View source: R/bmult_equalities_mult.R
mult_bf_equality | R Documentation |
Computes Bayes factor for equality constrained multinomial parameters
using the standard Bayesian multinomial test.
Null hypothesis H_0 states that category proportions are exactly equal to those
specified in p
.
Alternative hypothesis H_e states that category proportions are free to vary.
mult_bf_equality(x, a, p = rep(1/length(a), length(a)))
x |
numeric. Vector with data |
a |
numeric. Vector with concentration parameters of Dirichlet distribution. Must be the same length as |
p |
numeric. A vector of probabilities of the same length as |
The model assumes that data follow a multinomial distribution and assigns a Dirichlet distribution as prior for the model parameters (i.e., underlying category proportions). That is:
x ~ Multinomial(N, θ)
θ ~ Dirichlet(α)
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_equality()
,
binom_bf_inequality()
,
binom_bf_informed()
,
mult_bf_inequality()
,
mult_bf_informed()
data(lifestresses) x <- lifestresses$stress.freq a <- rep(1, nrow(lifestresses)) mult_bf_equality(x=x, a=a)
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