multibridge (version 1.1.0)

binom_bf_equality: Computes Bayes Factors For Equality Constrained Binomial Parameters

Description

Computes Bayes factor for equality constrained binomial parameters. Null hypothesis \(H_0\) states that binomial proportions are exactly equal or exactly equal and equal to p. Alternative hypothesis \(H_e\) states that binomial proportions are free to vary.

Usage

binom_bf_equality(x, n = NULL, a, b, p = NULL)

Value

Returns a data.frame containing the Bayes factors LogBFe0, BFe0, and BF0e

Arguments

x

a vector of counts of successes, or a two-dimensional table (or matrix) with 2 columns, giving the counts of successes and failures, respectively

n

numeric. Vector of counts of trials. Must be the same length as x. Ignored if x is a matrix or a table

a

numeric. Vector with alpha parameters. Must be the same length as x. Default sets all alpha parameters to 1

b

numeric. Vector with beta parameters. Must be the same length as x. Default sets all beta parameters to 1

p

numeric. Hypothesized probability of success. Must be greater than 0 and less than 1. Default sets all binomial proportions exactly equal without specifying a specific value.

Details

The model assumes that the data in x (i.e., \(x_1, ..., x_K\)) are the observations of \(K\) independent binomial experiments, based on \(n_1, ..., n_K\) observations. Hence, the underlying likelihood is the product of the \(k = 1, ..., K\) individual binomial functions: $$(x_1, ... x_K) ~ \prod Binomial(N_k, \theta_k)$$ Furthermore, the model assigns a beta distribution as prior to each model parameter (i.e., underlying binomial proportions). That is: $$\theta_k ~ Beta(\alpha_k, \beta_k)$$

References

damien2001samplingmultibridge

gronau2017tutorialmultibridge

fruhwirth2004estimatingmultibridge

sarafoglou2020evaluatingPreprintmultibridge

See Also

Other functions to evaluate informed hypotheses: binom_bf_inequality(), binom_bf_informed(), mult_bf_equality(), mult_bf_inequality(), mult_bf_informed()

Examples

data(journals)
x <- journals$errors
n <- journals$nr_NHST
a <- rep(1, nrow(journals))
b <- rep(1, nrow(journals))
binom_bf_equality(x=x, n=n, a=a, b=b)