Abstract
This chapter introduces the bicluster network model (BINET; Shojima, 2019), a combination of the Bayesian network model (BNM; Chap. 8, p. 349) and biclustering (Chap. 7, p. 259). This model also closely resembles local dependence biclustering (LDB; Chap. 10, p. 491). It is recommended that readers first read Chaps. 8 and 10 before going any further in this chapter.
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Notes
- 1.
For instance, Class 13 is characterized as 111111111111 (12 1s) because the class masters all the 12 fields.
- 2.
An empty graph is also a DAG.
- 3.
For Plans (A), (B), and (C), refer to Sect. 10.1.3 (p. 497).
- 4.
The PSR is essentially the same as the CRR, but the former is an expression that emphasizes the viewpoint from an item more.
- 5.
The subscript DC means “(local) dependence among classes.”
- 6.
In fact, \(\tilde{\boldsymbol{M}}_F\) was not used directly because the information contained was included in the parameter selection array (\(\boldsymbol{\Gamma }\)).
- 7.
As mentioned above, the LCEs estimated by the IRM and BINET were the same, except for five students. This array plot is, thus, almost identical to that sorted by the IRM shown in Fig. 11.4 (right) (p. 532).
- 8.
Note that the trend is not very firm because the classes are nominal clusters. If the clusters are ordinal (i.e., latent ranks), these marginal FRPs will be smoother. When analyzing with the ranks, it is recommended to set a smaller number of ranks because the field PSRs of each rank become less unique and similar to those of the adjacent ranks. This is because the ranks are created by making neighboring clusters similar. Accordingly, when the number of ranks is small, the PSRs of each individual rank become more unique, and it is then easy for any rank pair to find a field(s) for which PSRs differ remarkably.
- 9.
The maximum possible number of NRS patterns is 36 (0–35), but there were no students whose NRS was 32 or 33.
- 10.
Let \(0\times \ln 0=0\times (-\infty )=0\).
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Shojima, K. (2022). Bicluster Network Model. In: Test Data Engineering . Behaviormetrics: Quantitative Approaches to Human Behavior, vol 13. Springer, Singapore. https://doi.org/10.1007/978-981-16-9986-3_11
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