conting-package: Bayesian Analysis of Complete and Incomplete Contingency...
In conting: Bayesian Analysis of Contingency Tables
Description
Details
Author(s)
References
Examples
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.
Author(s)
Antony M. Overstall A.M.Overstall@soton.ac.uk
Maintainer: Antony M. Overstall A.M.Overstall@soton.ac.uk
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/
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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
conting documentation built on May 1, 2019, 8:47 p.m.
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Description Details Author(s) References Examples
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.
Author(s)
Antony M. Overstall A.M.Overstall@soton.ac.uk
Maintainer: Antony M. Overstall A.M.Overstall@soton.ac.uk
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 | 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
|
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