mult_bf_equality {multibridge} | 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, \theta)
\theta ~ Dirichlet(\alpha)
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
Damien P, Walker SG (2001). “Sampling truncated normal, beta, and gamma densities.” Journal of Computational and Graphical Statistics, 10, 206–215.
Gronau QF, Sarafoglou A, Matzke D, Ly A, Boehm U, Marsman M, Leslie DS, Forster JJ, Wagenmakers E, Steingroever H (2017). “A tutorial on bridge sampling.” Journal of Mathematical Psychology, 81, 80–97.
Frühwirth-Schnatter S (2004). “Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques.” The Econometrics Journal, 7, 143–167.
Sarafoglou A, Haaf JM, Ly A, Gronau QF, Wagenmakers EJ, Marsman M (2021). “Evaluating Multinomial Order Restrictions with Bridge Sampling.” Psychological Methods.
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)