View source: R/bmult_equalities_binom.R
binom_bf_equality | R Documentation |
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.
binom_bf_equality(x, n = NULL, a, b, p = NULL)
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 |
a |
numeric. Vector with alpha parameters. Must be the same length as |
b |
numeric. Vector with beta parameters. Must be the same length as |
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. |
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)
Returns a data.frame
containing the Bayes factors LogBFe0
, BFe0
, and BF0e
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
damien2001samplingmultibridge
\insertRefgronau2017tutorialmultibridge
\insertReffruhwirth2004estimatingmultibridge
\insertRefsarafoglou2020evaluatingPreprintmultibridge
Other functions to evaluate informed hypotheses:
binom_bf_inequality()
,
binom_bf_informed()
,
mult_bf_equality()
,
mult_bf_inequality()
,
mult_bf_informed()
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)
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