Prior Parameters in Log-linear Model

DESCRIPTION:

Constructs a class priorLoglin object, which represents the hyperparameters of the Dirichlet distribution used as a prior distribution for the multinomial model, or the constrained Dirichlet used for the loglinear model. In priorLoglin the prior is specified by a character string. There is one hyperparameter for each cell of the contingency table formed by the levels of the factors. Often the hyperparameters are set to a common value. The value of the hyperparameters eventually used depends on the algorithm used.

USAGE:

priorLoglin(type = "data.dependent", nPriorObs) 

REQUIRED ARGUMENTS:

type
character, the type of the prior. The possible priors are:
"data.dependent"

a data dependent prior. Estimate prior hyperparameters from the data assuming that the factors are independent. Under independence, the probability of a combination of factor levels is the product of the marginal probabilities. Estimate the marginal probabilities by the observed proportions. Then, for data augmentation, each hyperparameter equals the estimated probabilities multiplied by nPriorObs (see below). For the EM algorithm, add one to each hyperparameter.

"noninformative"
a noninformative prior. For the EM algorithm, all cell hyperparameters equal one. For data augmentation (or multiple imputation), all hyperparameters equal 0.5.
"ml"
produces maximum likelihood estimates. For the EM algorithm, all cell hyperparameters equal one. For data augmentation (and multiple imputation), all hyperparameters equal zero.

OPTIONAL ARGUMENTS:

nPriorObs
the sum of the prior hyperparameters for data augmentation when a "data.dependent" prior is used. Intuitively, nPriorObs is the number of prior observations. Not used for other prior types.

VALUE:

an object of class "priorLoglin" giving a specification of the prior. For "data.dependent" priors, the routine dataDepPrior is used to compute the actual prior in the context of the data and algorithm. See .

REFERENCES:

Schafer, J. L. (1997), Analysis of Incomplete Multivariate Data, Chapman & Hall, London.

SEE ALSO:

, .

EXAMPLES:

priorLoglin(type = "data.dependent", nPriorObs = 5)