exametrika (version 1.1.0)

StrLearningPBIL_LDLRA: Structure Learning for LDLRA by PBIL algorithm

Description

Generating DAG list from data using Population-Based Incremental learning

Usage

StrLearningPBIL_LDLRA(
  U,
  Z = NULL,
  w = NULL,
  na = NULL,
  seed = 123,
  ncls = 2,
  method = "R",
  population = 20,
  Rs = 0.5,
  Rm = 0.002,
  maxParents = 2,
  maxGeneration = 100,
  successiveLimit = 5,
  elitism = 0,
  alpha = 0.05,
  estimate = 1,
  filename = NULL,
  verbose = 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.

crr

correct response ratio

adj_list

adjacency matrix list

g_list

graph list

referenceMatrix

Learned Parameters.A three-dimensional array of patterns where item x rank x pattern.

IRP

Marginal Item Reference Matrix

IRPIndex

IRP Indices which include Alpha, Beta, Gamma.

TRP

Test Reference Profile matrix.

LRD

latent Rank/Class Distribution

RMD

Rank/Class Membership Distribution

TestFitIndices

Overall fit index for the test.See also TestFit

Estimation_table

Estimated parameters tables.

CCRR_table

Correct Response Rate tables

Studens

Student information. It includes estimated class membership, probability of class membership, RUO, and RDO.

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.

seed

seed for random.

ncls

number of latent class(rank). The default is 2.

method

specify the model to analyze the data.Local dependence latent class model is set to "C", latent rank model is set "R". The default is "R".

population

Population size. The default is 20

Rs

Survival Rate. The default is 0.5

Rm

Mutation Rate. The default is 0.002

maxParents

Maximum number of edges emanating from a single node. The default is 2.

maxGeneration

Maximum number of generations.

successiveLimit

Termination conditions. If the optimal individual does not change for this number of generations, it is considered to have converged.

elitism

Number of elites that remain without crossover when transitioning to the next generation.

alpha

Learning rate. The default is 0.05

estimate

In PBIL for estimating the adjacency matrix, specify by number from the following four methods: 1. Optimal adjacency matrix, 2. Rounded average of individuals in the last generation, 3. Rounded average of survivors in the last generation, 4. Rounded generational gene of the last generation. The default is 1.

filename

Specify the filename when saving the generated adjacency matrix in CSV format. The default is null, and no output is written to the file.

verbose

verbose output Flag. default is TRUE

Details

This function performs structural learning for each classes by using the Population-Based Incremental Learning model(PBIL) proposed by Fukuda et al.(2014) within the genetic algorithm framework. Instead of learning the adjacency matrix itself, the 'genes of genes' that generate the adjacency matrix are updated with each generation. For more details, please refer to Fukuda(2014) and Section 9.4.3 of the text(Shojima,2022).

References

Fukuda, S., Yamanaka, Y., & Yoshihiro, T. (2014). A Probability-based evolutionary algorithm with mutations to learn Bayesian networks. International Journal of Artificial Intelligence and Interactive Multimedia, 3, 7–13. DOI: 10.9781/ijimai.2014.311

Examples

# \donttest{
# Perform Structure Learning for LDLRA using PBIL algorithm
# This process may take considerable time due to evolutionary optimization
result.LDLRA.PBIL <- StrLearningPBIL_LDLRA(J35S515,
  seed = 123, # Set random seed for reproducibility
  ncls = 5, # Number of latent ranks
  method = "R", # Use rank model (vs. class model)
  elitism = 1, # Keep best solution in each generation
  successiveLimit = 15 # Convergence criterion
)

# Examine the learned network structure
# Plot Item Response Profiles showing item patterns across ranks
plot(result.LDLRA.PBIL, type = "IRP", nc = 4, nr = 3)

# Plot Test Response Profile showing overall response patterns
plot(result.LDLRA.PBIL, type = "TRP")

# Plot Latent Rank Distribution showing student distribution
plot(result.LDLRA.PBIL, type = "LRD")
# }