Bicluster Network Model: BINET is a model that combines the Bayesian network model and Biclustering. BINET is very similar to LDB and LDR. The most significant difference is that in LDB, the nodes represent the fields, whereas in BINET, they represent the class. BINET explores the local dependency structure among latent classes at each latent field, where each field is a locus.
Usage
BINET(
U,
Z = NULL,
w = NULL,
na = NULL,
conf = NULL,
ncls = NULL,
nfld = NULL,
g_list = NULL,
adj_list = NULL,
adj_file = NULL,
verbose = FALSE
)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.
- conf
For the confirmatory parameter, you can input either a vector with items and corresponding fields in sequence, or a field membership profile matrix. In the case of the former, the field membership profile matrix will be generated internally. When providing a membership profile matrix, it needs to be either matrix or data.frame. The number of fields(nfld) will be overwrite to the number of columns of this matrix.
- ncls
number of classes
- nfld
number of fields
- 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
Value
- nobs
Sample size. The number of rows in the dataset.
- msg
A character string indicating the model type.
- testlength
Length of the test. The number of items included in the test.
- Nclass
Optimal number of classes.
- Nfield
Optimal number of fields.
- crr
Correct Response Rate
- ItemLabel
Label of Items
- FieldLabel
Label of Fields
- all_adj
Integrated Adjacency matrix used to plot graph.
- all_g
Integrated graph object used to plot graph.see also plot.exametrika
- adj_list
List of Adjacency matrix used in the model
- params
A list of the estimated conditional probabilities. It indicates which path was obtained from which parent node(class) to which child node(class), held by
parent,child, andfield. The item Items contained in the field is infld. Namedchapincludes the conditional correct response answer rate of the child node, whilepapcontains the pass rate of the parent node.- PSRP
Response pattern by the students belonging to the parent classes of Class c. A more comprehensible arrangement of
params.- LCD
Latent Class Distribution. see also plot.exametrika
- LFD
Latent Field Distribution. see also plot.exametrika
- CMD
Class Membership Distribution.
- FRP
Marginal bicluster reference matrix.
- FRPIndex
Index of FFP includes the item location parameters B and Beta, the slope parameters A and Alpha, and the monotonicity indices C and Gamma.
- TRP
Test Reference Profile
- LDPSR
A rearranged set of parameters for output. It includes the field the items contained within that field, and the conditional correct response rate of parent nodes(class) and child node(class).
- FieldEstimated
Given vector which correspondence between items and the fields.
- Students
Rank Membership Profile matrix.The s-th row vector of \(\hat{M}_R\), \(\hat{m}_R\), is the rank membership profile of Student s, namely the posterior probability distribution representing the student's belonging to the respective latent classes.
- NextStage
The next class that easiest for students to move to, its membership probability, class-up odds, and the field required for more.
- MG_FitIndices
Multigroup as Null model.See also TestFit
- SM_FitIndices
Saturated Model as Null model.See also TestFit
Examples
# \donttest{
# Example: Bicluster Network Model (BINET)
# BINET combines Bayesian network model and Biclustering to explore
# local dependency structure among latent classes at each field
# Create field configuration vector based on field assignments
conf <- c(
1, 5, 5, 5, 9, 9, 6, 6, 6, 6, 2, 7, 7, 11, 11, 7, 7,
12, 12, 12, 2, 2, 3, 3, 4, 4, 4, 8, 8, 12, 1, 1, 6, 10, 10
)
# Create edge data for network structure between classes
edges_data <- data.frame(
"From Class (Parent) >>>" = c(
1, 2, 3, 4, 5, 7, 2, 4, 6, 8, 10, 6, 6, 11, 8, 9, 12
),
">>> To Class (Child)" = c(
2, 4, 5, 5, 6, 11, 3, 7, 9, 12, 12, 10, 8, 12, 12, 11, 13
),
"At Field (Locus)" = c(
1, 2, 2, 3, 4, 4, 5, 5, 5, 5, 5, 7, 8, 8, 9, 9, 12
)
)
# Save edge data to temporary CSV file
tmp_file <- tempfile(fileext = ".csv")
write.csv(edges_data, file = tmp_file, row.names = FALSE)
# Fit Bicluster Network Model
result.BINET <- BINET(
J35S515,
ncls = 13, # Maximum class number from edges (13)
nfld = 12, # Maximum field number from conf (12)
conf = conf, # Field configuration vector
adj_file = tmp_file # Path to the CSV file
)
#> No ID column detected. All columns treated as response data. Sequential IDs (Student1, Student2, ...) were generated. Use id= parameter to specify the ID column explicitly.
