Biclustering and Ranklustering

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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")
#> Biclustering Analysis
#> 
#> Biclustering Reference Matrix Profile
#>        Class1 Class2 Class3 Class4 Class5 Class6
#> Field1 0.6236 0.8636 0.8718  0.898  0.952  1.000
#> Field2 0.0627 0.3332 0.4255  0.919  0.990  1.000
#> Field3 0.2008 0.5431 0.2281  0.475  0.706  1.000
#> Field4 0.0495 0.2455 0.0782  0.233  0.648  0.983
#> Field5 0.0225 0.0545 0.0284  0.043  0.160  0.983
#> 
#> Field Reference Profile Indices
#>        Alpha     A Beta     B Gamma       C
#> Field1     1 0.240    1 0.624   0.0  0.0000
#> Field2     3 0.493    3 0.426   0.0  0.0000
#> Field3     1 0.342    4 0.475   0.2 -0.3149
#> Field4     4 0.415    5 0.648   0.2 -0.1673
#> Field5     5 0.823    5 0.160   0.2 -0.0261
#> 
#>                               Class 1 Class 2 Class 3 Class 4 Class 5 Class 6
#> Test Reference Profile          4.431  11.894   8.598  16.002  23.326  34.713
#> Latent Class Ditribution      157.000  64.000  82.000 106.000  89.000  17.000
#> Class Membership Distribution 146.105  73.232  85.753 106.414  86.529  16.968
#> 
#> Field Membership Profile
#>          CRR   LFE Field1 Field2 Field3 Field4 Field5
#> Item01 0.850 1.000  1.000  0.000  0.000  0.000  0.000
#> Item31 0.812 1.000  1.000  0.000  0.000  0.000  0.000
#> Item32 0.808 1.000  1.000  0.000  0.000  0.000  0.000
#> Item21 0.616 2.000  0.000  1.000  0.000  0.000  0.000
#> Item23 0.600 2.000  0.000  1.000  0.000  0.000  0.000
#> Item22 0.586 2.000  0.000  1.000  0.000  0.000  0.000
#> Item24 0.567 2.000  0.000  1.000  0.000  0.000  0.000
#> Item25 0.491 2.000  0.000  1.000  0.000  0.000  0.000
#> Item11 0.476 2.000  0.000  1.000  0.000  0.000  0.000
#> Item26 0.452 2.000  0.000  1.000  0.000  0.000  0.000
#> Item27 0.414 2.000  0.000  1.000  0.000  0.000  0.000
#> Item07 0.573 3.000  0.000  0.000  1.000  0.000  0.000
#> Item03 0.458 3.000  0.000  0.000  1.000  0.000  0.000
#> Item33 0.437 3.000  0.000  0.000  1.000  0.000  0.000
#> Item02 0.392 3.000  0.000  0.000  1.000  0.000  0.000
#> Item09 0.390 3.000  0.000  0.000  1.000  0.000  0.000
#> Item10 0.353 3.000  0.000  0.000  1.000  0.000  0.000
#> Item08 0.350 3.000  0.000  0.000  1.000  0.000  0.000
#> Item12 0.340 4.000  0.000  0.000  0.000  1.000  0.000
#> Item04 0.303 4.000  0.000  0.000  0.000  1.000  0.000
#> Item17 0.276 4.000  0.000  0.000  0.000  1.000  0.000
#> Item05 0.250 4.000  0.000  0.000  0.000  1.000  0.000
#> Item13 0.237 4.000  0.000  0.000  0.000  1.000  0.000
#> Item34 0.229 4.000  0.000  0.000  0.000  1.000  0.000
#> Item29 0.227 4.000  0.000  0.000  0.000  1.000  0.000
#> Item28 0.221 4.000  0.000  0.000  0.000  1.000  0.000
#> Item06 0.216 4.000  0.000  0.000  0.000  1.000  0.000
#> Item16 0.216 4.000  0.000  0.000  0.000  1.000  0.000
#> Item35 0.155 5.000  0.000  0.000  0.000  0.000  1.000
#> Item14 0.126 5.000  0.000  0.000  0.000  0.000  1.000
#> Item15 0.087 5.000  0.000  0.000  0.000  0.000  1.000
#> Item30 0.085 5.000  0.000  0.000  0.000  0.000  1.000
#> Item20 0.054 5.000  0.000  0.000  0.000  0.000  1.000
#> Item19 0.052 5.000  0.000  0.000  0.000  0.000  1.000
#> Item18 0.049 5.000  0.000  0.000  0.000  0.000  1.000
#> Latent Field Distribution
#>            Field 1 Field 2 Field 3 Field 4 Field 5
#> N of Items       3       8       7      10       7
#> 
#> Model Fit Indices
#> Number of Latent Class : 6
#> Number of Latent Field: 5
#> Number of EM cycle: 33 
#>                    value
#> model_log_like -6884.582
#> bench_log_like -5891.314
#> null_log_like  -9862.114
#> model_Chi_sq    1986.535
#> null_Chi_sq     7941.601
#> model_df        1160.000
#> null_df         1155.000
#> NFI                0.750
#> RFI                0.751
#> IFI                0.878
#> TLI                0.879
#> CFI                0.878
#> RMSEA              0.037
#> AIC             -333.465
#> CAIC           -6416.699
#> BIC            -5256.699

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")

Reference

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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.