- Pearl J (2010) "The Foundations of Causal Inference" Sociological Methodology, 40, 75-149.
- Vignette for the R package pcalg
- The Journal of Causal Inference
- A boosting algorithm for estimating generalized propensity scores with continuous treatments: a link through The Methodology Center at Penn State that has a very rich collection resources on causality and on missing data.
Granger causality and transfer functions
- (2007) Granger Causality Between Multiple Interdependent Neurobiological Time Series: Blockwise Versus Pairwise Methods
- On prewhitening
- Course by Jamie Monogan
Prediction versus Causality
An interesting excerpt from Bickel and Li (2006) "Regularization in Statistics":
These methods, often actually have two aims,
(I) To construct a good predictor. The values of coeﬃcients in the regression are then irrelevant.
(II) To give causal interpretations of the factors and determine which variables are “important”.
Regularization is important for both aims. But, as well shall see, the appropriate magnitude of the regularization parameter may be governed by which aim is more important.
Examples of Instrumental Variables
A very interesting example applying instrumental variables to assess the causal effect of watching Fox News on the propensity to vote Republican: It is quite rare that an instrumental variable provides a credible way of extracting an estimate of a causal effect from observational data. This might be one of those rare examples:
In the Toronto Star on January 6, 2015:
- Fox News really does make people vote Republican, study says --
- An ingenious new study estimates that, if there had been no Fox News on
- cable television in 2004 and 2008, the Republican vote share would have
- been 4 percentage points lower....
The original article:
- Bias in Cable News: Real Effects and Polarization by Gregory J. Martin and Ali Yurukoglu, December 22, 2014
Methods for adjustments for confounding factors
- Analysis of Observational Health Care Data Using SAS by Douglas E. Faries, Andrew C. Leon, Josep Maria Haro and Robert L. Obenchain, SAS Institute © 2010 (452 pages) Citation ISBN:9781607642275
Examples of Simpson's Paradox
- An animation of Simpson's Paradox for three continuous variables in 3d
- Paradoxical Association: The Smoking Example
- Robinson's Paradox: Class Size and Course Evaluations at the University of Texas
The between professor relationship between average class size and evaluation is positive (professors with larger average class sizes have higher average evaluations). However, within professors, the relationship is negative: you tend to get lower evaluations from your larger classes than from your smaller classes. The between professor effect is, possibly, a selection effect -- effective professors are recruited for large classes -- and the within professor effect is, possibly, an effect of class size controlling for between-professor confounding effects.
A more thorough analysis of the data might reveal richer possibilities. For example, there are a few classes whose size makes them outliers, potentially very influential in a model that only incorporates a linear effect of class size. A model allowing for a curvilinear relationship with class size suggests that the 'compositional effect' (the between-professor relationshiop with average class size) might be negative in the lower range (10 to 50) and positive in the higher range (100 to 500).