Biclustering {exametrika} | R Documentation |
Biclustering and Ranklustering Analysis
Description
Performs biclustering, ranklustering, or their confirmatory variants on binary response data. These methods simultaneously cluster both examinees and items into homogeneous groups (or ordered ranks for ranklustering). The analysis reveals latent structures and patterns in the data by creating a matrix with rows and columns arranged to highlight block structures.
Usage
Biclustering(
U,
ncls = 2,
nfld = 2,
Z = NULL,
w = NULL,
na = NULL,
method = "B",
conf = NULL,
mic = FALSE,
maxiter = 100,
verbose = TRUE
)
Arguments
U |
Either an object of class "exametrika" or raw data. When raw data is given,
it is converted to the exametrika class with the |
ncls |
Number of latent classes/ranks to identify (between 2 and 20). |
nfld |
Number of latent fields (item clusters) to identify. |
Z |
Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data. |
w |
Item weight vector specifying the relative importance of each item. |
na |
Values to be treated as missing values. |
method |
Analysis method to use (character string):
|
conf |
Confirmatory parameter for pre-specified field assignments. Can be either:
|
mic |
Logical; if TRUE, forces Field Reference Profiles to be monotonically increasing. Default is FALSE. |
maxiter |
Maximum number of EM algorithm iterations. Default is 100. |
verbose |
Logical; if TRUE, displays progress during estimation. Default is TRUE. |
Details
Biclustering simultaneously clusters both rows (examinees) and columns (items) of a data matrix. Unlike traditional clustering that groups either rows or columns, biclustering identifies submatrices with similar patterns. Ranklustering is a variant that imposes an ordinal structure on the classes, making it suitable for proficiency scaling.
The algorithm uses an Expectation-Maximization approach to iteratively estimate:
Field membership of items (which items belong to which fields)
Class/rank membership of examinees (which examinees belong to which classes)
Field Reference Profiles (probability patterns for each field-class combination)
The confirmatory option allows for pre-specified field assignments, which is useful when there is prior knowledge about item groupings or for testing hypothesized structures.
Value
An object of class "exametrika" and "Biclustering" containing:
- model
Model type indicator (1 for biclustering, 2 for ranklustering)
- mic
Logical value indicating whether monotonicity constraint was applied
- testlength
Number of items in the test
- nobs
Number of examinees in the dataset
- Nclass
Number of latent classes/ranks specified
- Nfield
Number of latent fields specified
- N_Cycle
Number of EM iterations performed
- LFD
Latent Field Distribution - counts of items assigned to each field
- LRD/LCD
Latent Rank/Class Distribution - counts of examinees assigned to each class/rank
- FRP
Field Reference Profile matrix - probability of correct response for each field-class combination
- FRPIndex
Field Reference Profile indices including location parameters, slope parameters, and monotonicity indices
- TRP
Test Reference Profile - expected score for examinees in each class/rank
- CMD/RMD
Class/Rank Membership Distribution - sum of membership probabilities across examinees
- FieldMembership
Matrix showing the probabilities of each item belonging to each field
- ClassMembership
Matrix showing the probabilities of each examinee belonging to each class/rank
- SmoothedMembership
Matrix of smoothed class membership probabilities after filtering
- FieldEstimated
Vector of the most likely field assignments for each item
- ClassEstimated
Vector of the most likely class/rank assignments for each examinee
- Students
Data frame containing membership probabilities and classification information for each examinee
- FieldAnalysis
Matrix showing field analysis results with item-level information
- TestFitIndices
Model fit indices for evaluating the quality of the clustering solution
- SOACflg
Logical flag indicating whether Strongly Ordinal Alignment Condition is satisfied
- WOACflg
Logical flag indicating whether Weakly Ordinal Alignment Condition is satisfied
References
Shojima, K. (2012). Biclustering of binary data matrices using bilinear models. Behaviormetrika, 39(2), 161-178.
Examples
# Perform Biclustering with Binary method (B)
# Analyze data with 5 fields and 6 classes
result.Bi <- Biclustering(J35S515, nfld = 5, ncls = 6, method = "B")
# Perform Biclustering with Rank method (R)
# Store results for further analysis and visualization
result.Rank <- Biclustering(J35S515, nfld = 5, ncls = 6, method = "R")
# Display the Bicluster Reference Matrix (BRM) as a heatmap
plot(result.Rank, type = "Array")
# Plot Field Reference Profiles (FRP) in a 2x3 grid
# Shows the probability patterns for each field
plot(result.Rank, type = "FRP", nc = 2, nr = 3)
# Plot Rank Membership Profiles (RMP) for students 1-9 in a 3x3 grid
# Shows posterior probability distribution of rank membership
plot(result.Rank, type = "RMP", students = 1:9, nc = 3, nr = 3)
# Example of confirmatory analysis with pre-specified fields
# Assign items 1-10 to field 1, 11-20 to field 2, etc.
field_assignments <- c(rep(1, 10), rep(2, 10), rep(3, 15))
result.Conf <- Biclustering(J35S515, nfld = 3, ncls = 5, conf = field_assignments)