Causal model
Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for.
They can allow some questions to be answered from existing observational data without the need for an interventional study such as a randomized controlled trial.
Some interventional studies are inappropriate for ethical or practical reasons, meaning that without a causal model, some hypotheses cannot be tested.
Causal models can help with the question of external validity (whether results from one study apply to unstudied populations).
They have also been applied to topics of interest to philosophers, such as the logic of counterfactuals, decision theory, and the analysis of actual causation.
Pearson founded Biometrika and the Biometrics Lab at University College London, which became the world leader in statistics.
[4] In 1908 Hardy and Weinberg solved the problem of trait stability that had led Galton to abandon causality, by resurrecting Mendelian inheritance.
He backed up his then-heretical claims by showing how such analyses could explain the relationship between guinea pig birth weight, in utero time and litter size.
Instead scientists relied on correlations, partly at the behest of Wright's critic (and leading statistician), Fisher.
Economists adopted the algebraic part of path analysis, calling it simultaneous equation modeling.
[4] Sixty years after his first paper, Wright published a piece that recapitulated it, following Karlin et al.'s critique, which objected that it handled only linear relationships and that robust, model-free presentations of data were more revealing.
[4]: 269 In 1983 Cartwright proposed that any factor that is "causally relevant" to an effect be conditioned on, moving beyond simple probability as the only guide.
[4]: 48 In 1986 Baron and Kenny introduced principles for detecting and evaluating mediation in a system of linear equations.
[4]: 324 That year Greenland and Robins introduced the "exchangeability" approach to handling confounding by considering a counterfactual.
[4]: 154 Pearl's causal metamodel involves a three-level abstraction he calls the ladder of causation.
The lowest level, Association (seeing/observing), entails the sensing of regularities or patterns in the input data, expressed as correlations.
The middle level, Intervention (doing), predicts the effects of deliberate actions, expressed as causal relationships.
[6] The highest level, counterfactual, involves consideration of an alternate version of a past event, or what would happen under different circumstances for the same experimental unit.
[4]: 257 Definition: Mendelian randomization uses measured variation in genes of known function to examine the causal effect of a modifiable exposure on disease in observational studies.
[4]: 158 The backdoor criterion is a sufficient but not necessary condition to find a set of variables Z to decounfound the analysis of the causal effect of X on y.
Mathematically, such queries take the form (from the example):[4]: 8 where the do operator indicates that the experiment explicitly modified the price of toothpaste.
Expressions that do not include the do operator can be estimated from observational data alone, without the need for an experimental intervention, which might be expensive, lengthy or even unethical (e.g., asking subjects to take up smoking).
In those cases, it may be possible to substitute a variable that is subject to manipulation (e.g., diet) in place of one that is not (e.g., blood cholesterol), which can then be transformed to remove the do.
Example: Counterfactuals consider possibilities that are not found in data, such as whether a nonsmoker would have developed cancer had they instead been a heavy smoker.
[4]: 270 The conventional approach to potential outcomes is data-, not model-driven, limiting its ability to untangle causal relationships.
It treats causal questions as problems of missing data and gives incorrect answers to even standard scenarios.
For linear models, the indirect effect can be computed by taking the product of all the path coefficients along a mediated pathway.
For nonlinear models, the seemingly obvious equivalence[4]: 322 does not apply because of anomalies such as threshold effects and binary values.
[4]: 352 Transport offers a solution to the question of external validity, whether a study can be applied in a different context.
[4]: 121 Bayesian networks are used commercially in applications such as wireless data error correction and DNA analysis.