#> No ID column detected. All columns treated as response data. Sequential IDs (Student1, Student2, ...) were generated. Use id= parameter to specify the ID column explicitly.
# Clean up temporary file
unlink(tmp_file)
# Display model results
print(result.BINET)
#> Total Graph
#> Class01 Class02 Class03 Class04 Class05 Class06 Class07 Class08 Class09
#> Class01 0 1 0 0 0 0 0 0 0
#> Class02 0 0 1 1 0 0 0 0 0
#> Class03 0 0 0 0 1 0 0 0 0
#> Class04 0 0 0 0 1 0 1 0 0
#> Class05 0 0 0 0 0 1 0 0 0
#> Class06 0 0 0 0 0 0 0 1 1
#> Class07 0 0 0 0 0 0 0 0 0
#> Class08 0 0 0 0 0 0 0 0 0
#> Class09 0 0 0 0 0 0 0 0 0
#> Class10 0 0 0 0 0 0 0 0 0
#> Class11 0 0 0 0 0 0 0 0 0
#> Class12 0 0 0 0 0 0 0 0 0
#> Class13 0 0 0 0 0 0 0 0 0
#> Class10 Class11 Class12 Class13
#> Class01 0 0 0 0
#> Class02 0 0 0 0
#> Class03 0 0 0 0
#> Class04 0 0 0 0
#> Class05 0 0 0 0
#> Class06 1 0 0 0
#> Class07 0 1 0 0
#> Class08 0 0 1 0
#> Class09 0 1 0 0
#> Class10 0 0 1 0
#> Class11 0 0 1 0
#> Class12 0 0 0 1
#> Class13 0 0 0 0
#> Estimation of Parameter set
#> Field 1
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.000
#> Class 2 0.554 0.558 0.649
#> Class 3 0.740
#> Class 4 0.859
#> Class 5 0.875
#> Class 6 0.910
#> Class 7 0.868
#> Class 8 0.889
#> Class 9 0.961
#> Class 10 0.932
#> Class 11 0.898
#> Class 12 0.975
#> Class 13 1.000
#> Field 2
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.0000
#> Class 2 0.0090
#> Class 3 0.0396
#> Class 4 0.6813 0.785 0.637
#> Class 5 0.4040 0.728 0.696
#> Class 6 0.6877
#> Class 7 0.8316
#> Class 8 0.8218
#> Class 9 1.0000
#> Class 10 0.9836
#> Class 11 1.0000
#> Class 12 1.0000
#> Class 13 1.0000
#> Field 3
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.000
#> Class 2 0.177
#> Class 3 0.219
#> Class 4 0.206
#> Class 5 0.189 0.253
#> Class 6 1.000
#> Class 7 1.000
#> Class 8 1.000
#> Class 9 0.986
#> Class 10 1.000
#> Class 11 0.973
#> Class 12 1.000
#> Class 13 1.000
#> Field 4
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.0000
#> Class 2 0.0127
#> Class 3 0.1228
#> Class 4 0.0468
#> Class 5 0.1131
#> Class 6 0.6131 0.436 0.179
#> Class 7 0.9775
#> Class 8 0.9539
#> Class 9 0.9751
#> Class 10 0.9660
#> Class 11 0.9411 0.925 0.757
#> Class 12 1.0000
#> Class 13 1.0000
#> Field 5
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.0000
#> Class 2 0.0157
#> Class 3 0.0731 0.330 0.06789
#> Class 4 0.9626
#> Class 5 0.1028
#> Class 6 0.2199
#> Class 7 0.1446 0.265 0.00602
#> Class 8 0.9403
#> Class 9 0.2936 0.298 0.12080
#> Class 10 0.8255
#> Class 11 0.9123
#> Class 12 1.0000 1.000 1.00000
#> Class 13 1.0000
#> Field 6
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.000
#> Class 2 0.236
#> Class 3 0.275
#> Class 4 0.449
#> Class 5 0.414
#> Class 6 0.302
#> Class 7 0.415
#> Class 8 0.469
#> Class 9 0.560
#> Class 10 0.564
#> Class 11 0.614
#> Class 12 0.764
#> Class 13 1.000
#> Field 7
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.0000
#> Class 2 0.0731
#> Class 3 0.0810
#> Class 4 0.1924
#> Class 5 0.1596
#> Class 6 0.1316
#> Class 7 0.1263
#> Class 8 0.1792
#> Class 9 0.7542
