# Bayesian Loglinear Models

This feature requires SPSS® Statistics Standard Edition or the Advanced Statistics option.

The design for testing the independence of two factors requires two categorical variables for the construction of a contingency table, and makes Bayesian inference on the row-column association. You can estimate the Bayes factors by assuming different models, and characterize the desired posterior distribution by simulating the simultaneous credible interval for the interaction terms.

- From the menus choose:
- Select a single, non-scale, row variable from the Available variables list. You must select at least one non-scale variable.
- Select a single, non-scale, column variable from the Available variables list. You must select at least one non-scale variable.
- Select the desired Bayesian Analysis:
- Characterize Posterior Distribution: When selected, the Bayesian inference is made from a perspective that is approached by characterizing posterior distributions. You can investigate the marginal posterior distribution of the parameter(s) of interest by integrating out the other nuisance parameters, and further construct credible intervals to draw direct inference. This is the default setting.
- Estimate Bayes Factor: When selected, estimating Bayes factors (one of
the notable methodologies in Bayesian inference) constitutes a natural ratio to compare the marginal
likelihoods between a null and an alternative hypothesis.
Table 1. Commonly used thresholds to define significance of evidence Bayes Factor Evidence Category Bayes Factor Evidence Category Bayes Factor Evidence Category >100 Extreme Evidence for H1 1-3 Anecdotal Evidence for H1 1/30-1/10 Strong Evidence for H0 30-100 Very Strong Evidence for H1 1 No Evidence 1/100-1/30 Very Strong Evidence for H0 10-30 Strong Evidence for H1 1/3-1 Anecdotal Evidence for H0 1/100 Extreme Evidence for H0 3-10 Moderate Evidence for H1 1/10-1/3 Moderate Evidence for H0 *H0: Null Hypothesis**H1: Alternative Hypothesis* - Use Both Methods: When selected, both the Characterize Posterior Distribution and Estimate Bayes Factor inference methods as used.

Optionally, you can:

- Click Criteria to specify the credible interval percentage and numerical method settings.
- Click Bayes Factor to specify Bayes factor settings.
- Click Print specify how the contents display in the output tables.

^{1}Lee, M.D., and Wagenmakers, E.-J. 2013.

*Bayesian Modeling for Cognitive Science: A Practical Course*. Cambridge University Press.

^{2}Jeffreys, H. 1961.

*Theory of probability*. Oxford University Press.