Type:	Package
Title:	Bayesian Estimation of the Reduced Reparameterized Unified Model with Gibbs Sampling
Version:	0.2.1
Description:	Implementation of Gibbs sampling algorithm for Bayesian Estimation of the Reduced Reparameterized Unified Model ('rrum'), described by Culpepper and Hudson (2017) <doi:10.1177/0146621617707511>.
URL:	https://tmsalab.github.io/rrum/, https://github.com/tmsalab/rrum
BugReports:	https://github.com/tmsalab/rrum/issues
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 4.1.0), simcdm (≥ 0.1.0)
Imports:	Rcpp (≥ 1.0.11)
LinkingTo:	Rcpp, RcppArmadillo (≥ 0.12.6.6.0), rgen, simcdm
Suggests:	testthat, covr
Encoding:	UTF-8
RoxygenNote:	7.2.3
NeedsCompilation:	yes
Packaged:	2023-11-29 07:25:13 UTC; ronin
Author:	Steven Andrew Culpepper [aut, cph], Aaron Hudson [aut, cph], James Joseph Balamuta [aut, cph, cre]
Maintainer:	James Joseph Balamuta <balamut2@illinois.edu>
Repository:	CRAN
Date/Publication:	2023-11-29 07:40:02 UTC

rrum: Bayesian Estimation of the Reduced Reparameterized Unified Model with Gibbs Sampling

Description

Implementation of Gibbs sampling algorithm for Bayesian Estimation of the Reduced Reparameterized Unified Model ('rrum'), described by Culpepper and Hudson (2017) doi: 10.1177/0146621617707511.

Details

Implemention of a Bayesian estimation for the reduced Reparameterized Unified Model (rRUM).

Author(s)

Maintainer: James Joseph Balamuta balamut2@illinois.edu (ORCID) [copyright holder]

Authors:

• Steven Andrew Culpepper sculpepp@illinois.edu (ORCID) [copyright holder]

• Aaron Hudson awhudson@uw.edu (ORCID) [copyright holder]

References

Culpepper, S. A. & Hudson, A. (In Press). An improved strategy for Bayesian estimation of the reduced reparameterized unified model. Applied Psychological Measurement.

Hudson, A., Culpepper, S. A., & Douglas, J. (2016, July). Bayesian estimation of the generalized NIDA model with Gibbs sampling. Paper presented at the annual International Meeting of the Psychometric Society, Asheville, North Carolina.

See Also

Useful links:

• https://tmsalab.github.io/rrum/

• https://github.com/tmsalab/rrum

• Report bugs at https://github.com/tmsalab/rrum/issues

Gibbs sampler to estimate the rRUM

Description

Obtains samples from posterior distributon for the reduced Reparametrized Unified Model (rRUM).

Usage

rrum(
  Y,
  Q,
  chain_length = 10000L,
  as = 1,
  bs = 1,
  ag = 1,
  bg = 1,
  delta0 = rep(1, 2^ncol(Q))
)

Arguments

Value

A list that contains

• PISTAR: A matrix where each column represents one draw from the posterior distribution of pistar.

• RSTAR: A J x K x chain_length array where J reperesents the number of items, and K represents the number of attributes. Each slice represents one draw from the posterior distribution of rstar.

• PI: A matrix where each column reperesents one draw from the posterior distribution of pi.

• ALPHA: An N x K x chain_length array where N reperesents the number of individuals, and K represents the number of attributes. Each slice represents one draw from the posterior distribution of alpha.

Author(s)

Steven Andrew Culpepper, Aaron Hudson, and James Joseph Balamuta

References

Culpepper, S. A. & Hudson, A. (In Press). An improved strategy for Bayesian estimation of the reduced reparameterized unified model. Applied Psychological Measurement.

Hudson, A., Culpepper, S. A., & Douglas, J. (2016, July). Bayesian estimation of the generalized NIDA model with Gibbs sampling. Paper presented at the annual International Meeting of the Psychometric Society, Asheville, North Carolina.

See Also

simcdm::sim_rrum_items()

Examples

# Set seed for reproducibility
set.seed(217)

## Define Simulation Parameters

N = 1000 # Number of Individuals
J = 6    # Number of Items
K = 2    # Number of Attributes

# Matrix where rows represent attribute classes
As = attribute_classes(K) 

# Latent Class probabilities
pis = c(.1, .2, .3, .4) 

# Q Matrix
Q = rbind(c(1, 0),
          c(0, 1),
          c(1, 0),
          c(0, 1),
          c(1, 1),
          c(1, 1)
    )
    
# The probabiliies of answering each item correctly for individuals 
# who do not lack any required attribute
pistar = rep(.9, J)

# Penalties for failing to have each of the required attributes
rstar  = .5 * Q

# Randomized alpha profiles
alpha  = As[sample(1:(K ^ 2), N, replace = TRUE, pis),]

# Simulate data
rrum_items = simcdm::sim_rrum_items(Q, rstar, pistar, alpha)

## Not run: 
# Note: This portion of the code is computationally intensive.

# Recover simulation parameters with Gibbs Sampler
Gibbs.out = rrum(rrum_items, Q)

# Iterations to be discarded from chain as burnin
burnin = 1:5000 

# Calculate summarizes of posterior distributions
rstar.mean  = with(Gibbs.out, apply(RSTAR[,,-burnin], c(1, 2), mean))
pistar.mean = with(Gibbs.out, apply(PISTAR[,-burnin], 1, mean))
pis.mean    = with(Gibbs.out, apply(PI[,-burnin], 1 ,mean))

## End(Not run)