#> Class 10 0.9818 0.883 0.933 0.975
#> Class 11 0.3047
#> Class 12 0.7862
#> Class 13 1.0000
#> Field 8
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.00e+00
#> Class 2 9.83e-05
#> Class 3 3.70e-02
#> Class 4 3.91e-02
#> Class 5 4.21e-02
#> Class 6 6.88e-02
#> Class 7 4.56e-01
#> Class 8 1.65e-01 0.192
#> Class 9 6.15e-01
#> Class 10 3.88e-01
#> Class 11 3.16e-01
#> Class 12 1.00e+00 1.000
#> Class 13 1.00e+00
#> Field 9
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.00e+00
#> Class 2 2.47e-16
#> Class 3 1.61e-02
#> Class 4 6.15e-01
#> Class 5 3.46e-02
#> Class 6 5.26e-02
#> Class 7 1.44e-11
#> Class 8 2.09e-01
#> Class 9 9.51e-18
#> Class 10 8.09e-01
#> Class 11 1.00e+00 1.000
#> Class 12 7.81e-01 0.703
#> Class 13 1.00e+00
#> Field 10
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.0000
#> Class 2 0.0952
#> Class 3 0.1798
#> Class 4 0.1741
#> Class 5 0.1594
#> Class 6 0.1789
#> Class 7 0.1208
#> Class 8 0.1550
#> Class 9 0.2228
#> Class 10 0.2602
#> Class 11 0.1724
#> Class 12 0.3109
#> Class 13 1.0000
#> Field 11
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.00e+00
#> Class 2 6.09e-14
#> Class 3 8.84e-07
#> Class 4 8.14e-02
#> Class 5 2.46e-02
#> Class 6 2.13e-02
#> Class 7 2.56e-02
#> Class 8 2.76e-16
#> Class 9 2.44e-01
#> Class 10 4.30e-01
#> Class 11 3.84e-02
#> Class 12 5.86e-01
#> Class 13 1.00e+00
#> Field 12
#> PSRP 1 PSRP 2 PSRP 3 PSRP 4
#> Class 1 0.00e+00
#> Class 2 2.35e-03
#> Class 3 5.57e-02
#> Class 4 0.00e+00
#> Class 5 2.02e-02
#> Class 6 1.67e-02
#> Class 7 1.93e-02
#> Class 8 4.62e-02
#> Class 9 1.85e-02
#> Class 10 2.54e-02
#> Class 11 5.68e-15
#> Class 12 2.26e-01
#> Class 13 1.00e+00 1 1 1
#> Local Dependence Passing Student Rate
#> Field Field Item 1 Field Item 2 Field Item 3 Field Item 4 Parent Class
#> 1 1.000 Item01 Item31 Item32 1.000
#> 2 2.000 Item11 Item21 Item22 2.000
#> 3 2.000 Item11 Item21 Item22 3.000
#> 4 3.000 Item23 Item24 4.000
#> 5 4.000 Item25 Item26 Item27 5.000
#> 6 4.000 Item25 Item26 Item27 7.000
#> 7 5.000 Item02 Item03 Item04 2.000
#> 8 5.000 Item02 Item03 Item04 4.000
#> 9 5.000 Item02 Item03 Item04 6.000
#> 10 5.000 Item02 Item03 Item04 8.000
#> 11 5.000 Item02 Item03 Item04 10.000
#> 12 7.000 Item12 Item13 Item16 Item17 6.000
#> 13 8.000 Item28 Item29 6.000
#> 14 8.000 Item28 Item29 11.000
#> 15 9.000 Item05 Item06 8.000
#> 16 9.000 Item05 Item06 9.000
#> 17 12.000 Item18 Item19 Item20 Item30 12.000
#> Parent CCR 1 Parent CCR 2 Parent CCR 3 Parent CCR 4 Child Class Child CCR 1
#> 1 0.000 0.000 0.000 2.000 0.554
#> 2 0.005 0.018 0.003 4.000 0.681
#> 3 0.034 0.068 0.016 5.000 0.404
#> 4 0.221 0.190 5.000 0.189
#> 5 0.147 0.050 0.142 6.000 0.613
#> 6 0.999 0.991 0.943 11.000 0.941
#> 7 0.005 0.040 0.002 3.000 0.073
#> 8 0.996 0.998 0.893 7.000 0.145
#> 9 0.263 0.334 0.063 9.000 0.294
#> 10 0.980 0.958 0.882 12.000 1.000
#> 11 0.943 0.800 0.733 12.000 1.000
#> 12 0.181 0.146 0.037 0.162 10.000 0.982
#> 13 0.009 0.129 8.000 0.165
#> 14 0.359 0.273 12.000 1.000
#> 15 0.266 0.152 12.000 0.781
#> 16 0.000 0.000 11.000 1.000
#> 17 0.158 0.178 0.217 0.352 13.000 1.000
