Biclustering with Infinite Relational Model — Biclustering

This function performs Biclustering structure learning using the Infinite Relational Model (IRM) to automatically determine 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. This method incorporates the Chinese restaurant process and Gibbs sampling. In detail, See Section 7.8 in Shojima(2022).

Usage

Biclustering_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
)

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: Random seed for reproducibility. When a numeric value is provided, set.seed(seed) is called before the Gibbs sampling begins, ensuring reproducible results. The default is 123, which guarantees deterministic output. Set to NULL to disable seed setting and let the results depend on the current state of the random number generator.
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.
n_class: Optimal number of classes (new naming convention).
n_field: Optimal number of fields (new naming convention).
em_cycle: Number of EM algorithm iterations (new naming convention).
Nclass: Optimal number of classes (deprecated, use n_class).
Nfield: Optimal number of fields (deprecated, use n_field).
EM_Cycle: Number of EM algorithm iterations (deprecated, use em_cycle).
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

Examples

# \donttest{
# Fit a Biclustering model with automatic structure learning using IRM
# gamma_c and gamma_f are concentration parameters for the Chinese Restaurant Process
result <- Biclustering_IRM(J35S515, gamma_c = 1, gamma_f = 1, verbose = TRUE)
#> iter 1: match=0 nfld=15 ncls=30
#> iter 2: match=0 nfld=12 ncls=27
#> iter 3: match=1 nfld=12 ncls=24
#> iter 4: match=2 nfld=12 ncls=23
#> iter 5: match=3 nfld=12 ncls=23
#> iter 6: match=0 nfld=12 ncls=23
#> iter 7: match=1 nfld=12 ncls=23
#> iter 8: match=2 nfld=12 ncls=23
#> iter 9: match=3 nfld=12 ncls=21
#> iter 10: match=4 nfld=12 ncls=21
#> iter 11: match=5 nfld=12 ncls=21
#> Adjusting classes: BIC=-99592.5 ncls=21 (min size < 20)
#> Adjusting classes: BIC=-99980.4 ncls=20 (min size < 20)
#> Adjusting classes: BIC=-99959.7 ncls=19 (min size < 20)
#> Adjusting classes: BIC=-99988.3 ncls=18 (min size < 20)
#> Adjusting classes: BIC=-100001.3 ncls=17 (min size < 20)

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


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





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

# }