Biclustering and Ranklustering

In exametrika: Test Data Engineering

knitr::opts_chunk$set(
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Note: Some computationally intensive examples below are shown with eval=FALSE to keep CRAN build times short. For full rendered output, see the pkgdown site.

library(exametrika)

Biclustering and Ranklustering

Biclustering and Ranklustering simultaneously cluster items into fields and examinees into classes/ranks. The difference is specified via the method option:

• method = "B": Biclustering (no filtering matrix)
• method = "R": Ranklustering (with filtering matrix for ordered ranks)

Biclustering

Biclustering(J35S515, nfld = 5, ncls = 6, method = "B")

Ranklustering

result.Ranklustering <- Biclustering(J35S515, nfld = 5, ncls = 6, method = "R")

plot(result.Ranklustering, type = "Array")
plot(result.Ranklustering, type = "FRP", nc = 2, nr = 3)
plot(result.Ranklustering, type = "RRV")
plot(result.Ranklustering, type = "RMP", students = 1:9, nc = 3, nr = 3)
plot(result.Ranklustering, type = "LRD")

Finding Optimal Number of Classes and Fields

Grid Search

GridSearch() systematically evaluates multiple parameter combinations and selects the best-fitting model:

result <- GridSearch(J35S515, method = "R", max_ncls = 10, max_nfld = 10, index = "BIC")
result$optimal_ncls
result$optimal_nfld
result$optimal_result

Infinite Relational Model (IRM)

The IRM uses the Chinese Restaurant Process to automatically determine the optimal number of fields and classes:

result.IRM <- Biclustering_IRM(J35S515, gamma_c = 1, gamma_f = 1, verbose = TRUE)
plot(result.IRM, type = "Array")
plot(result.IRM, type = "FRP", nc = 3)
plot(result.IRM, type = "TRP")

Biclustering for Polytomous Data

Ordinal Data

result.B.ord <- Biclustering(J35S500, ncls = 5, nfld = 5, method = "R")
result.B.ord
plot(result.B.ord, type = "Array")

FRP (Field Reference Profile) shows the expected score per field across latent ranks:

plot(result.B.ord, type = "FRP", nc = 3, nr = 2)

FCRP (Field Category Response Profile) shows category probabilities across ranks. The style parameter can be "line" or "bar":

plot(result.B.ord, type = "FCRP", nc = 3, nr = 2)
plot(result.B.ord, type = "FCRP", style = "bar", nc = 3, nr = 2)

FCBR (Field Cumulative Boundary Reference) shows cumulative boundary probabilities (ordinal only):

plot(result.B.ord, type = "FCBR", nc = 3, nr = 2)

ScoreField and RRV plots:

plot(result.B.ord, type = "ScoreField")
plot(result.B.ord, type = "RRV")

Nominal Data

result.B.nom <- Biclustering(J20S600, ncls = 5, nfld = 4)
result.B.nom
plot(result.B.nom, type = "Array")

Nominal Biclustering supports FRP, FCRP, ScoreField, and RRV (but not FCBR):

plot(result.B.nom, type = "FRP", nc = 2, nr = 2)
plot(result.B.nom, type = "FCRP", nc = 2, nr = 2)
plot(result.B.nom, type = "FCRP", style = "bar", nc = 2, nr = 2)
plot(result.B.nom, type = "ScoreField")
plot(result.B.nom, type = "RRV")

Rated Data (Multiple-Choice with Correct Answers)

Rated data has both multiple response categories and correct answers. Biclustering.rated() internally runs nominal Biclustering, then sorts classes by correct response rate:

result.B.rated <- Biclustering(J21S300, ncls = 5, nfld = 3, method = "R", maxiter = 300)
result.B.rated
plot(result.B.rated, type = "Array")
plot(result.B.rated, type = "FRP", nc = 3, nr = 1)

Two layers of fit indices are reported: binary (with CFI/RMSEA) and nominal (AIC/BIC/CAIC only). Access them via result$TestFitIndices and result$TestFitIndices_nominal.

Rated IRM

The IRM also supports rated data:

result.IRM.rated <- Biclustering_IRM(J21S300, gamma_c = 1, gamma_f = 1, verbose = FALSE)
plot(result.IRM.rated, type = "Array")
plot(result.IRM.rated, type = "FRP", nc = 3, nr = 1)

Distractor Analysis

DistractorAnalysis() examines how examinees in each rank/class respond to each item's categories. It computes observed frequencies, proportions, chi-square statistics, p-values, and Cramer's V (effect size) for each item-by-rank cell.

result.B.rated <- Biclustering(J21S300, ncls = 5, nfld = 3, method = "R", maxiter = 300)
da <- DistractorAnalysis(result.B.rated)

# Full output (grouped by field for Biclustering)
print(da)

# Filter by items and/or ranks
print(da, items = 1:7, ranks = c(1, 5))

# Plot distractor bar charts
plot(da, items = 1:6, nc = 3, nr = 2)

DistractorAnalysis() also works with LRA() results for rated data:

result.LRA.rated <- LRA(J21S300, nrank = 5, mic = TRUE)
da_lra <- DistractorAnalysis(result.LRA.rated)
print(da_lra, items = 1:3)
plot(da_lra, items = 1:6, nc = 3, nr = 2)

Reference

Shojima, K. (2022). Test Data Engineering. Springer.

exametrika documentation built on Aug. 20, 2026, 5:08 p.m.