#> Child CCR 2 Child CCR 3 Child CCR 4
#> 1 0.558 0.649
#> 2 0.785 0.637
#> 3 0.728 0.696
#> 4 0.253
#> 5 0.436 0.179
#> 6 0.925 0.757
#> 7 0.330 0.068
#> 8 0.265 0.006
#> 9 0.298 0.121
#> 10 1.000 1.000
#> 11 1.000 1.000
#> 12 0.883 0.933 0.975
#> 13 0.192
#> 14 1.000
#> 15 0.703
#> 16 1.000
#> 17 1.000 1.000 1.000
#> Marginal Bicluster Reference Matrix
#> Class1 Class2 Class3 Class4 Class5 Class6 Class7 Class8 Class9 Class10
#> Field1 0 0.587 0.740 0.859 0.875 0.910 0.868 0.889 0.961 0.932
#> Field2 0 0.009 0.040 0.701 0.609 0.688 0.832 0.822 1.000 0.984
#> Field3 0 0.177 0.219 0.206 0.221 1.000 1.000 1.000 0.986 1.000
#> Field4 0 0.013 0.123 0.047 0.113 0.410 0.978 0.954 0.975 0.966
#> Field5 0 0.016 0.157 0.963 0.103 0.220 0.138 0.940 0.237 0.825
#> Field6 0 0.236 0.275 0.449 0.414 0.302 0.415 0.469 0.560 0.564
#> Field7 0 0.073 0.081 0.192 0.160 0.132 0.126 0.179 0.754 0.943
#> Field8 0 0.000 0.037 0.039 0.042 0.069 0.456 0.179 0.615 0.388
#> Field9 0 0.000 0.016 0.615 0.035 0.053 0.000 0.209 0.000 0.809
#> Field10 0 0.095 0.180 0.174 0.159 0.179 0.121 0.155 0.223 0.260
#> Field11 0 0.000 0.000 0.081 0.025 0.021 0.026 0.000 0.244 0.430
#> Field12 0 0.002 0.056 0.000 0.020 0.017 0.019 0.046 0.019 0.025
#> Class11 Class12 Class13
#> Field1 0.898 0.975 1
#> Field2 1.000 1.000 1
#> Field3 0.973 1.000 1
#> Field4 0.874 1.000 1
#> Field5 0.912 1.000 1
#> Field6 0.614 0.764 1
#> Field7 0.305 0.786 1
#> Field8 0.316 1.000 1
#> Field9 1.000 0.742 1
#> Field10 0.172 0.311 1
#> Field11 0.038 0.586 1
#> Field12 0.000 0.226 1
#> Class 1 Class 2 Class 3 Class 4 Class 5 Class 6
#> Test Reference Profile 0.000 3.900 6.001 12.951 8.853 11.428
#> Latent Class Ditribution 2.000 95.000 73.000 37.000 60.000 44.000
#> Class Membership Dsitribution 1.987 82.567 86.281 37.258 60.781 43.222
#> Class 7 Class 8 Class 9 Class 10 Class 11
#> Test Reference Profile 14.305 17.148 19.544 23.589 20.343
#> Latent Class Ditribution 43.000 30.000 34.000 18.000 37.000
#> Class Membership Dsitribution 43.062 30.087 34.435 20.063 34.811
#> Class 12 Class 13
#> Test Reference Profile 27.076 35
#> Latent Class Ditribution 27.000 15
#> Class Membership Dsitribution 25.445 15
#>
#> Model Fit Indices
#> Multigroup Model Saturated Moodel
#> model_log_like -5786.942 -5786.942
#> bench_log_like -5891.314 0
#> null_log_like -9862.114 -9862.114
#> model_Chi_sq -208.744 11573.88
#> null_Chi_sq 7941.601 19724.23
#> model_df 1005 16895
#> null_df 1155 17045
#> NFI 1 0.4132149
#> RFI 1 0.4080052
#> IFI 1 1
#> TLI 1 1
#> CFI 1 1
#> RMSEA 0 0
#> AIC -2218.744 -22216.12
#> CAIC -7489.132 -110816.3
#> BIC -6484.132 -93921.32
# Visualize different aspects of the model
plot(result.BINET, type = "Array") # Show bicluster structure
plot(result.BINET, type = "TRP") # Test Response Profile
plot(result.BINET, type = "LRD") # Latent Rank Distribution
plot(result.BINET,
type = "RMP", # Rank Membership Profiles
students = 1:9, nc = 3, nr = 3
)
plot(result.BINET,
type = "FRP", # Field Reference Profiles
nc = 3, nr = 2
)
plot(result.BINET,
type = "LDPSR", # Locally Dependent Passing Student Rates
nc = 3, nr = 2
)
# }