Abstract
In several fields, sample data are observed at discrete instead of continuous levels. For example, in psychology an individual’s disease level is typically observed as ‘mild’, ‘moderate’ or ‘strong’, while the underlying mental disorder intensity is potentially a continuous variable. Implications of such discretization in linear regression are well-known: uncertainty increases and estimated causal relations become biased and inconsistent. For more complex models, implications of discretization are not theoretically studied. This paper considers an empirical study of complex models where causal relationships are unknown, some variables are discretized and graphical causal models are used to estimate causal relationships and effects. We study the implications of discretization on the obtained results using simulations. We show that discretization affects the correct estimation of causal relations and the uncertainty of obtained causal relations between discretized variables and non-discretized variables. In addition, we show that discretization influences estimated causal effects and we relate this influence to the properties of discretized data and sample size.
We thank David JeanJean for his preliminary research on this project. Baştürk, Hanoch and Habtewold are financially supported by the Netherlands Organization for Scientific Research (NWO) under grant number 195.187.
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Notes
- 1.
Similar conclusions with more involved derivations hold when a constant is included and \(X_1, X_2,X_3\) are matrices.
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Hanoch, O., Baştürk, N., Almeida, R.J., Habtewold, T.D. (2022). Analysis of Graphical Causal Models with Discretized Data. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1602. Springer, Cham. https://doi.org/10.1007/978-3-031-08974-9_18
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