Yesterday I had an interesting discussion with a friend about how parameters are thought of in Bayesian inference. Coming from a predominantly frequentist statistical education, I had somewhere along the line picked up the notion that for Bayesians, like frequentists, the model parameters (their true values) are unknown but fixed quantities. The prior distribution then represents the prior belief about the location of this fixed value, before the data are seen. Thus the prior distribution represents our uncertainty about the location of the unknown, but fixed, parameter value.
Jonathan Bartlett
Potential outcomes, counterfactuals, causal effects, and randomization
Next week I’ll be attending the third UK Causal Inference Meeting, in Bristol. Causal inference has seen a tremendous amount of methodological development over the last 20 years, and recently a number of books have been published on the topic. In advance of attending the conference, I’ve been reading through a draft of the excellent book by Miguel Hernán (who is giving a pre-conference course) and James Robins on ‘Causal Inference’ (freely downloadable here). So far I’ve found the book highly readable and intuitive. As I’m working through it, I thought I’d write some posts giving overviews of some of the material covered, which I personally find useful to help cement the ideas in my own mind, and possibly might be of use to others.
Estimating risk ratios from observational data in Stata
When analysing binary outcomes, logistic regression is the analyst’s default approach for regression modelling. The logit link used in logistic regression is the so called canonical link function for the binomial distribution. Estimates from logistic regression are odds ratios, which measure how each predictor is estimated to increase the odds of a positive outcome, holding the other predictors constant. However, most people find risk ratios easier to interpret than odds ratios. In randomized studies it is of course easy to estimate the risk ratio comparing the two treatment (intervention) groups. With observational data, where the exposure or treatment is not randomly allocated, estimating the risk ratio for the effect of the treatment is somewhat trickier.