Checking the asumption of independence in binomial trials using posterior predictive checking

As put by Gelman et al. (2013, page 148): ‘because a probability model can fail to reflect the process that generated the data in any number of ways, posterior predictive p-values can be computed for a variety of test quantities in order to evaluate more than one possible model failure’.

Using R to make sense of the generalised linear model

What is the difference between the errors and the residuals ? What does it mean for a model to predict something ? What is a link function ? In the current post, we use four R functions (viz., the predict, fitted, residuals and simulate functions) to illustrate the mechanisms and assumptions of the generalised linear model.