Enhancing Bayesian Networks with Psychometric Models

I. Pérez, J. Vomlel
Proceedings of The 12th International Conference on Probabilistic Graphical Models, PMLR 246:401-414, 2024.

Abstract

Bayesian networks (BNs) are a popular framework in education and other fields. In this paper, we consider two-layer BNs, where the first layer consists of hidden binary variables that are assumed to be independent of each other, and the second layer consists of observed binary variables. The variables in the second layer depend on the variables in the first layer. The dependence is characterized by conditional probability tables, which represent Noisy-AND models. We refer to this class of models as BN2A models. We found that these models are also popular in the psychometric community, where they can be found under the name of Cognitive Diagnostic Models (CDMs), which are used to classify test takers into some latent classes according to the similarity of their responses to test questions. This paper shows the relation between some BN2A models and their corresponding CDMs. In particular, we compare the performance of these models on large-scale tests conducted in the Czech Republic in 2022. The BN2A model with general conditional probability tables produced the best absolute fit. However, when we added monotonic constraints to the General model, we obtained better predictive results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v246-perez24a, title = {Enhancing Bayesian Networks with Psychometric Models}, author = {P{\'e}rez, I. and Vomlel, J.}, booktitle = {Proceedings of The 12th International Conference on Probabilistic Graphical Models}, pages = {401--414}, year = {2024}, editor = {Kwisthout, Johan and Renooij, Silja}, volume = {246}, series = {Proceedings of Machine Learning Research}, month = {11--13 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v246/main/assets/perez24a/perez24a.pdf}, url = {https://proceedings.mlr.press/v246/perez24a.html}, abstract = {Bayesian networks (BNs) are a popular framework in education and other fields. In this paper, we consider two-layer BNs, where the first layer consists of hidden binary variables that are assumed to be independent of each other, and the second layer consists of observed binary variables. The variables in the second layer depend on the variables in the first layer. The dependence is characterized by conditional probability tables, which represent Noisy-AND models. We refer to this class of models as BN2A models. We found that these models are also popular in the psychometric community, where they can be found under the name of Cognitive Diagnostic Models (CDMs), which are used to classify test takers into some latent classes according to the similarity of their responses to test questions. This paper shows the relation between some BN2A models and their corresponding CDMs. In particular, we compare the performance of these models on large-scale tests conducted in the Czech Republic in 2022. The BN2A model with general conditional probability tables produced the best absolute fit. However, when we added monotonic constraints to the General model, we obtained better predictive results.} }
Endnote
%0 Conference Paper %T Enhancing Bayesian Networks with Psychometric Models %A I. Pérez %A J. Vomlel %B Proceedings of The 12th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2024 %E Johan Kwisthout %E Silja Renooij %F pmlr-v246-perez24a %I PMLR %P 401--414 %U https://proceedings.mlr.press/v246/perez24a.html %V 246 %X Bayesian networks (BNs) are a popular framework in education and other fields. In this paper, we consider two-layer BNs, where the first layer consists of hidden binary variables that are assumed to be independent of each other, and the second layer consists of observed binary variables. The variables in the second layer depend on the variables in the first layer. The dependence is characterized by conditional probability tables, which represent Noisy-AND models. We refer to this class of models as BN2A models. We found that these models are also popular in the psychometric community, where they can be found under the name of Cognitive Diagnostic Models (CDMs), which are used to classify test takers into some latent classes according to the similarity of their responses to test questions. This paper shows the relation between some BN2A models and their corresponding CDMs. In particular, we compare the performance of these models on large-scale tests conducted in the Czech Republic in 2022. The BN2A model with general conditional probability tables produced the best absolute fit. However, when we added monotonic constraints to the General model, we obtained better predictive results.
APA
Pérez, I. & Vomlel, J.. (2024). Enhancing Bayesian Networks with Psychometric Models. Proceedings of The 12th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 246:401-414 Available from https://proceedings.mlr.press/v246/perez24a.html.

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