Description Usage Arguments Details Value Note Author(s) References See Also Examples
These functions implement a Bayesian analysis of complete contingency tables. This is accomplished using an MCMC algorithm where the null moves are performed using a MetropolisHastings algorithm and the between models moves are performed using a reversible jump algorithm.
bcct
should be used initially, and bcctu
should be used to do additional
MCMC iterations, if required.
bcctsubset
and bcctsubsetu
operate on a subset of models.
1 2 3 4 5 6 7 8 9 10 11  bcct(formula, data, n.sample, prior = "SBH", start.formula = NULL,
start.beta = NULL, start.sig = NULL, save = 0, name = NULL, null.move.prob=0.5,
a = 0.001, b = 0.001, progress = FALSE)
bcctu(object, n.sample, save = NULL, name = NULL, progress = FALSE)
bcctsubset(subsetformula, data, n.sample, prior = "SBH", start.formula = NULL,
start.beta = NULL, start.sig = NULL, save = 0, name = NULL, null.move.prob=0.5,
a = 0.001, b = 0.001, progress = FALSE)
bcctsubsetu(object, n.sample, save = NULL, name = NULL, progress = FALSE)

formula 
An object of class 
subsetformula 
A list with elements of class 
object 
An object of class 
data 
An object of class 
n.sample 
A numeric scalar giving the number of (additional, in the case of 
prior 
An optional argument giving the prior to be used in the analysis. It can be one of

start.formula 
An optional argument giving an object of class 
start.beta 
An optional argument giving the starting values of the loglinear parameters for the MCMC algorithm.
It should be a vector of the same length as the number of loglinear parameters in the starting model
implied by the argument 
start.sig 
An optional argument giving the starting value of sigma^2 (under the SabanesBove & Held prior) for the
MCMC algorithm when the argument of prior is 
save 
An optional argument for saving the MCMC output midalgorithm. For For 
name 
An optional argument giving a prefix to the file name of the external files saved if the argument 
null.move.prob 
An optional scalar argument giving the probability of performing a null move in the reversible jump algorithm, i.e. proposing a move to the current model. The default value is 0.5. 
a 
The shape hyperparameter of the SabanesBove & Held prior, see Overstall & King (2014). The default value
is 0.001. A value of 
b 
The scale hyperparameter of the SabanesBove & Held prior, see Overstall & King (2014). The default value
is 0.001. A value of 
progress 
Logical argument. If 
For identifiability, the parameters are constrained. The contingpackage
uses sumtozero constraints.
See Overstall & King (2014), and the references therein, for more details.
The MetropolisHastings algorithm employed is the iterated weighted least squares method for generalised linear models (GLMs) proposed by Gamerman (1997). The reversible jump algorithm employed is that orthogonal projections method for GLMs proposed by Forster et al (2012). For details on these methods applied to loglinear models see Overstall & King (2014), and the references therein.
For details on the unit information and SabanesBove & Held priors for generalised linear models see Ntzoufras et al (2003) and SabanesBove & Held (2011), respectively. See Overstall & King (2014), and the references therein, for their application to loglinear models and contingency tables.
The functions will return an object of class "bcct"
which is a list with the following components:
BETA 
An 
MODEL 
A vector of length 
SIG 
A vector of length 
rj_acc 
A binary vector of the same length as the number of reversible jump moves attempted. A 0 indicates that the proposal was rejected, and a 1 that the proposal was accepted. 
mh_acc 
A binary vector of the same length as the number of MetropolisHastings moves attempted. A 0 indicates that the proposal was rejected, and a 1 that the proposal was accepted. 
priornum 
A numeric scalar indicating which prior was used: 1 = 
maximal.mod 
An object of class 
IP 
A p by p matrix giving the inverse of the prior scale matrix for the maximal model. 
eta.hat 
A vector of length n (number of cells) giving the posterior mode of the linear predictor under the maximal model. 
save 
The argument 
name 
The argument 
null.move.prob 
The argument 
time 
The total computer time (in seconds) used for the MCMC computations. 
a 
The argument 
b 
The argument 
subset.index 
Model indicators (in hexidecimal format) of the subset of models. 
These functions are wrappers for bcct.fit
.
In Version 1.0 of contingpackage
, note that the default value for prior
was "UIP"
. From
Version 1.1 onwards, the default value is "SBH"
.
Antony M. Overstall [email protected].
SabanesBove, D. & Held, L. (2011) Hyperg priors for generalized linear models. Bayesian Analysis, 6 (3), 387–410.
Forster, J.J., Gill, R.C. & Overstall, A.M. (2012) Reversible jump methods for generalised linear models and generalised linear mixed models. Statistics and Computing, 22 (1), 107–120.
Gamerman, D. (1997) Sampling from the posterior distribution in generalised linear mixed models. Statistics and Computing, 7 (1), 57–68.
Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models(Comment on Article by Browne and Draper). Bayesian Analysis, 1 (3), 515–534.
Nztoufras, I., Dellaportas, P. & Forster, J.J. (2003) Bayesian variable and link determination for generalised linear models. Journal of Statistical Planning and Inference, 111 (1), 165–180.
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/
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  set.seed(1)
## Set seed for reproducibility.
data(AOH)
## Load the AOH data
test1<bcct(formula=y~(alc+hyp+obe)^3,data=AOH,n.sample=50,prior="UIP")
## Let the maximal model be the saturated model. Starting from the
## posterior mode of the maximal model do 50 iterations under the unit
## information prior.
test1<bcctu(object=test1,n.sample=50)
## Do another 50 iterations
test1
## Printing out a bcct object produces this simple summary
#Number of cells in table = 24
#
#Maximal model =
#y ~ (alc + hyp + obe)^3
#
#Number of loglinear parameters in maximal model = 24
#
#Number of MCMC iterations = 100
#
#Computer time for MCMC = 00:00:01
#
#Prior distribution for loglinear parameters = UIP
summary(test1)
## Printing out a summary produces a bit more:
#Posterior summary statistics of loglinear 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 pvalue = 0.28
## For more examples see Overstall & King (2014).

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