conting (version 1.7)

conting-package: Bayesian Analysis of Complete and Incomplete Contingency Tables

Description

Performs Bayesian analysis of complete and incomplete contingency tables incorporating model uncertainty using log-linear models. These analyses can be used to identify associations/interactions between categorical factors and to estimate unknown closed populations.

Details

Package:	conting
Type:	Package
Version:	1.6.1
Date:	2018-01-17
License:	GPL-2

For the Bayesian analysis of complete contingency tables the key function is bcct which uses MCMC methods to generate a sample from the joint posterior distribution of the model parameters and model indicator. Further MCMC iterations can be performed by using bcctu.

For the Bayesian analysis of incomplete contingency tables the key function is bict which uses MCMC methods to generate a sample from the joint posterior distribution of the model parameters, model indicator and the missing, and, possibly, censored cell entries. Further MCMC iterations can be performed by using bictu.

In both cases see Overstall & King (2014), and the references therein, for details on the statistical and computational methods, as well as detailed examples.

References

Overstall, A.M. & King, R. (2014) conting: An R package for Bayesian analysis of complete and incomplete contingency tables. Journal of Statistical Software, 58 (7), 1--27. http://www.jstatsoft.org/v58/i07/

Examples

# NOT RUN {
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")
## Bayesian analysis of complete contingency table. Let the saturated model
## be the maximal model and do 100 iterations.

summary(test1)
## Summarise the result. Will get:
#Posterior summary statistics of log-linear parameters:
#            post_prob post_mean post_var lower_lim upper_lim
#(Intercept)         1  2.877924 0.002574   2.78778   2.97185
#alc1                1 -0.060274 0.008845  -0.27772   0.06655
#alc2                1 -0.049450 0.006940  -0.20157   0.11786
#alc3                1  0.073111 0.005673  -0.05929   0.20185
#hyp1                1 -0.544988 0.003485  -0.65004  -0.42620
#obe1                1 -0.054672 0.007812  -0.19623   0.12031
#obe2                1  0.007809 0.004127  -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
#
#Posterior model probabilities:
#  prob model_formula                                 
#1 0.45 ~alc + hyp + obe                              
#2 0.30 ~alc + hyp + obe + hyp:obe                    
#3 0.11 ~alc + hyp + obe + alc:hyp + hyp:obe          
#4 0.06 ~alc + hyp + obe + alc:hyp + alc:obe + hyp:obe
#5 0.05 ~alc + hyp + obe + alc:hyp                    
#
#Total number of models visited =  7
#
#Under the X2 statistic 
#
#Summary statistics for T_pred 
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#  11.79   20.16   23.98   24.70   28.77   52.40 
#
#Summary statistics for T_obs 
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#   8.18   24.22   31.51   30.12   35.63   42.49 
#
#Bayesian p-value =  0.28

set.seed(1)
## Set seed for reproducibility
data(spina)
## Load spina data
test2<-bict(formula=y~(S1+S2+S3+eth)^2,data=spina,n.sample=100,prior="UIP")
## Bayesian analysis of incomplete contingency table. Let the model with two-way 
## interactions be the maximal model and do 100 iterations.

summary(test2)
## Summarise the result. Will get:

#Posterior summary statistics of log-linear parameters:
#            post_prob post_mean post_var lower_lim upper_lim
#(Intercept)         1    1.0427 0.033967    0.6498    1.4213
#S11                 1   -0.3159 0.015785   -0.4477   -0.1203
#S21                 1    0.8030 0.018797    0.6127    1.1865
#S31                 1    0.7951 0.003890    0.6703    0.8818
#eth1                1    2.8502 0.033455    2.4075    3.1764
#eth2                1    0.1435 0.072437   -0.4084    0.5048
#S21:S31             1   -0.4725 0.002416   -0.5555   -0.3928
#NB: lower_lim and upper_lim refer to the lower and upper values of the
#95 % highest posterior density intervals, respectively
#
#Posterior model probabilities:
#  prob model_formula                                                         
#1 0.36 ~S1 + S2 + S3 + eth + S2:S3                                           
#2 0.19 ~S1 + S2 + S3 + eth + S2:S3 + S2:eth                                  
#3 0.12 ~S1 + S2 + S3 + eth + S1:eth + S2:S3                                  
#4 0.12 ~S1 + S2 + S3 + eth + S1:S2 + S1:S3 + S1:eth + S2:S3 + S2:eth + S3:eth
#5 0.10 ~S1 + S2 + S3 + eth + S1:S3 + S1:eth + S2:S3                          
#6 0.06 ~S1 + S2 + S3 + eth + S1:S3 + S1:eth + S2:S3 + S2:eth                 
#Total number of models visited =  8 
#
#Posterior mean of total population size = 726.75 
#95 % highest posterior density interval for total population size = ( 706 758 ) 
#
#Under the X2 statistic 
#
#Summary statistics for T_pred 
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#  8.329  15.190  20.040  22.550  24.180 105.200 
#
#Summary statistics for T_obs 
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
# 5.329  18.270  22.580  21.290  24.110  37.940 
#
#Bayesian p-value =  0.45 
# }