Note: Some computationally intensive examples below are shown with
eval=FALSEto keep CRAN build times short. For full rendered output, see the pkgdown site.
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")
#> 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 -5256.699Ranklustering
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_resultInfinite 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:
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):