exametrika (version 1.1.0)

IRM: Infinite Relational Model

Description

The purpose of this method is to find the optimal number of classes C, and optimal number of fields F. It can be found in a single run of the analysis, but it takes a long computation time when the sample size S is large. In addition, this method incorporates the Chinese restaurant process and Gibbs sampling. In detail, See Section 7.8 in Shojima(2022).

Usage

IRM(
  U,
  Z = NULL,
  w = NULL,
  na = NULL,
  gamma_c = 1,
  gamma_f = 1,
  max_iter = 100,
  stable_limit = 5,
  minSize = 20,
  EM_limit = 20,
  seed = 123,
  verbose = TRUE
)

Value

nobs

Sample size. The number of rows in the dataset.

testlength

Length of the test. The number of items included in the test.

Nclass

Optimal number of classes.

Nfield

Optimal number of fields.

BRM

Bicluster Reference Matrix

FRP

Field Reference Profile

FRPIndex

Index of FFP includes the item location parameters B and Beta, the slope parameters A and Alpha, and the monotonicity indices C and Gamma.

TRP

Test Reference Profile

FMP

Field Membership Profile

Students

Rank Membership Profile matrix.The s-th row vector of \(\hat{M}_R\), \(\hat{m}_R\), is the rank membership profile of Student s, namely the posterior probability distribution representing the student's belonging to the respective latent classes. It also includes the rank with the maximum estimated membership probability, as well as the rank-up odds and rank-down odds.

LRD

Latent Rank Distribution. see also plot.exametrika

LFD

Latent Field Distribution. see also plot.exametrika

RMD

Rank Membership Distribution.

TestFitIndices

Overall fit index for the test.See also TestFit

Arguments

U

U is either a data class of exametrika, or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.

Z

Z is a missing indicator matrix of the type matrix or data.frame

w

w is item weight vector

na

na argument specifies the numbers or characters to be treated as missing values.

gamma_c

\(\gamma_C\) is the hyperparameter of the CRP and represents the attractiveness of a new Class. As \(\gamma_C\) increases, the student is more likely to be seated at a vacant class. The default is 1.

gamma_f

\(\gamma_F\) is the hyperparameter of the CRP and represents the attractiveness of a new Field. The greater this value it more likely to be classified in the new field. The default is 1.

max_iter

A maximum iteration number of IRM process. The default is 100.

stable_limit

The IRM process exits the loop when the FRM stabilizes and no longer changes significantly. This option sets the maximum number of stable iterations, with a default of 5.

minSize

A value used for readjusting the number of classes.If the size of each class is less than minSize, the number of classes will be reduced. Note that this under limit of size is not used for either all correct or all incorrect class.

EM_limit

After IRM process, resizing the number of classes process will starts. This process using EM algorithm,EM_limit is the maximum number of iteration with default of 20.

seed

seed value for random numbers.

verbose

verbose output Flag. default is TRUE

Examples

# \donttest{
# Fit an Infinite Relational Model (IRM) to determine optimal number of classes and fields
# gamma_c and gamma_f are concentration parameters for the Chinese Restaurant Process
result.IRM <- IRM(J35S515, gamma_c = 1, gamma_f = 1, verbose = TRUE)

# Display the Bicluster Reference Matrix (BRM) as a heatmap
# Shows the discovered clustering structure of items and students
plot(result.IRM, type = "Array")

# Plot Field Reference Profiles (FRP) in a 3-column grid
# Shows the probability patterns for each automatically determined field
plot(result.IRM, type = "FRP", nc = 3)

# Plot Test Reference Profile (TRP)
# Shows the overall response pattern across all fields
plot(result.IRM, type = "TRP")
# }