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.Rproj.user | ||
.Rhistory | ||
.RData | ||
.Ruserdata |
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Package: fourPNO | ||
Type: Package | ||
Title: Bayesian 4 Parameter Item Response Model | ||
Version: 1.0 | ||
Date: 2015-10-11 | ||
Authors@R: c(person("Steven Andrew", "Culpepper", role = c("aut", "cph","cre"), email = | ||
"[email protected]")) | ||
Maintainer: Steven Andrew Culpepper <[email protected]> | ||
Description: Estimate Lord & Barton's four parameter IRT model with lower and upper asymptotes using Bayesian formulation described by Culpepper (2015). | ||
License: GPL (>= 2) | ||
Imports: Rcpp | ||
LinkingTo: Rcpp, RcppArmadillo | ||
Depends: R (>= 3.0.1) |
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useDynLib(fourPNO) | ||
#import(RcppArmadillo) | ||
importFrom("Rcpp", evalCpp) | ||
exportPattern("^[[:alpha:]]+") |
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# This file was generated by Rcpp::compileAttributes | ||
# Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 | ||
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#' @title Generate Random Multivariate Normal Distribution | ||
#' @description Creates a random Multivariate Normal when given number of obs, mean, and sigma. | ||
#' @usage rmvnorm(n, mu, sigma) | ||
#' @param n An \code{int}, which gives the number of observations. (> 0) | ||
#' @param mu A \code{vector} length m that represents the means of the normals. | ||
#' @param sigma A \code{matrix} with dimensions m x m that provides the covariance matrix. | ||
#' @return A \code{matrix} that is a Multivariate Normal distribution | ||
#' @author James J Balamuta | ||
#' @examples | ||
#' #Call with the following data: | ||
#' rmvnorm(2, c(0,0), diag(2)) | ||
#' | ||
rmvnorm <- function(n, mu, sigma) { | ||
.Call('fourPNO_rmvnorm', PACKAGE = 'fourPNO', n, mu, sigma) | ||
} | ||
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#' @title Initialize Thresholds | ||
#' @description Internal function for initializing item thresholds. | ||
#' @param Ms A \code{vector} with the number of scale values. | ||
#' @return A \code{matrix} that is a Multivariate Normal distribution | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
kappa_initialize <- function(Ms) { | ||
.Call('fourPNO_kappa_initialize', PACKAGE = 'fourPNO', Ms) | ||
} | ||
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#' @title Internal Function for Updating Theta in Gibbs Sampler | ||
#' @description Update theta in Gibbs sampler | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param Z A \code{matrix} N by J of continuous augmented data. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @param mu_theta The prior mean for theta. | ||
#' @param Sigma_theta_inv The prior inverse variance for theta. | ||
#' @return A \code{vector} of thetas. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
update_theta <- function(N, Z, as, bs, theta, mu_theta, Sigma_theta_inv) { | ||
.Call('fourPNO_update_theta', PACKAGE = 'fourPNO', N, Z, as, bs, theta, mu_theta, Sigma_theta_inv) | ||
} | ||
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#' @title Update a and b Parameters of 2PNO, 3PNO, 4PNO | ||
#' @description Update item slope and threshold | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param J An \code{int}, which gives the number of items. (> 0) | ||
#' @param Z A \code{matrix} N by J of continuous augmented data. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @param mu_xi A two dimensional \code{vector} of prior item parameter means. | ||
#' @param Sigma_xi_inv A two dimensional identity \code{matrix} of prior item parameter VC matrix. | ||
#' @return A list of item parameters. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
update_ab_NA <- function(N, J, Z, as, bs, theta, mu_xi, Sigma_xi_inv) { | ||
.Call('fourPNO_update_ab_NA', PACKAGE = 'fourPNO', N, J, Z, as, bs, theta, mu_xi, Sigma_xi_inv) | ||
} | ||
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#' @title Update a and b Parameters of 4pno without alpha > 0 Restriction | ||
#' @description Update item slope and threshold | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param J An \code{int}, which gives the number of items. (> 0) | ||
#' @param Z A \code{matrix} N by J of continuous augmented data. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @param mu_xi A two dimensional \code{vector} of prior item parameter means. | ||
#' @param Sigma_xi_inv A two dimensional identity \code{matrix} of prior item parameter VC matrix. | ||
#' @return A list of item parameters. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
update_ab_norestriction <- function(N, J, Z, as, bs, theta, mu_xi, Sigma_xi_inv) { | ||
.Call('fourPNO_update_ab_norestriction', PACKAGE = 'fourPNO', N, J, Z, as, bs, theta, mu_xi, Sigma_xi_inv) | ||
} | ||
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#' @title Update Lower and Upper Asymptote Parameters of 4PNO | ||
#' @description Internal function to update item lower and upper asymptote | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @param Ysum A \code{vector} of item total scores. | ||
#' @param Z A \code{matrix} N by J of continuous augmented data. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param cs A \code{vector} of item lower asymptote parameters. | ||
#' @param ss A \code{vector} of item upper asymptote parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @param Kaps A \code{matrix} for item thresholds (used for internal computations). | ||
#' @param alpha_c The lower asymptote prior 'a' parameter. | ||
#' @param beta_c The lower asymptote prior 'b' parameter. | ||
#' @param alpha_s The upper asymptote prior 'a' parameter. | ||
#' @param beta_s The upper asymptote prior 'b' parameter. | ||
#' @param gwg_reps The number of Gibbs within Gibbs MCMC samples for marginal distribution of gamma. | ||
#' @return A list of item threshold parameters. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
