bet {bmet}

Posterior based Bayesian multigroup equivalence testing

Description

Function provides the necessary tools to carry out Bayesian multigroup equivalence testing based on sampling of the posterior distribution. The function returns posterior samples of the average differences amongst groups, as well as posterior samples of group variances.

Usage

bet(values, groups, em, A, B = 10000, test = "mean")

Arguments

values

A vector of measurements sorted in the same order as the groups variable.

groups

A vector of groups labels corresponding to the individual measurements in the groups variable.

em

A c x 2 matrix of lower and upper equivalence margins. Here, c is the number of pairwise comparisons of interest.

A

A c x k matrix of pairwise contrasts. Here, k is the number of groups, i.e., length(unique(groups)).

B

A positive integer specifying the number of posterior samples to draw. By default B is set to 10000.

test

Setting this to anything other than "mean" tells the function to not calculate the posterior probability that the average differences fall within the equivalence margins (applicable when testing equivalence based on something other than just average differences).

Value

The function returns a list object containing the following:

• prob: The posterior probability that the average differences fall within the equivalence margins. Only returned if test == "mean".

• delta: A B x c matrix of posterior samples of the average difference for each pairwise comparison of interest.

• sigma2: A B x k matrix of posterior samples of the variance for each group.

References

Pourmohamad, T. and Lee, H.K.H. (2023). Equivalence Testing for Multiple Groups. Stat, e645.

Examples

### Multigroup equivalence test for A vs. B and A vs. C
values <- rnorm(75)
groups <- rep(LETTERS[1:3], each = 25)

mad1 <- 0.65  # The equivalence margin for A vs. B
mad2 <- 0.65  # The equivalence margin for A vs. C
mads <- c(mad1, mad2)
mads <- cbind(-mads, mads)

A <- apc(3)
A <- A[1:2, ]

out <- bet(values, groups, mads, A, B = 10000)

out$prob   # The posterior probability that the average
           # differences fall within the equivalence margins