# Bayesian Loglinear Regression

## Abstract

In studies with both a binary outcome (for example event yes/no) and binary predictor variable (for example treatment group 1 or 2) for traditional analysis, a 2 × 2 interaction matrix can be drawn with the predictor in two rows and the outcome in two columns. Instead of a 2 × 2 chi-square test also a Bayesian loglinear regression is possible. The mathematical model of a linear regression and loglinear regression are respectively

- 1.
Gaussian 95% confidence interval 0.148 and 2.624

- 2.
Bootstrap 95% confidence interval 0.176 and 3.043

- 3.
Bayesian 95% credible interval 0.176 and 2.528.

Obviously, the Gaussian confidence interval, the bootstrap confidence interval, and the Bayesian credible interval had very much similarly sized intervals. Overfitting was not obvious.

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