)
nes_m1 <- hgrm(y, x, z)
nes_m1