ESTBF Subcommand (BAYES LOGLINEAR command)

ESTBF specifies the model that is assumed for the observed data, fixed marginal totals for the contingency table, prior distribution type when estimating the Bayes factor, shape parameters a_rs for Gamma distribution, the scale parameter b for Gamma distribution, and the parameters for the Dirichlet priors

[MODEL]. Specify the model that is assumed for the observed data. Valid values include MULTINOMIAL, POISSON, and NONPARAMETRIC. Multinomial distribution (MULTINOMIAL) is the default setting.

[FIX_MARGINS]. Specify if there are any fixed marginal totals for the contingency table. Valid values include TOTAL, COLUMN, and ROW. This parameter is required when MODEL is not POISSON. A fixed grand total (TOTAL) is the default setting when FIXMARGINS is specified with no keywords. When MODEL = POISSON, this parameter has no affect. When MODEL = NONPARAMETRIC, this parameter can be either COLUMN or ROW (TOTAL cannot be specified).

PRIOR_TYPE. Specify the type of the prior distribution when estimating the Bayes factor. The parameter is required. Valid values include CONJUGATE, MIXTURE_DIRICHLET, and INTRINSIC. A natural conjugate prior (CONJUGATE) is the default setting. The parameter has no affect when MODEL = POISSON.

SHAPEPARAMS = values. Specify the shape parameters a_rs for Gamma distribution. The parameter is required when PRIOR = CONJUGATE. When a single value is specified, all a_rs’s are assumed to be equal to this value. a_rs= 1 is the default setting. When more than one value is specified, the values are separated by blank spaces. Different rows must be separated by semicolon characters. The number of the numerical values that are specified in each row and each column must match the contingency table dimensions. All specified values must be > 0.

SCALEPARAM = value. Specify the scale parameter b for Gamma distribution. Only a single value > 0 is allowed. DATA is the default setting, which is equal to R × S × min(a_rs)/Y, where R and S are the number of rows and columns for the contingency table, a_rs are the values specified for SHAPEPARAMS, and Y is the total cell count.

LAMBDAS = values. Specify the parameters for the Dirichlet priors. The parameter is required when MODEL = NONPARAMETRIC. If a single value is specified, all λ_s are assumed to be equal to this value. λ_s = 1 is the default setting. If more than one value is specified, the values are separated by blank spaces. All specified values must be > 0. The number of the specified numerical values must match the row and column dimensions that are not fixed for the contingency table.