Title:	Bayesian Estimation of an Exploratory Deterministic Input, Noisy and Gate Model
Version:	0.1.1
Description:	Perform a Bayesian estimation of the exploratory deterministic input, noisy and gate (EDINA) cognitive diagnostic model described by Chen et al. (2018) <doi:10.1007/s11336-017-9579-4>.
URL:	https://github.com/tmsalab/edina
BugReports:	https://github.com/tmsalab/edina/issues
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 3.5.0)
Imports:	Rcpp, ggplot2, jjb, reshape2
LinkingTo:	Rcpp, RcppArmadillo, rgen
Suggests:	simcdm
LazyData:	true
RoxygenNote:	7.1.0
Encoding:	UTF-8
Language:	en-US
NeedsCompilation:	yes
Packaged:	2020-03-24 15:04:45 UTC; ronin
Author:	James Joseph Balamuta [aut, cre, cph], Steven Andrew Culpepper [aut, cph], Jeffrey A. Douglas [aut]
Maintainer:	James Joseph Balamuta <balamut2@illinois.edu>
Repository:	CRAN
Date/Publication:	2020-03-25 13:50:15 UTC

edina: Bayesian Estimation of an Exploratory Deterministic Input, Noisy and Gate Model

Description

Perform a Bayesian estimation of the exploratory deterministic input, noisy and gate (EDINA) cognitive diagnostic model described by Chen et al. (2018) <doi:10.1007/s11336-017-9579-4>.

Author(s)

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

Authors:

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

• Jeffrey A. Douglas jeffdoug@illinois.edu

See Also

Useful links:

• https://github.com/tmsalab/edina

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

Bayesian Information Criterion (BIC)

Description

Calculate BIC for EDINA models.

Usage

## S3 method for class 'edina'
BIC(object, ...)

Arguments

Value

The BIC value of the given model.

BIC Computation Procedure

BIC = -2 \log p\left( {\mathbf{y}| \mathbf{\hat{\theta}} } \right) + ((k+2)*j + 2^k)\log(n)

See Also

PPP.edina(), DIC.edina()

PPP.edina(), DIC.edina()

Deviance Information Criterion (DIC)

Description

Calculate DIC for EDINA models.

Usage

DIC(object, ...)

## S3 method for class 'edina'
DIC(object, ...)

Arguments

Value

The DIC value of the given model.

DIC Computation Procedure

DIC = -2\left({\log p\left( {\mathbf{y}| \mathbf{\hat{\theta}} } \right) - 2\left( {\log p\left( {\mathbf{y}| \mathbf{\hat{\theta}} } \right) - \frac{1}{N}\sum\limits_{n = 1}^N {\log p\left( {\mathbf{y}|{\mathbf{\theta} _s}} \right)} } \right)} \right)

See Also

PPP.edina(), BIC.edina()

Posterior Predictive Probabilities (PPPs)

Description

Computes posterior predictive probabilities (PPPs) based on the odds ratios for each pair of items.

Usage

PPP(object, ...)

## S3 method for class 'edina'
PPP(object, alpha = 0.05, ...)

Arguments

Details

PPPs that smaller than 0.05 or greater than 0.95 tend to be extreme and evidence of misfit. As a result, this is more of a heuristic metric.

Value

The PPP value given the specified alpha value.

PPP Computation Procedure

1. simulate observed responses \mathbf Y^{(r)} using model parameters from iteration r of the MCMC sampler

2. computing the odds ratio for each pair of items at iteration r as

   OR^{(r)} = n_{11}^{(r)}n_{00}^{(r)}/\left(n_{10}^{(r)}n_{01}^{(r)}\right)

   , where n_{11}^{(r)} is the frequency of ones on both variables at iteration r, n_{10}^{(r)} is the frequency of ones on the first item and zeros on the second at iteration r, etc.; and

3. computing PPPs for each item pair as the proportion of generated OR^{(r)}'s that exceeded elements of the observed odds ratios.

Coerce data.frame and matrix classes to Q Matrix.

Description

as.q_matrix acts as an aliases.

Usage

as_q_matrix(x, ...)

## S3 method for class 'data.frame'
as_q_matrix(x, ...)

## S3 method for class 'matrix'
as_q_matrix(x, ...)

## Default S3 method:
as_q_matrix(x, ...)

Arguments

Value

A q_matrix object.'

See Also

q_matrix()

Examples

# Q matrix values
x = matrix(c(1, 0, 0, 1), nrow = 2)

# Construct class
q_mat = as_q_matrix(x)

Auto EDINA model selection routine

Description

Automatically select an appropriate K dimension for a Q matrix under the Exploratory Deterministic Input, Noise And gate (EDINA) Model.

Usage

auto_edina(data, k = 2:4, burnin = 10000, chain_length = 20000)

Arguments

Value

An auto_edina object that contains:

• edina_models: A list containing all estimated edina model objects.

