exametrika (version 1.1.0)

LDLRA: Local Dependence Latent Rank Analysis

Description

performs local dependence latent lank analysis(LD_LRA) by Shojima(2011)

Usage

LDLRA(
  U,
  Z = NULL,
  w = NULL,
  na = NULL,
  ncls = 2,
  method = "R",
  g_list = NULL,
  adj_list = NULL,
  adj_file = NULL,
  verbose = FALSE
)

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.

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".

g_list

A list compiling graph-type objects for each rank/class.

adj_list

A list compiling matrix-type adjacency matrices for each rank/class.

adj_file

A file detailing the relationships of the graph for each rank/class, listed in the order of starting point, ending point, and rank(class).

verbose

verbose output Flag. default is TRUE

Details

This function is intended to perform LD-LRA. LD-LRA is an analysis that combines LRA and BNM, and it is used to analyze the network structure among items in the latent rank. In this function, structural learning is not performed, so you need to provide item graphs for each rank as separate files. The file format for this is plain text CSV that includes edges (From, To) and rank numbers.

Examples

# \donttest{
# Create sample DAG structure with different rank levels
# Format: From, To, Rank
DAG_dat <- matrix(c(
  "From", "To", "Rank",
  "Item01", "Item02", "1", # Simple structure for Rank 1
  "Item01", "Item02", "2", # More complex structure for Rank 2
  "Item02", "Item03", "2",
  "Item01", "Item02", "3", # Additional connections for Rank 3
  "Item02", "Item03", "3",
  "Item03", "Item04", "3"
), ncol = 3, byrow = TRUE)

# Method 1: Directly use graph and adjacency lists
g_list <- list()
adj_list <- list()

for (i in 1:3) {
  adj_R <- DAG_dat[DAG_dat[, 3] == as.character(i), 1:2, drop = FALSE]
  g_tmp <- igraph::graph_from_data_frame(
    d = data.frame(
      From = adj_R[, 1],
      To = adj_R[, 2]
    ),
    directed = TRUE
  )
  adj_tmp <- igraph::as_adjacency_matrix(g_tmp)
  g_list[[i]] <- g_tmp
  adj_list[[i]] <- adj_tmp
}

# Fit Local Dependence Latent Rank Analysis
result.LDLRA1 <- LDLRA(J12S5000,
  ncls = 3,
  g_list = g_list,
  adj_list = adj_list
)

# Plot Item Reference Profiles (IRP) in a 4x3 grid
# Shows the probability patterns of correct responses for each item across ranks
plot(result.LDLRA1, type = "IRP", nc = 4, nr = 3)

# Plot Test Reference Profile (TRP)
# Displays the overall pattern of correct response probabilities across ranks
plot(result.LDLRA1, type = "TRP")

# Plot Latent Rank Distribution (LRD)
# Shows the distribution of students across different ranks
plot(result.LDLRA1, type = "LRD")
# }