On the correspondence from Bayesian log-linear modelling to logistic regression modelling with g-priors

g - priors for Linear Regression

where X is the design matrix, ∼ N (0, σI), and β ∼ N (β0, gσ(XTX)−1). The prior on σ is the Jeffreys prior, π(σ) ∝ 1 σ2 , and usually, β0 is taken to be 0 for simplification purposes. The appeal of the method is that there is only one free parameter g for all linear regression. Furthermore, the simplicity of the g-prior model generally leads to easily obtained analytical results. However, we st...

Log-linear modelling

Log-linear analysis has become a widely used method for the analysis of multivariate frequency tables obtained by crossclassifying sets of nominal, ordinal, or discrete interval level variables. Examples of textbooks discussing categorical data analysis by means of log-linear models are [4], [2], [14], [15], [16], and [27]. We start by introducing the standard hierarchical log-linear modelling ...

Log - Linear Modeling and Logistic Regression

Deterministic regression smoothness priors TVAR modelling

In this paper we propose a method for the estimation of time-varying autoregressive processes. The approach is essentially to regularize the heavily underdetermined unconstrained prediction equations with a smoothness priors type side constraint. The implementation of nonhomogenous smoothness properties is straightforward. The method is compared to the usual determistic regression approach (TVA...

Conditional Log-linear Structures for Log-linear Modelling

A log-linear modelling will take quite a long time if the data involves many variables and if we try to deal with all the variables at once. Fienberg and Kim (1999) investigated the relationship between log-linear model and its conditional, and we will show how this relationship is employed to make the log-linear modelling easier. The result of this article applies to all the hierarchical log-l...