Description Usage Arguments Details Value Note Author(s) References See Also Examples
These functions implement a Bayesian analysis of incomplete contingency tables. This is accomplished using a data augmentation MCMC algorithm where the null moves are performed using the MetropolisHastings algorithm and the between models moves are performed using the reversible jump algorithm. This function can also accomodate cases where one of the sources observes a mixture of individuals from target and nontarget populations. This results in the some of the cell counts being censored.
bict
should be used initially, and bictu
should be used to do additional
MCMC iterations, if needed.
1 2 3 4 5 
formula 
An object of class 
object 
An object of class 
data 
An object of class 
n.sample 
A numeric scalar giving the number of MCMC iterations to peform. 
prior 
An optional argument giving the prior to be used in the analysis. It can be one of

cens 
A numeric vector indicating the row numbers of the data.frame in 
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 
start.y0 
An optional argument giving the starting values of the missing and censored cell counts. This should have the same length as the number of missing and censored cell counts. 
save 
An optional argument for saving the MCMC output midalgorithm. For For 
name 
An optional argument giving a prefix to 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 the orthogonal projections method for GLMs proposed by Forster et al (2012). For details on these methods applied to loglinear models through the dataaugmentation algorithm see Overstall & King (2014), and the references therein. For details on the censored approach see Overstall et al (2014).
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 "bict"
which is a list with the following components.
BETA 
An 
MODEL 
A vector of length 
SIG 
A vector of length 
Y0 
An 
missing1 
A vector of the same length as the number of missing cell counts giving the row numbers of
the 
missing2 
A vector of the same length as the number of censored cell counts giving the row numbers of
the 
missing_details 
The rows of the 
censored_details 
The rows of the 
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 
These functions are wrappers for bict.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/
Overstall, A.M., King, R., Bird, S.M., Hutchinson, S.J. & Hay, G. (2014) Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland. Statistics in Medicine, 33 (9), 1564–1579.
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  set.seed(1)
## Set seed for reproducibility.
data(spina)
## Load the spina data
test1<bict(formula=y~(S1 + S2 + S3 + eth)^2,data=spina,n.sample=50, prior="UIP")
## Let the maximal model be the model with twoway interactions. Starting from the
## posterior mode of the model with twoway interactions, do 50 iterations under the
## unit information prior.
test1<bictu(object=test1,n.sample=50)
## Do another 50 iterations
test1
#Number of cells in table = 24
#
#Maximal model =
#y ~ (S1 + S2 + S3 + eth)^2
#
#Number of loglinear parameters in maximal model = 15
#
#Number of MCMC iterations = 100
#
#Computer time for MCMC = 00:00:01
#
#Prior distribution for loglinear parameters = UIP
#
#Number of missing cells = 3
#
#Number of censored cells = 0
summary(test1)
## Summarise the result. Will get:
#Posterior summary statistics of loglinear 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 pvalue = 0.45

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