bipf {cat}

Bayesian Iterative Proportional Fitting (BIPF)

Description

Markov-Chain Monte Carlo method for simulating posterior draws of cell probabilities under a hierarchical loglinear model

Usage

bipf(table,margins, prior=0.5, start, steps=1, showits=FALSE)

Arguments

table

contingency table (array) to be fitted by a log-linear model. All elements must be non-negative.

margins

vector describing the marginal totals to be fitted. A margin is described by the factors not summed over, and margins are separated by zeros. Thus c(1,2,0,2,3,0,1,3) would indicate fitting the (1,2), (2,3), and (1,3) margins in a three-way table, i.e., the model of no three-way association.

prior

optional array of hyperparameters specifying a Dirichlet prior distribution. The default is the Jeffreys prior (all hyperparameters = .5). If structural zeros appear in table, a prior should be supplied with hyperparameters set to NA for those cells.

start

starting value for the algorithm. The default is a uniform table. If structural zeros appear in table, start should contain zeros in those cells and ones elsewhere.

steps

number of cycles of Bayesian IPF to be performed.

showits

if TRUE, reports the iterations so the user can monitor the progress of the algorithm.

Value

array like table, but containing simulated cell probabilities that satisfy the loglinear model. If the algorithm has converged, this will be a draw from the actual posterior distribution of the parameters.

Note

The random number generator seed must be set at least once by the function rngseed before this function can be used.

The starting value must lie in the interior of the parameter space. Hence, caution should be used when using a maximum likelihood estimate (e.g., from ipf) as a starting value. Random zeros in a table may produce mle's with expected cell counts of zero, and any zero in a starting value is interpreted by bipf as a structural zero. This difficulty can be overcome by using as a starting value calculated by ipf after adding a small positive constant (e.g., 1/2) to each cell.

References

Schafer (1996) Analysis of Incomplete Multivariate Data. Chapman & Hall, Chapter 8.

See Also

ipf and rngseed.

Examples

data(HairEyeColor)                     # load data
m=c(1,2,0,1,3,0,2,3)                   # no three-way interaction
thetahat <- ipf(HairEyeColor,margins=m,
            showits=TRUE)              # fit model
thetahat <- ipf(HairEyeColor+.5,m)     # find an interior starting value 
rngseed(1234567)                       # set random generator seed
theta <- bipf(HairEyeColor,m,
              start=thetahat,prior=0.5,
              steps=50)                # take 50 steps