postprob {multinomineq}

Transform Bayes Factors to Posterior Model Probabilities

Description

Computes posterior model probabilities based on Bayes factors.

Usage

postprob(..., prior, include_unconstr = TRUE)

Arguments

...

one or more Bayes-factor objects for different models as returned by the functions bf_binom, bf_multinom and count_to_bf (i.e., a 3x4 matrix containing a row "bf0u" and a column "bf"). Note that the Bayes factors must have been computed for the same data and using the same prior (this is not checked internally).

prior

a vector of prior model probabilities (default: uniform). The order must be identical to that of the Bayes factors supplied via .... If include_unconstr=TRUE, the unconstrained model is automatically added to the list of models (at the last position).

include_unconstr

whether to include the unconstrained, encompassing model without inequality constraints (i.e., the saturated model).

Examples

# data: binomial frequencies in 4 conditions
n <- 100
k <- c(59, 54, 74)

# Hypothesis 1: p1 < p2 < p3
A1 <- matrix(c(
  1, -1, 0,
  0, 1, -1
), 2, 3, TRUE)
b1 <- c(0, 0)

# Hypothesis 2: p1 < p2 and p1 < p3
A2 <- matrix(c(
  1, -1, 0,
  1, 0, -1
), 2, 3, TRUE)
b2 <- c(0, 0)

# get posterior probability for hypothesis
bf1 <- bf_binom(k, n, A = A1, b = b1)
bf2 <- bf_binom(k, n, A = A2, b = b2)
postprob(bf1, bf2,
  prior = c(bf1 = 1 / 3, bf2 = 1 / 3, unconstr = 1 / 3)
)