Biclustering_IRM: Biclustering with Infinite Relational Model
In exametrika: Test Data Engineering
Biclustering_IRM R Documentation
Biclustering with Infinite Relational Model
Description
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 dispatches to the appropriate method based on the data type:
binary, ordinal, or nominal. For binary data, see Section 7.8 in Shojima(2022).
For nominal data, a Dirichlet-Multinomial collapsed Gibbs sampler is used.
Usage
Biclustering_IRM(U, ...)
## Default S3 method:
Biclustering_IRM(U, na = NULL, Z = NULL, w = NULL, ...)
## S3 method for class 'binary'
Biclustering_IRM(
U,
na = NULL,
Z = NULL,
w = NULL,
gamma_c = 1,
gamma_f = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'nominal'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'ordinal'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
mic = FALSE,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'rated'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
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.
...
Additional arguments passed to specific methods.
na
na argument specifies the numbers or characters to be treated as missing values.
Z
Z is a missing indicator matrix of the type matrix or data.frame
w
w is item weight vector
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.
maxiter
A maximum iteration number of IRM process. The default is 100.
(Renamed from max_iter in v1.15.0; the old name is still accepted
with a deprecation warning.)
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 FALSE
alpha
Dirichlet distribution concentration parameter for the prior density of
field reference probabilities (rated/nominal IRM). Must be positive. The default is 1.
mic
Logical; if TRUE, relabels the classes in ascending order of their
total expected score, summed over all fields (ordinal IRM only). Default is
FALSE. Note that this is a cosmetic reordering of class labels: it makes the
Test Reference Profile monotone (WOAC) but does not impose the per-field
stochastic order (SOAC), and it leaves the estimates themselves unchanged.
IRM classes come from a CRP prior and are exchangeable, so there is no rank
axis for an order restriction to act on; use ordinal Ranklustering
(Biclustering(method = "R", estimation = "isotonic")) when a genuine
order restriction is wanted.
Value
An object of class "exametrika" containing the IRM results.
See Biclustering_IRM.binary or Biclustering_IRM.nominal for details.
- 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).
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- 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
For nominal data, the returned list includes:
- Q
Response matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile, a 3D array (nfld x ncls x maxQ).
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- TestFitIndices
Overall fit index for the test.
- log_lik
Log-likelihood of the model.
For ordinal data, the returned list includes:
- Q
Response matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile (BCRM), a 3D array (nfld x ncls x maxQ).
- FRPIndex
Index of FRP 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.
- BFRP
Bicluster Field Reference Profile (expected scores), a list with
Weighted and Observed components.
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- TestFitIndices
Overall fit index for the test.
- log_lik
Log-likelihood of the model.
- SOACflg
Logical; TRUE if Strongly Ordinal Alignment Condition is satisfied.
- WOACflg
Logical; TRUE if Weakly Ordinal Alignment Condition is satisfied.
For rated data, the returned list includes:
- Q
Response matrix.
- U
Binary correct/incorrect matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile (BCRM), a 3D array (nfld x ncls x maxQ).
- FieldFRP
Field Reference Profile based on binary correct rates (nfld x ncls).
- quasiFRP
Item-level correct response rate per class (nitems x ncls).
- FRPIndex
Index of FRP 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.
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- FieldAnalysis
Field analysis with CRR and field memberships.
- TestFitIndices
Overall fit index for the test (binary layer, default).
- TestFitIndices_nominal
Fit indices for the nominal layer (AIC/BIC/CAIC only).
- log_lik
Log-likelihood of the binary layer model.
- log_lik_nominal
Log-likelihood of the nominal layer model.
- SOACflg
Logical; TRUE if Strongly Ordinal Alignment Condition is satisfied.
- WOACflg
Logical; TRUE if Weakly Ordinal Alignment Condition is satisfied.
Examples
# 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(J15S500, gamma_c = 1, gamma_f = 1)
# Display the Bicluster Reference Matrix (BRM) as a heatmap
plot(result, type = "Array")
# Plot Field Reference Profiles (FRP) in a 3-column grid
plot(result, type = "FRP", nc = 3)
result <- Biclustering_IRM(J15S500, gamma_c = 1, gamma_f = 1)
plot(result, type = "Array")
# Fit a nominal Biclustering IRM model
result <- Biclustering_IRM(J20S600, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
# Fit an ordinal Biclustering IRM model
result <- Biclustering_IRM(J35S500, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
# Fit a rated Biclustering IRM model
result <- Biclustering_IRM(J21S300, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
exametrika documentation built on Aug. 20, 2026, 5:08 p.m.
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| Biclustering_IRM | R Documentation |
Biclustering with Infinite Relational Model
Description
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 dispatches to the appropriate method based on the data type: binary, ordinal, or nominal. For binary data, see Section 7.8 in Shojima(2022). For nominal data, a Dirichlet-Multinomial collapsed Gibbs sampler is used.
Usage
Biclustering_IRM(U, ...)