• criterions: Information criterions calculated for each model

• k_checked: Varying k dimensions checked.

• j: Number of Items

See Also

autoplot.auto_edina(), best_model(), model_selection_graph(), parameter_evolution_graph()

Examples

if(requireNamespace("simcdm", quietly = TRUE)) {

# Set a seed for reproducibility
set.seed(1512)

# Setup data simulation parameters
N = 15   # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes

# Note:
# Sample size and attributes have been reduced to create a minimally
# viable example that can be run during CRAN's automatic check.
# Please make sure to have a larger sample size...

# Assign slipping and guessing values for each item
ss = gs = rep(.2, J)

# Simulate an identifiable Q matrix
Q = simcdm::sim_q_matrix(J, K)

# Simulate subject attributes
subject_alphas = simcdm::sim_subject_attributes(N, K)

# Simulate items under the DINA model
items_dina = simcdm::sim_dina_items(subject_alphas, Q, ss, gs)


# Requires at least 15 seconds of execution time.
# Three EDINA models will be fit with increasing number of attributes.
model_set_edina = auto_edina(items_dina, k = 2:4)

# Display results
model_set_edina

# Retrieve criterion table
table = summary(model_set_edina)

# Extract "best model"
best_model(model_set_edina)

}

Graph the Auto EDINA Object

Description

Presents either the fitting of model heuristics or the evolution of parameters on a graph

Usage

## S3 method for class 'auto_edina'
autoplot(
  object,
  type = c("selection", "guessing", "slipping", "evolution"),
  ...
)

Arguments

Value

A ggplot2 object.

See Also

auto_edina(), best_model(), model_selection_graph(), parameter_evolution_graph()

Examples

if(requireNamespace("simcdm", quietly = TRUE)) {

# Set a seed for reproducibility
set.seed(1512)

# Setup data simulation parameters
N = 2    # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes

# Note:
# Sample size and attributes have been reduced to create a minimally
# viable example that can be run during CRAN's automatic check.
# Please make sure to have a larger sample size...

# Assign slipping and guessing values for each item
ss = gs = rep(.2, J)

# Simulate an identifiable Q matrix
Q = simcdm::sim_q_matrix(J, K)

# Simulate subject attributes
subject_alphas = simcdm::sim_subject_attributes(N, K)

# Simulate items under the DINA model
items_dina = simcdm::sim_dina_items(subject_alphas, Q, ss, gs)


# Requires at least 15 seconds of execution time.
# Three EDINA models will be fit with increasing number of attributes.
model_set_edina = auto_edina(items_dina, k = 2:4)

# Visualize results results
autoplot(model_set_edina, type = "selection")

# Equivalent to:
model_selection_graph(model_set_edina)

# View model parameters
autoplot(model_set_edina, type = "guessing")

# Or directly call with:
parameter_evolution_graph(model_set_edina, type = "guessing")

}

Extract the Best Model

Description

Extracts the best model from the ⁠auto_*()⁠ search procedure.

Usage

best_model(x, ...)

## S3 method for class 'auto_edina'
best_model(x, ic = c("ppp", "bic", "dic"), ...)

Arguments

Value

An edina model object corresponding to the smallest value of requested information criterion.

See Also

DIC.edina(), BIC.edina(), PPP.edina()

EDINA Estimation Routine

Description

Performs the Exploratory Deterministic Input, Noise and Gate Model (EDINA) estimation on a given data set with a prespecified k value.

Usage

edina(data, k = 3, burnin = 10000, chain_length = 20000)

Arguments

Value

An edina object that contains:

• coefficients: Estimated coefficients of the model fit

• loglike_summed: Summed log-likelihood

• loglike_pmean: Mean of log-likelihood

• pi_classes: Latent classes

• avg_q: Estimated Averaged Q Matrix

• est_q: Estimated Dichotomous Q Matrix

• or_tested: Odds Ratio used in the model selection.

• sample_or: Odds Ratio for the sample.

• n: Number of Observations

• j: Number of Items

• k: Number of Traits

• burnin: Amount of iterations to discard

• chain_length: Amount of iterations to retain.

• timing: Duration of the run

• dataset_name: Name of the data set used in estimation.

See Also

auto_edina(), summary.edina(), print.edina()

Examples

if(requireNamespace("simcdm", quietly = TRUE)) {

# Set a seed for reproducibility
set.seed(1512)

# Setup data simulation parameters
N = 1    # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes

# Note:
# Sample size and attributes have been reduced to create a minimally
# viable example that can be run during CRAN's automatic check.
# Please make sure to have a larger sample size...

