exametrika (version 1.1.0)

LRA: Latent Rank Analysis

Description

A function for estimating LRA by SOM/GTM

Usage

LRA(
  U,
  nrank = 2,
  na = NULL,
  Z = NULL,
  w = NULL,
  method = "GTM",
  mic = FALSE,
  maxiter = 100,
  BIC.check = FALSE,
  seed = NULL
)

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

number of classes you set

TRP

Test Reference Profile matrix. The TRP is the column sum vector of estimated class reference matrix, \(\hat{\Pi}_c\)

LCD

Latent Class Distribution table.see also plot.exametrika

CMD

Class Membership Distribution table. see also plot.exametrika

Students

Class Membership Profile matrix.The s-th row vector of \(\hat{M}_c\), \(\hat{m}_c\), is the class 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.

IRP

Item Reference Profile matrix.The IRP of item j is the j-th row vector in the class reference matrix, \(\hat{\pi}_c\)

IRPIndex

The IRP information includes the item location parameters B and Beta, the slope parameters A and Alpha, and the monotonicity indices C and Gamma.

ItemFitIndices

Fit index for each item.See also ItemFit

TestFitIndices

Overall fit index for the test.See also TestFit

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.

nrank

number of latent rank

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

method

Specify either "SOM" or "GTM". SOM refers to the estimation method using Self-Organizing Mapping, which is suitable when the data size is small. However, as the sample size increases, it takes time to execute. GTM is a batch learning type of SOM, equivalent to applying a gentle filter to LCA (Shojima, 2022).

mic

Monotonic increasing IRP option. The default is FALSE.

maxiter

Maximum number of iterations. default is 100.

BIC.check

During estimation with SOM, this parameter determines whether to use the change in BIC as the convergence criterion. By default, it is FALSE and iteration continues until the maximum number of iterations is reached. If set to TRUE, iteration continues until the overall change in BIC falls below a negligible amount, or until the iteration count reaches ten times the maximum number of iterations.

seed

random seed for SOM.If not specified, a value derived from the original data will be automatically assigned.

Examples

# \donttest{
# Fit a Latent Rank Analysis model with 6 ranks to the sample dataset
result.LRA <- LRA(J15S500, nrank = 6)

# Display the first few rows of student rank membership profiles
# This shows posterior probabilities of students belonging to each rank
head(result.LRA$Students)

# Plot Item Reference Profiles (IRP) for items 1-6 in a 2x3 grid
# Shows the probability of correct response for each rank
plot(result.LRA, type = "IRP", items = 1:6, nc = 2, nr = 3)

# Plot Rank Membership Profiles (RMP) for students 1-9 in a 3x3 grid
# Shows the posterior probability distribution of rank membership for each student
plot(result.LRA, type = "RMP", students = 1:9, nc = 3, nr = 3)

# Plot Test Reference Profile (TRP)
# Shows the column sum vector of estimated rank reference matrix
plot(result.LRA, type = "TRP")

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