update_WKappaZ_NA <- function(Y, Ysum, Z, as, bs, cs, ss, theta, Kaps, alpha_c, beta_c, alpha_s, beta_s, gwg_reps) { | ||
.Call('fourPNO_update_WKappaZ_NA', PACKAGE = 'fourPNO', Y, Ysum, Z, as, bs, cs, ss, theta, Kaps, alpha_c, beta_c, alpha_s, beta_s, gwg_reps) | ||
} | ||
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#' @title Compute 4PNO Deviance | ||
#' @description Internal function to -2LL | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param J An \code{int}, which gives the number of items. (> 0) | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param cs A \code{vector} of item lower asymptote parameters. | ||
#' @param ss A \code{vector} of item upper asymptote parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @return -2LL. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
min2LL_4pno <- function(N, J, Y, as, bs, cs, ss, theta) { | ||
.Call('fourPNO_min2LL_4pno', PACKAGE = 'fourPNO', N, J, Y, as, bs, cs, ss, theta) | ||
} | ||
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#' @title Simulate from 4PNO Model | ||
#' @description Generate item responses under the 4PNO | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param J An \code{int}, which gives the number of items. (> 0) | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param cs A \code{vector} of item lower asymptote parameters. | ||
#' @param ss A \code{vector} of item upper asymptote parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @return A N by J \code{matrix} of dichotomous item responses. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
Y_4pno_simulate <- function(N, J, as, bs, cs, ss, theta) { | ||
.Call('fourPNO_Y_4pno_simulate', PACKAGE = 'fourPNO', N, J, as, bs, cs, ss, theta) | ||
} | ||
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#' @title Calculate Tabulated Total Scores | ||
#' @description Internal function to -2LL | ||
#' @param N An \code{int}, which gives the number of observations. (> 0) | ||
#' @param J An \code{int}, which gives the number of items. (> 0) | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @return A vector of tabulated total scores. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
Total_Tabulate <- function(N, J, Y) { | ||
.Call('fourPNO_Total_Tabulate', PACKAGE = 'fourPNO', N, J, Y) | ||
} | ||
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#' @title Gibbs Implementation of 4PNO | ||
#' @description Internal function to -2LL | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @param mu_xi A two dimensional \code{vector} of prior item parameter means. | ||
#' @param Sigma_xi_inv A two dimensional identity \code{matrix} of prior item parameter VC matrix. | ||
#' @param mu_theta The prior mean for theta. | ||
#' @param Sigma_theta_inv The prior inverse variance for theta. | ||
#' @param alpha_c The lower asymptote prior 'a' parameter. | ||
#' @param beta_c The lower asymptote prior 'b' parameter. | ||
#' @param alpha_s The upper asymptote prior 'a' parameter. | ||
#' @param beta_s The upper asymptote prior 'b' parameter. | ||
#' @param burnin The number of MCMC samples to discard. | ||
#' @param cTF A J dimensional \code{vector} indicating which lower asymptotes to estimate. | ||
#' @param sTF A J dimensional \code{vector} indicating which upper asymptotes to estimate. | ||
#' @param gwg_reps The number of Gibbs within Gibbs MCMC samples for marginal distribution of gamma. | ||
#' @param chain_length The number of MCMC samples. | ||
#' @return Samples from posterior. | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
Gibbs_4PNO <- function(Y, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv, alpha_c, beta_c, alpha_s, beta_s, burnin, cTF, sTF, gwg_reps, chain_length = 10000L) { | ||
.Call('fourPNO_Gibbs_4PNO', PACKAGE = 'fourPNO', Y, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv, alpha_c, beta_c, alpha_s, beta_s, burnin, cTF, sTF, gwg_reps, chain_length) | ||
} | ||
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#' @title Update 2PNO Model Parameters | ||
#' @description Internal function to update 2PNO parameters | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @param Z A \code{matrix} N by J of continuous augmented data. | ||
#' @param as A \code{vector} of item discrimination parameters. | ||
#' @param bs A \code{vector} of item threshold parameters. | ||
#' @param theta A \code{vector} of prior thetas. | ||
#' @param Kaps A \code{matrix} for item thresholds (used for internal computations). | ||
#' @return A list of item parameters. | ||
#' @seealso \code{\link{Gibbs_4PNO}} | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
update_2pno <- function(N, J, Y, Z, as, bs, theta, Kaps, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv) { | ||
.Call('fourPNO_update_2pno', PACKAGE = 'fourPNO', N, J, Y, Z, as, bs, theta, Kaps, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv) | ||
} | ||
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#' @title Gibbs Implementation of 2PNO | ||
#' @description Implement Gibbs 2PNO Sampler | ||
#' @param Y A N by J \code{matrix} of item responses. | ||
#' @param mu_xi A two dimensional \code{vector} of prior item parameter means. | ||
#' @param Sigma_xi_inv A two dimensional identity \code{matrix} of prior item parameter VC matrix. | ||
#' @param mu_theta The prior mean for theta. | ||
#' @param Sigma_theta_inv The prior inverse variance for theta. | ||
#' @param burnin The number of MCMC samples to discard. | ||
#' @param chain_length The number of MCMC samples. | ||
#' @return Samples from posterior. | ||
#' @author Steven Andrew Culpepper | ||
#' | ||
Gibbs_2PNO <- function(Y, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv, burnin, chain_length = 10000L) { | ||
.Call('fourPNO_Gibbs_2PNO', PACKAGE = 'fourPNO', Y, mu_xi, Sigma_xi_inv, mu_theta, Sigma_theta_inv, burnin, chain_length) | ||
} | ||
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.Random.seed <- | ||
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