BINET: Bicluster Network Model

In exametrika: Test Theory Analysis and Biclustering

Bicluster Network Model

Description

Bicluster Network Model: BINET is a model that combines the Bayesian network model and Biclustering. BINET is very similar to LDB and LDR. The most significant difference is that in LDB, the nodes represent the fields, whereas in BINET, they represent the class. BINET explores the local dependency structure among latent classes at each latent field, where each field is a locus.

Usage

BINET(
  U,
  Z = NULL,
  w = NULL,
  na = NULL,
  conf = NULL,
  ncls = NULL,
  nfld = NULL,
  g_list = NULL,
  adj_list = NULL,
  adj_file = NULL,
  verbose = FALSE
)

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.
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.
ncls	number of classes
nfld	number of fields
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

Value

nobs

Sample size. The number of rows in the dataset.

msg

A character string indicating the model type.

testlength

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

Nclass

Optimal number of classes.

Nfield

Optimal number of fields.

crr

Correct Response Rate

ItemLabel

Label of Items

FieldLabel

Label of Fields

all_adj

Integrated Adjacency matrix used to plot graph.

all_g

Integrated graph object used to plot graph.see also plot.exametrika

adj_list

List of Adjacency matrix used in the model

params

A list of the estimated conditional probabilities. It indicates which path was obtained from which parent node(class) to which child node(class), held by parent, child, and field. The item Items contained in the field is in fld. Named chap includes the conditional correct response answer rate of the child node, while pap contains the pass rate of the parent node.

PSRP

Response pattern by the students belonging to the parent classes of Class c. A more comprehensible arrangement of params.

LCD

Latent Class Distribution. see also plot.exametrika

LFD

Latent Field Distribution. see also plot.exametrika

CMD

Class Membership Distribution.

FRP

Marginal bicluster 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.

TRP

Test Reference Profile

LDPSR

A rearranged set of parameters for output. It includes the field the items contained within that field, and the conditional correct response rate of parent nodes(class) and child node(class).

FieldEstimated

Given vector which correspondence between items and the fields.

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.

NextStage

The next class that easiest for students to move to, its membership probability, class-up odds, and the field required for more.

MG_FitIndices

Multigroup as Null model.See also TestFit

SM_FitIndices

Saturated Model as Null model.See also TestFit

Examples

# Example: Bicluster Network Model (BINET)
# BINET combines Bayesian network model and Biclustering to explore
# local dependency structure among latent classes at each field

# Create field configuration vector based on field assignments
conf <- c(
  1, 5, 5, 5, 9, 9, 6, 6, 6, 6, 2, 7, 7, 11, 11, 7, 7,
  12, 12, 12, 2, 2, 3, 3, 4, 4, 4, 8, 8, 12, 1, 1, 6, 10, 10
)

# Create edge data for network structure between classes
edges_data <- data.frame(
  "From Class (Parent) >>>" = c(
    1, 2, 3, 4, 5, 7, 2, 4, 6, 8, 10, 6, 6, 11, 8, 9, 12
  ),
  ">>> To Class (Child)" = c(
    2, 4, 5, 5, 6, 11, 3, 7, 9, 12, 12, 10, 8, 12, 12, 11, 13
  ),
  "At Field (Locus)" = c(
    1, 2, 2, 3, 4, 4, 5, 5, 5, 5, 5, 7, 8, 8, 9, 9, 12
  )
)

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

# Fit Bicluster Network Model
result.BINET <- BINET(
  J35S515,
  ncls = 13, # Maximum class number from edges (13)
  nfld = 12, # Maximum field number from conf (12)
  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.BINET)

# Visualize different aspects of the model
plot(result.BINET, type = "Array") # Show bicluster structure
plot(result.BINET, type = "TRP") # Test Response Profile
plot(result.BINET, type = "LRD") # Latent Rank Distribution
plot(result.BINET,
  type = "RMP", # Rank Membership Profiles
  students = 1:9, nc = 3, nr = 3
)
plot(result.BINET,
  type = "FRP", # Field Reference Profiles
  nc = 3, nr = 2
)
plot(result.BINET,
  type = "LDPSR", # Locally Dependent Passing Student Rates
  nc = 3, nr = 2
)

exametrika documentation built on Aug. 21, 2025, 5:27 p.m.