bma.cr {dga}  R Documentation 
This function averages over all decomposable graphical models for p lists.
bma.cr(
Y,
Nmissing,
delta,
graphs,
logprior = NULL,
log.prior.model.weights = NULL
)
Y 
a 
Nmissing 
A vector of all possible values for the number of individuals that appear on no list. 
delta 
The hyperparameter for the hyperDirichlet prior distribution
on list intersection probabilities. A smaller value indicates fewer prior
observations per cell. A suggested default is 
graphs 
A precomputed list of all decomposable graphical models for

logprior 
The log of the prior probability of each value in Nmissing. If left blank, this will default to the log(Nmissing). 
log.prior.model.weights 
Prior weights on the graphs. This should be a vector of length length(graphs). 
This is the main function in this package. It performs capturerecapture (or multiple systems estimation) using Bayesian model averaging as outlined in Madigan and York (1997).
Y can be created by the array() command from a vector that is ordered lexigraphically by the cell names, e.g., c(x000, x001, x010, x011, x100, x101, x110, x111).
This function returns a matrix of weights, where rows correspond to
models and columns correspond to values of Nmissing. Thus, the ij
th
entry of the matrix is the posterior probability of the i
th model and
the j
th entry of Nmissing. Row sums return posterior probabilities by
model.Column sums return posterior probabilities by value of Nmissing.
This function is pretty robust relative to the more common loglinear model approach to capturerecapture. It will not fail (or issue a numerical warning) even if there are no overlaps among the lists. The user should take care that there is adequate list overlap and that there are sufficient cases in the stratum.
James Johndrow james.johndrow@gmail.com and Kristian Lum (kl@hrdag.org)
Madigan, David, and Jeremy C. York. "Bayesian methods for estimation of the size of a closed population." Biometrika 84.1 (1997): 1931.
#### 5 list example from M & Y ##########
delta < .5
Y < c(0, 27, 37, 19, 4, 4, 1, 1, 97, 22, 37, 25, 2, 1, 3, 5,
83, 36, 34, 18, 3, 5, 0, 2, 30, 5, 23, 8, 0, 3, 0, 2)
Y < array(Y, dim = c(2, 2, 2, 2, 2))
Nmissing < 1:300
N < Nmissing + sum(Y)
data(graphs5)
weights < bma.cr(Y, Nmissing, delta, graphs5)
plotPosteriorN(weights, N)
##### 3 list example from M & Y #######
Y < c(0, 60, 49, 4, 247, 112, 142, 12)
Y < array(Y, dim = c(2, 2, 2))
delta < 1
a < 13.14
b < 55.17
Nmissing < 1:300
N < Nmissing + sum(Y)
logprior < N * log(b)  (N + a) * log(1 + b) + lgamma(N + a)  lgamma(N + 1)  lgamma(a)
data(graphs3)
weights < bma.cr(Y, Nmissing, delta, graphs3, logprior)
plotPosteriorN(weights, N)