# Assign slipping and guessing values for each item
ss = gs = rep(.2, J)

# Simulate an identifiable Q matrix
Q = simcdm::sim_q_matrix(J, K)

# Simulate subject attributes
subject_alphas = simcdm::sim_subject_attributes(N, K)

# Simulate items under the DINA model
items_dina = simcdm::sim_dina_items(subject_alphas, Q, ss, gs)

# Compute the edina model
edina_model = edina(items_dina, k = K)

# Display results
edina_model

# Provide a summary overview
summary(edina_model)
}

Extract Q Matrix

Description

Given a modeling object, extract the Q Matrix

Usage

extract_q_matrix(x, ...)

## S3 method for class 'q_matrix'
extract_q_matrix(x, ...)

## S3 method for class 'edina'
extract_q_matrix(x, binary = TRUE, ...)

## Default S3 method:
extract_q_matrix(x, ...)

Arguments

Value

A matrix that is either dichotomous or estimated depending on the value of the binary parameter.

See Also

q_matrix(), as_q_matrix(), edina(), auto_edina()

Examples

# Q matrix values
x = matrix(c(1, 0, 0, 1), nrow = 2)

# Show Q matrix structure
Q = q_matrix(x)

# Retrieve Q matrix
extract_q_matrix(Q)

View Model Selection Statistics Across Models

Description

Displays information about the value of each model information criterion for a given model across the dimensions the Q matrix is estimated.

Usage

model_selection_graph(x, ...)

Arguments

Value

A ggplot2 object

See Also

autoplot.auto_edina()

View Slipping and Guessing Parameter Changes Across Models

Description

Displays the slipping and guessing parameter changes for each model across the dimensions the Q matrix is estimated.

Usage

parameter_evolution_graph(x, ...)

Arguments

Value

A ggplot2 object

See Also

autoplot.auto_edina()

Print method for auto_edina

Description

Custom print method for displaying the results of the Auto EDINA method.

Usage

## S3 method for class 'auto_edina'
print(x, ...)

Arguments

Value

None.

The function provides a side-effect of displaying the overview of computed results across all models estimated.

Printing out the EDINA Object

Description

Custom print method for computing the EDINA.

Usage

## S3 method for class 'edina'
print(x, binary = FALSE, ...)

Arguments

Value

None.

The function provides a side-effect of displaying the overview of the model estimated.

Printing out a Q Matrix Object

Description

Custom print method for the Q Matrix Object.

Usage

## S3 method for class 'q_matrix'
print(x, ...)

Arguments

Value

An invisible matrix without the q_matrix class displayed as a part of the output displayed.

See Also

q_matrix(), as_q_matrix()

Examples

# Q matrix values
x = matrix(c(1, 0, 0, 1), nrow = 2)

# Show Q matrix structure
q_matrix(x)

Print the auto_edina model summary

Description

Custom method for displaying the results of the summary(auto_edina).

Usage

## S3 method for class 'summary_auto_edina'
print(x, ...)

Arguments

Value

None.

The function provides a side-effect of displaying the overview of computed results across all models estimated.

Printing out the Summary EDINA Object

Description

Custom print method for displaying the EDINA model summary information.

Usage

## S3 method for class 'summary_edina'
print(x, binary = FALSE, ...)

Arguments

Value

None.

The function provides a side-effect of displaying the overview of the model estimated.

Graph Q Matrix

Description

Provides a heatmap approach to showing the estimated binary or averaged values of the Q Matrix.

Usage

q_graph(x, ...)

## S3 method for class 'auto_edina'
q_graph(x, binary = TRUE, ic = c("ppp", "bic", "dic"), ...)

## S3 method for class 'edina'
q_graph(x, binary = TRUE, ...)

## S3 method for class 'matrix'
q_graph(x, ...)

## S3 method for class 'q_matrix'
q_graph(x, ...)

Arguments

Value

A ggplot2 object with a heatmap overview of the estimated Q matrix.

Examples

q = q_matrix(matrix(c(1, 0, 1, 1, 0, 1), ncol = 3))
q_graph(q)

Create a Q Matrix Object

Description

Provides a way to create an object as a "q_matrix".

Usage

q_matrix(x)

Arguments

Value

A q_matrix object.

See Also

as_q_matrix()

Examples

# Q matrix values
x = matrix(c(1, 0, 0, 1), nrow = 2)

# Q matrix wrapper
q_mat = q_matrix(x)

# Data Frame encoding of Q
q_df = data.frame(
   k1 = c(1, 0),
   k2 = c(0, 1)
)

# Create a Q matrix
q_mat = q_matrix(q_df)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

ggplot2

autoplot

Summarize auto_edina model data

Description

Custom method for displaying the results of the auto_edina.

Usage

## S3 method for class 'auto_edina'
summary(object, ...)

Arguments

Value

The original auto_edina object with an added class of summary.auto_edina.

Summarize the EDINA Object

Description

Provide a more detailed view inside of edina model object.

Usage

## S3 method for class 'edina'
summary(object, alpha = 0.05, ...)

Arguments

Value

A summary object that includes everything in the original edina() object and:

• model_fit: Matrix of model fit summary statistics.

• alpha: Alpha-value used to compute PPP()s.