Measurement bias and effect restoration in causal inference

Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.

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confidence: 67%

“…While this includes an analysis of the model with the DAG above, our motivation is different from that of Kuroki and Pearl [9], and results were obtained independently. We make a thorough study of networks with up to five binary variables, one of which is unobservable and parental to all observable ones, as shown in Table 3 of the Appendix.…”

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confidence: 99%

Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables

Allman

Rhodes

Stanghellini

et al. 2015

“…These tools have recently been applied to new territories of statistical inference, meta analysis, and missing data and have led to the results summarized in Sections 5 and 6. Additional applications involving selection bias [39,40], heterogeneity [41], measurement error [42,43], and bias amplification [44] are discussed in the corresponding citations and have not been described here. The common threads underlying these developments are the two fundamental principles of causal inference described in Section 2.1.…”

Section: Discussionmentioning

confidence: 99%

The Deductive Approach to Causal Inference

Pearl

2014

This paper reviews concepts, principles, and tools that have led to a coherent mathematical theory that unifies the graphical, structural, and potential outcome approaches to causal inference. The theory provides solutions to a number of pending problems in causal analysis, including questions of confounding control, policy analysis, mediation, missing data, and the integration of data from diverse studies.

“…Moreover, if δ can be estimated from an external pilot study, the causal effect α can be identified [ See 30,31] Remarkably, identical behavior emerges in the model of Figure 13(b) in which Z is a driver of U, rather than a proxy. The same treatment can be applied to errors in measurements of X or of Y and, in each case, the formula of σ xyÁz reveals what model parameters are the ones affecting the resulting bias.…”

Section: ½27mentioning

confidence: 94%

Linear Models: A Useful “Microscope” for Causal Analysis

Pearl

2013

111

113

This note reviews basic techniques of linear path analysis and demonstrates, using simple examples, how causal phenomena of non-trivial character can be understood, exemplified and analyzed using diagrams and a few algebraic steps. The techniques allow for swift assessment of how various features of the model impact the phenomenon under investigation. This includes: Simpson's paradox, case-control bias, selection bias, missing data, collider bias, reverse regression, bias amplification, near instruments, and measurement errors.