IRM {exametrika} | R Documentation |
Infinite Relational Model
Description
The purpose of this method is to find 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. In addition, this method incorporates the Chinese restaurant process and Gibbs sampling. In detail, See Section 7.8 in Shojima(2022).
Usage
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_f |
|
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 |
EM_limit |
After IRM process, resizing the number of classes process will starts.
This process using EM algorithm, |
seed |
seed value for random numbers. |
verbose |
verbose output Flag. default is TRUE |
Value
- nobs
Sample size. The number of rows in the dataset.
- testlength
Length of the test. The number of items included in the test.
- Nclass
Optimal number of classes.
- Nfield
Optimal number of fields.
- 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
# Fit an Infinite Relational Model (IRM) to determine optimal number of classes and fields
# gamma_c and gamma_f are concentration parameters for the Chinese Restaurant Process
result.IRM <- IRM(J35S515, gamma_c = 1, gamma_f = 1, verbose = TRUE)
# Display the Bicluster Reference Matrix (BRM) as a heatmap
# Shows the discovered clustering structure of items and students
plot(result.IRM, type = "Array")
# Plot Field Reference Profiles (FRP) in a 3-column grid
# Shows the probability patterns for each automatically determined field
plot(result.IRM, type = "FRP", nc = 3)
# Plot Test Reference Profile (TRP)
# Shows the overall response pattern across all fields
plot(result.IRM, type = "TRP")