Package 'hIRT' reference manual

Title:	Hierarchical Item Response Theory Models
Description:	Implementation of a class of hierarchical item response theory (IRT) models where both the mean and the variance of latent preferences (ability parameters) may depend on observed covariates. The current implementation includes both the two-parameter latent trait model for binary data and the graded response model for ordinal data. Both are fitted via the Expectation-Maximization (EM) algorithm. Asymptotic standard errors are derived from the observed information matrix.
Authors:	Xiang Zhou [aut, cre]
Maintainer:	Xiang Zhou <[email protected]>
License:	GPL (>= 3)
Version:	0.4.0
Built:	2024-11-08 04:43:52 UTC
Source:	https://github.com/xiangzhou09/hirt

Parameter Estimates from Hierarchical IRT Models.

Description

Parameter estimates from either hltm or hgrm or hgrmDIF models. code_item reports estimates of item parameters. coef_mean reports results for the mean equation. coef_var reports results for the variance equation.

Usage

coef_item(x, by_item = TRUE, digits = 3)

coef_mean(x, digits = 3)

coef_var(x, digits = 3)
coef_item(x, by_item = TRUE, digits = 3)

coef_mean(x, digits = 3)

coef_var(x, digits = 3)

Arguments

`x`	An object of class `hIRT`
`by_item`	Logical. Should item parameters be stored item by item (if `TRUE`) or put together in a data frame (if `FALSE`)?
`digits`	The number of significant digits to use when printing

Value

Parameter estimates, standard errors, z values, and p values organized as a data frame (if by_item = TRUE) or a list (if by_item = FALSE).

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

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()
)
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
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

Hierarchical Graded Response Models with Known Item Parameters

Description

hgrm2 fits a hierarchical graded response model where the item parameters are known and supplied by the user.

Usage

hgrm2(y, x = NULL, z = NULL, item_coefs, control = list())
hgrm2(y, x = NULL, z = NULL, item_coefs, 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.
`item_coefs`	A list of known item parameters. The parameters of item $j$ are given by the $j$ th element, which should be a vector of length $H_j$ , containing $H_j - 1$ item difficulty parameters (in descending order) and one item discrimination parameter.
`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.

Examples


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

n <- nrow(nes_econ2008)
id_train <- sample.int(n, n/4)
id_test <- setdiff(1:n, id_train)

y_train <- y[id_train, ]
x_train <- x[id_train, ]
z_train <- z[id_train, ]

mod_train <- hgrm(y_train, x_train, z_train)

y_test <- y[id_test, ]
x_test <- x[id_test, ]
z_test <- z[id_test, ]

item_coefs <- lapply(coef_item(mod_train), `[[`, "Estimate")

model_test <- hgrm2(y_test, x_test, z_test, item_coefs = item_coefs)
y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)

n <- nrow(nes_econ2008)
id_train <- sample.int(n, n/4)
id_test <- setdiff(1:n, id_train)

y_train <- y[id_train, ]
x_train <- x[id_train, ]
z_train <- z[id_train, ]

mod_train <- hgrm(y_train, x_train, z_train)

y_test <- y[id_test, ]
x_test <- x[id_test, ]
z_test <- z[id_test, ]

item_coefs <- lapply(coef_item(mod_train), `[[`, "Estimate")

model_test <- hgrm2(y_test, x_test, z_test, item_coefs = item_coefs)

Hierarchical Graded Response Models with Differential Item Functioning

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()
)
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 $\beta_{n}$ 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.
`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)
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)

Fitting Hierarchical Latent Trait Models (for Binary Responses).

Description

hltm fits a hierarchical latent trait 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.

Usage

hltm(
  y,
  x = NULL,
  z = NULL,
  constr = c("latent_scale", "items"),
  beta_set = 1L,
  sign_set = TRUE,
  init = c("naive", "glm", "irt"),
  control = list()
)
hltm(
  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 hltm.

`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)

dichotomize <- function(x) findInterval(x, c(mean(x, na.rm = TRUE)))
y[] <- lapply(y, dichotomize)
nes_m1 <- hltm(y, x, z)
nes_m1
y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)

dichotomize <- function(x) findInterval(x, c(mean(x, na.rm = TRUE)))
y[] <- lapply(y, dichotomize)
nes_m1 <- hltm(y, x, z)
nes_m1

Hierarchical Latent Trait Models with Known Item Parameters.

Description

hltm2 fits a hierarchical latent trait model where the item parameters are known and supplied by the user.

Usage

hltm2(y, x = NULL, z = NULL, item_coefs, control = list())
hltm2(y, x = NULL, z = NULL, item_coefs, 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.
`item_coefs`	A list of known item parameters. The parameters of item $j$ are given by the $j$ th element, which should be a vector of length 2, containing the item difficulty parameter and item discrimination parameter.
`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 hltm.

`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.