## Default S3 method:
Biclustering_IRM(U, na = NULL, Z = NULL, w = NULL, ...)
## S3 method for class 'binary'
Biclustering_IRM(
U,
na = NULL,
Z = NULL,
w = NULL,
gamma_c = 1,
gamma_f = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'nominal'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'ordinal'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
mic = FALSE,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
verbose = FALSE,
...
)
## S3 method for class 'rated'
Biclustering_IRM(
U,
gamma_c = 1,
gamma_f = 1,
alpha = 1,
maxiter = 100,
stable_limit = 5,
minSize = 20,
EM_limit = 20,
seed = 123,
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. |
... |
Additional arguments passed to specific methods. |
na |
na argument specifies the numbers or characters to be treated as missing values. |
Z |
Z is a missing indicator matrix of the type matrix or data.frame |
w |
w is item weight vector |
gamma_c |
|
gamma_f |
|
maxiter |
A maximum iteration number of IRM process. The default is 100.
(Renamed from |
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 |
EM_limit |
After IRM process, resizing the number of classes process will starts.
This process using EM algorithm, |
seed |
Random seed for reproducibility. When a numeric value is provided,
|
verbose |
verbose output Flag. default is FALSE |
alpha |
Dirichlet distribution concentration parameter for the prior density of field reference probabilities (rated/nominal IRM). Must be positive. The default is 1. |
mic |
Logical; if TRUE, relabels the classes in ascending order of their
total expected score, summed over all fields (ordinal IRM only). Default is
FALSE. Note that this is a cosmetic reordering of class labels: it makes the
Test Reference Profile monotone (WOAC) but does not impose the per-field
stochastic order (SOAC), and it leaves the estimates themselves unchanged.
IRM classes come from a CRP prior and are exchangeable, so there is no rank
axis for an order restriction to act on; use ordinal Ranklustering
( |
Value
An object of class "exametrika" containing the IRM results.
See Biclustering_IRM.binary or Biclustering_IRM.nominal for details.
- 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).
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- 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
For nominal data, the returned list includes:
- Q
Response matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile, a 3D array (nfld x ncls x maxQ).
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- TestFitIndices
Overall fit index for the test.
- log_lik
Log-likelihood of the model.
For ordinal data, the returned list includes:
- Q
Response matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile (BCRM), a 3D array (nfld x ncls x maxQ).
- FRPIndex
Index of FRP 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.
- BFRP
Bicluster Field Reference Profile (expected scores), a list with Weighted and Observed components.
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- TestFitIndices
Overall fit index for the test.
- log_lik
Log-likelihood of the model.
- SOACflg
Logical; TRUE if Strongly Ordinal Alignment Condition is satisfied.
- WOACflg
Logical; TRUE if Weakly Ordinal Alignment Condition is satisfied.
For rated data, the returned list includes:
- Q
Response matrix.
- U
Binary correct/incorrect matrix.
- Z
Missing indicator matrix.
- testlength
Number of items.
- nobs
Sample size.
- n_class
Optimal number of classes.
- n_field
Optimal number of fields.
- n_cycle
Number of EM algorithm iterations.
- FRP
Field Reference Profile (BCRM), a 3D array (nfld x ncls x maxQ).
- FieldFRP
Field Reference Profile based on binary correct rates (nfld x ncls).
- quasiFRP
Item-level correct response rate per class (nitems x ncls).
- FRPIndex
Index of FRP 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.
- LFD
Latent Field Distribution.
- LCD
Latent Class Distribution.
- FieldMembership
Field membership probability matrix.
- ClassMembership
Class membership probability matrix.
- FieldEstimated
Estimated field assignment for each item.
- ClassEstimated
Estimated class assignment for each student.
- Students
Rank Membership Profile matrix with estimated class.
- FieldAnalysis
Field analysis with CRR and field memberships.
- TestFitIndices
Overall fit index for the test (binary layer, default).
- TestFitIndices_nominal
Fit indices for the nominal layer (AIC/BIC/CAIC only).
- log_lik
Log-likelihood of the binary layer model.
- log_lik_nominal
Log-likelihood of the nominal layer model.
- SOACflg
Logical; TRUE if Strongly Ordinal Alignment Condition is satisfied.
- WOACflg
Logical; TRUE if Weakly Ordinal Alignment Condition is satisfied.
Examples
# 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(J15S500, gamma_c = 1, gamma_f = 1)
# Display the Bicluster Reference Matrix (BRM) as a heatmap
plot(result, type = "Array")
# Plot Field Reference Profiles (FRP) in a 3-column grid
plot(result, type = "FRP", nc = 3)
result <- Biclustering_IRM(J15S500, gamma_c = 1, gamma_f = 1)
plot(result, type = "Array")
# Fit a nominal Biclustering IRM model
result <- Biclustering_IRM(J20S600, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
# Fit an ordinal Biclustering IRM model
result <- Biclustering_IRM(J35S500, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
# Fit a rated Biclustering IRM model
result <- Biclustering_IRM(J21S300, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result, type = "Array")
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