binom_bf_equality: Computes Bayes Factors For Equality Constrained Binomial...

In multibridge: Evaluating Multinomial Order Restrictions with Bridge Sampling

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)

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) ~ ∏ Binomial(N_k, θ_k)

Furthermore, the model assigns a beta distribution as prior to each model parameter (i.e., underlying binomial proportions). That is:

θ_k ~ Beta(α_k, β_k)

Value

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

Note

The following signs can be used to encode restricted hypotheses: "<" and ">" for inequality constraints, "=" for equality constraints, "," for free parameters, and "&" for independent hypotheses. The restricted hypothesis can either be a string or a character vector. For instance, the hypothesis c("theta1 < theta2, theta3") means

• theta1 is smaller than both theta2 and theta3

• The parameters theta2 and theta3 both have theta1 as lower bound, but are not influenced by each other.

The hypothesis c("theta1 < theta2 = theta3 & theta4 > theta5") means that

• Two independent hypotheses are stipulated: "theta1 < theta2 = theta3" and "theta4 > theta5"

• The restrictions on the parameters theta1, theta2, and theta3 do not influence the restrictions on the parameters theta4 and theta5.

• theta1 is smaller than theta2 and theta3

• theta2 and theta3 are assumed to be equal

• theta4 is larger than theta5

References

\insertRef

damien2001samplingmultibridge

\insertRef

gronau2017tutorialmultibridge

\insertRef

fruhwirth2004estimatingmultibridge

\insertRef

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)

multibridge documentation built on Nov. 1, 2022, 5:05 p.m.