inter_stats: Compute Posterior Summary Statistics of the Log-Linear...
In conting: Bayesian Analysis of Contingency Tables

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

This function computes the posterior summary statistics of the log-linear parameters using the MCMC output of "bcct" and "bict" objects. The posterior summary statistics are posterior probability, posterior mean, posterior variance and lower and upper limits highest posterior density intervals (HPDIs).

1	inter_stats(object, cutoff = 0.75, n.burnin = 0, thin = 1, prob.level = 0.95)

`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.
`prob.level`	An optional argument giving the probability content of the HPDIs. The default value is 0.95.

This function provides an expanded version of what inter_probs 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 will return an object of class "interstat" which is a list with the following components:

`term`	A vector of term labels for each parameter.
`prob`	A vector of posterior probabilities for each parameter.
`post_mean`	A vector of posterior means for each parameter.
`post_var`	A vector of posterior variances for each parameter.
`lower`	A vector of lower limits for the 100*`prob.level`% HPDI for each parameter.
`upper`	A vector of upper limits for the 100*`prob.level`% HPDI for each parameter.
`prob.level`	The argument `prob.level`.

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.interstat inter_probs

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_stats(test1,n.burnin=10,cutoff=0.5)
## Calculate posterior summary statistics 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 summary statistics of log-linear parameters:
#            post_prob post_mean post_var lower_lim upper_lim
#(Intercept)         1   2.88291 0.002565   2.78778   2.97185
#alc1                1  -0.05246 0.008762  -0.27772   0.06655
#alc2                1  -0.05644 0.006407  -0.20596   0.11786
#alc3                1   0.06822 0.005950  -0.09635   0.18596
#hyp1                1  -0.53895 0.003452  -0.63301  -0.39888
#obe1                1  -0.04686 0.007661  -0.20929   0.12031
#obe2                1   0.01395 0.004024  -0.11024   0.11783
#NB: lower_lim and upper_lim refer to the lower and upper values of the
#95 % highest posterior density intervals, respectively