Abstract
This chapter discussed tools for checking and improving the structure of Bayesian networks. We are interested in fit indices that highlight particular kinds of model misfit that we know can appear in assessment data and distort our uses of the model. The initial sections introduce some fit indices and looks at the technique of posterior predictive model checking (PPMC). Subsequent sections address graphical methods for assessing model fit, differential task functioning, and model comparison. Key ideas from the model selection literature and the pitfalls in attempting to learn "causality" from data are reviewed.
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Notes
- 1.
Yes, this is frequentist reasoning in a book about Bayesian inference. Rubin (1984) explains that this is appropriate logic for Bayesians who want to compare features of an observed data set against the corresponding features in a sample of data sets generated from a posited model.
- 2.
In IRT, the most popular method for detecting DIF is the nonparametric Mantel– Haenszel test (Holland and Thayer 1988), which conditions on observed score. See Exercise 10.9 and Sect. 13.2.2.
- 3.
The term “faithful” has a precise technical definition in the literature of causal discovery: Roughly, the d-separation relationships in the digraph correspond completely to the conditional independencies in the probability distribution.
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Almond, R., Mislevy, R., Steinberg, L., Yan, D., Williamson, D. (2015). Critiquing and Learning Model Structure. In: Bayesian Networks in Educational Assessment. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2125-6_10
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DOI: https://doi.org/10.1007/978-1-4939-2125-6_10
Publisher Name: Springer, New York, NY
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