Examples

y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)
dichotomize <- function(x) findInterval(x, c(mean(x, na.rm = TRUE)))
y_bin <- y
y_bin[] <- lapply(y, dichotomize)

n <- nrow(nes_econ2008)
id_train <- sample.int(n, n/4)
id_test <- setdiff(1:n, id_train)

y_bin_train <- y_bin[id_train, ]
x_train <- x[id_train, ]
z_train <- z[id_train, ]

mod_train <- hltm(y_bin_train, x_train, z_train)

y_bin_test <- y_bin[id_test, ]
x_test <- x[id_test, ]
z_test <- z[id_test, ]

item_coefs <- lapply(coef_item(mod_train), `[[`, "Estimate")

model_test <- hltm2(y_bin_test, x_test, z_test, item_coefs = item_coefs)
y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)
dichotomize <- function(x) findInterval(x, c(mean(x, na.rm = TRUE)))
y_bin <- y
y_bin[] <- lapply(y, dichotomize)

n <- nrow(nes_econ2008)
id_train <- sample.int(n, n/4)
id_test <- setdiff(1:n, id_train)

y_bin_train <- y_bin[id_train, ]
x_train <- x[id_train, ]
z_train <- z[id_train, ]

mod_train <- hltm(y_bin_train, x_train, z_train)

y_bin_test <- y_bin[id_test, ]
x_test <- x[id_test, ]
z_test <- z[id_test, ]

item_coefs <- lapply(coef_item(mod_train), `[[`, "Estimate")

model_test <- hltm2(y_bin_test, x_test, z_test, item_coefs = item_coefs)

Estimates of Latent Preferences/Abilities

Description

EAP estimates of latent preferences for either hltm or hgrm models.

Usage

latent_scores(x, digits = 3)
latent_scores(x, digits = 3)

Arguments

`x`	An object of class `hIRT`
`digits`	The number of significant digits to use when printing

Value

A data frame of EAP estimates of latent preferences and their approximate standard errors.

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)
pref <- latent_scores(nes_m1)
require(ggplot2)
ggplot(data = nes_econ2008) +
geom_density(aes(x = pref$post_mean, col = party))
y <- nes_econ2008[, -(1:3)]
x <- model.matrix( ~ party * educ, nes_econ2008)
z <- model.matrix( ~ party, nes_econ2008)
nes_m1 <- hgrm(y, x, z)
pref <- latent_scores(nes_m1)
require(ggplot2)
ggplot(data = nes_econ2008) +
geom_density(aes(x = pref$post_mean, col = party))

Public Attitudes on Economic Issues in ANES 2008

Description

A dataset containing gender, party ID, education, and responses to 10 survey items on economic issues from the American National Election Studies, 2008.

Usage

nes_econ2008
nes_econ2008

Format

A data frame with 2268 rows and 13 variables:

gender: gender. 1: male; 2: female
party: party identification: Democrat, independent, or Republican
educ: education. 1: high school or less; 2: some college or above
health_ins7: Support for government or private health insurance, 7 categories
jobs_guar7: Support for government guarantee jobs and income, 7 categories
gov_services7: Should government reduce or increase spending on services?, 7 categories
FS_poor3: Federal spending on the poor, 3 categories
FS_childcare3: Federal spending on child care, 3 categories
FS_crime3: Federal spending on crime, 3 categories
FS_publicschools3: Federal spending on public schools, 3 categories
FS_welfare3: Federal spending on welfare, 3 categories
FS_envir3: Federal spending on environment, 3 categories
FS_socsec3: Federal spending on Social Security, 3 categories

Printing an object of class `hIRT`

Description

Printing an object of class hIRT

Usage

## S3 method for class 'hIRT'
print(x, digits = 3, ...)
## S3 method for class 'hIRT'
print(x, digits = 3, ...)

Arguments

`x`	An object of class `hIRT`
`digits`	The number of significant digits to use when printing
`...`	further arguments passed to `print`.

Summarizing Hierarchical Item Response Theory Models

Description

Summarizing the fit of either hltm or hgrm.

Usage

## S3 method for class 'hIRT'
summary(object, by_item = FALSE, digits = 3, ...)

## S3 method for class 'summary_hIRT'
print(x, digits = 3, ...)
## S3 method for class 'hIRT'
summary(object, by_item = FALSE, digits = 3, ...)

## S3 method for class 'summary_hIRT'
print(x, digits = 3, ...)

Arguments

`object`	An object of class `hIRT`.
`by_item`	Logical. Should item parameters be stored item by item (if `TRUE`) or put together in a data frame (if `FALSE`)?
`digits`	the number of significant digits to use when printing.
`...`	further arguments passed to `print`.
`x`	An object of class `hIRT`

Value

An object of class summary_hIRT.

`call`	The matched call.
`model`	Model fit statistics: Log likelihood, AIC, and BIC.
`item_coefs`	Item parameter estimates, standard errors, z values, and p values.
`mean_coefs`	Parameter estimates for the mean equation.
`var_coefs`	Parameter estimates for the variance equation.

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

Package 'hIRT'

Help Index

Parameter Estimates from Hierarchical IRT Models.

Description

Usage

Arguments

Value

Examples

Fitting Hierarchical Graded Response Models (for Ordinal Responses)

Description

Usage

Arguments

Value

References

Examples

Hierarchical Graded Response Models with Known Item Parameters

Description

Usage

Arguments

Value

Examples

Hierarchical Graded Response Models with Differential Item Functioning

Description

Usage

Arguments

Value

Examples

Fitting Hierarchical Latent Trait Models (for Binary Responses).

Description

Usage

Arguments

Value

References

Examples

Hierarchical Latent Trait Models with Known Item Parameters.

Description

Usage

Arguments

Value

Examples

Estimates of Latent Preferences/Abilities

Description

Usage

Arguments

Value

Examples

Public Attitudes on Economic Issues in ANES 2008

Description

Usage

Format

Printing an object of class hIRT

Description

Usage

Arguments

Summarizing Hierarchical Item Response Theory Models

Description

Usage

Arguments

Value

Examples

Printing an object of class `hIRT`