LDB: Local Dependence Biclustering

In exametrika: Test Theory Analysis and Biclustering

Local Dependence Biclustering

Description

Latent dependence Biclustering, which incorporates biclustering and a Bayesian network model.

Usage

LDB(
  U,
  Z = NULL,
  w = NULL,
  na = NULL,
  ncls = 2,
  method = "R",
  conf = NULL,
  g_list = NULL,
  adj_list = NULL,
  adj_file = NULL,
  verbose = FALSE,
  beta1 = 1,
  beta2 = 1
)

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.
ncls	number of latent class(rank). The default is 2.
method	specify the model to analyze the data.Local dependence latent class model is set to "C", latent rank model is set "R". The default is "R".
conf	For the confirmatory parameter, you can input either a vector with items and corresponding fields in sequence, or a field membership profile matrix. In the case of the former, the field membership profile matrix will be generated internally. When providing a membership profile matrix, it needs to be either matrix or data.frame. The number of fields(nfld) will be overwrite to the number of columns of this matrix.
g_list	A list compiling graph-type objects for each rank/class.
adj_list	A list compiling matrix-type adjacency matrices for each rank/class.
adj_file	A file detailing the relationships of the graph for each rank/class, listed in the order of starting point, ending point, and rank(class).
verbose	verbose output Flag. default is TRUE
beta1	Beta distribution parameter 1 for prior density. Default is 1.
beta2	Beta distribution parameter 2 for prior density. Default is 1.

Value

nobs

Sample size. The number of rows in the dataset.

testlength

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

msg

A character string indicating the model type.

Nclass

Optimal number of classes.

Nfield

Optimal number of fields.

crr

Correct Response Rate

ItemLabel

Label of Items

FieldLabel

Label of Fields

adj_list

List of Adjacency matrix used in the model

g_list

List of graph object used in the model

IRP

List of Estimated Parameters. This object is three-dimensional PIRP array, where each dimension represents the number of rank,number of field, and Dmax. Dmax denotes the maximum number of correct response patterns for each field.

LFD

Latent Field Distribution. see also plot.exametrika

LRD

Latent Rank Distribution. see also plot.exametrika

FRP

Marginal Field Reference Matrix

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.

CCRR_table

This table is a rearrangement of IRP into a data.frame format for output, consisting of combinations of rank ,field and PIRP.

TRP

Test Reference Profile

RMD

Rank Membership Distribution.

FieldEstimated

Given vector which correspondence between items and the fields.

ClassEstimated

An index indicating which class a student belongs to, estimated by confirmatory Ranklustering.

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.

TestFitIndices

Overall fit index for the test.See also TestFit

Examples

# Example: Latent Dirichlet Bayesian Network model
# Create field configuration vector based on field assignments
conf <- c(
  1, 6, 6, 8, 9, 9, 4, 7, 7, 7, 5, 8, 9, 10, 10, 9, 9,
  10, 10, 10, 2, 2, 3, 3, 5, 5, 6, 9, 9, 10, 1, 1, 7, 9, 10
)

# Create edge data for the network structure between fields
edges_data <- data.frame(
  "From Field (Parent) >>>" = c(
    6, 4, 5, 1, 1, 4, # Class/Rank 2
    3, 4, 6, 2, 4, 4, # Class/Rank 3
    3, 6, 4, 1, # Class/Rank 4
    7, 9, 6, 7 # Class/Rank 5
  ),
  ">>> To Field (Child)" = c(
    8, 7, 8, 7, 2, 5, # Class/Rank 2
    5, 8, 8, 4, 6, 7, # Class/Rank 3
    5, 8, 5, 8, # Class/Rank 4
    10, 10, 8, 9 # Class/Rank 5
  ),
  "At Class/Rank (Locus)" = c(
    2, 2, 2, 2, 2, 2, # Class/Rank 2
    3, 3, 3, 3, 3, 3, # Class/Rank 3
    4, 4, 4, 4, # Class/Rank 4
    5, 5, 5, 5 # Class/Rank 5
  )
)

# Save edge data to temporary CSV file
tmp_file <- tempfile(fileext = ".csv")
write.csv(edges_data, file = tmp_file, row.names = FALSE)

# Fit Latent Dirichlet Bayesian Network model
result.LDB <- LDB(
  U = J35S515,
  ncls = 5, # Number of latent classes
  conf = conf, # Field configuration vector
  adj_file = tmp_file # Path to the CSV file
)

# Clean up temporary file
unlink(tmp_file)

# Display model results
print(result.LDB)

# Visualize different aspects of the model
plot(result.LDB, type = "Array") # Show bicluster structure
plot(result.LDB, type = "TRP") # Test Response Profile
plot(result.LDB, type = "LRD") # Latent Rank Distribution
plot(result.LDB,
  type = "RMP", # Rank Membership Profiles
  students = 1:9, nc = 3, nr = 3
)
plot(result.LDB,
  type = "FRP", # Field Reference Profiles
  nc = 3, nr = 2
)
# Field PIRP Profile showing correct answer counts for each rank and field
plot(result.LDB, type = "FieldPIRP")

exametrika documentation built on Feb. 17, 2026, 5:07 p.m.