inter_probs: Calculate Posterior Probability of Each Term
In conting: Bayesian Analysis of Contingency Tables

Description Usage Arguments Details Value Author(s) See Also Examples

This function computes the posterior probability of each term using the MCMC output of "bcct" and "bict" objects.

1	inter_probs(object, cutoff = 0.75, n.burnin = 0, thin = 1)

`object`	An object of class `"bcct"` or `"bict"`.
`cutoff`	An optional argument giving the cutoff posterior probability for displaying posterior summary statistics of the log-linear parameters. Only those log-linear parameters with a posterior probability greater than `cutoff` will be returned as part of the output. The default value is 0.75.
`n.burnin`	An optional argument giving the number of iterations to use as burn-in. The default value is 0.
`thin`	An optional argument giving the amount of thinning to use, i.e. the computations are based on every `thin`-th value in the MCMC sample. The default value is 1, i.e. no thinning.

This function provides a scaled back version of what inter_stats provides.

The use of thinning is recommended when the number of MCMC iterations and/or the number of log-linear parameters in the maximal model are/is large, which may cause problems with comuter memory storage.

This function returns an object of class "interprob" which is a list with the following components.

`term`	A vector of term labels.
`prob`	A vector of posterior probabilities.
`thin`	The value of the argument `thin`.

The function will only return elements in the above list if prob > cutoff.

Antony M. Overstall A.M.Overstall@soton.ac.uk.

bcct, bict, print.interprob, inter_stats.

set.seed(1)
## Set seed for reproducibility
data(AOH)
## Load AOH data

test1<-bcct(formula=y~(alc+hyp+obe)^3,data=AOH,n.sample=100,prior="UIP")
## Starting from maximal model of saturated model do 100 iterations of MCMC
## algorithm.

inter_probs(test1,n.burnin=10,cutoff=0)
## Calculate posterior probabilities having used a burn-in phase of 
## 10 iterations and a cutoff of 0 (i.e. display all terms with 
## non-zero posterior probability). Will get the following:

#Posterior probabilities of log-linear parameters:
#            post_prob
#(Intercept)    1.0000
#alc            1.0000
#hyp            1.0000
#obe            1.0000
#alc:hyp        0.1778
#alc:obe        0.0000
#hyp:obe        0.4444
#alc:hyp:obe    0.0000

## Note that the MCMC chain (after burn-in) does not visit any models 
## with the alc:obe or alc:hyp:obe interactions.