R: Bayes factors for informative hypotheses

bain {bain} | R Documentation

## Bayes factors for informative hypotheses

### Description

`bain` is an acronym for "Bayesian informative hypotheses evaluation". It uses the Bayes factor to evaluate hypotheses specified using equality and inequality constraints among (linear combinations of) parameters in a wide range of statistical models. A tutorial by Hoijtink, Mulder, van Lissa, and Gu (2018), was published in Psychological Methods. The preprint of that tutorial is available at DOI:10.31234/osf.io/v3shc, or on the bain website at https://informative-hypotheses.sites.uu.nl/software/bain/ Users are advised to read the tutorial AND the vignette that is provided with this package before using `bain`.

### Usage

    bain(x, hypothesis, fraction = 1, ...)

### Arguments

`x` | An R object containing the outcome of a statistical analysis. Currently, the following objects can be processed: `lm()`, `t_test()`, `lavaan` objects created with the `sem()`, `cfa()`, and `growth()` functions, and named vector objects. See the vignette for elaborations.
`hypothesis` | A character string containing the informative hypotheses to evaluate. See the vignette for elaborations.
`fraction` | A number representing the fraction of information in the data used to construct the prior distribution (see the tutorial DOI: 10.1037/met0000201): The default value 1 denotes the minimal fraction, 2 denotes twice the minimal fraction, etc.
`...` | Additional arguments. See the vignette for elaborations.

### Value

The main output resulting from analyses with `bain` are Bayes factors and posterior model probabilities associated with the hypotheses that are evaluated. See the tutorial and the vignette for further elaborations.

### Author(s)

The main authors of the bain package are Xin Gu, Caspar van Lissa, Herbert Hoijtink and Joris Mulder. Contributions were made by Marlyne Bosman and Camiel van Zundert. Contact information can be found on the bain website at https://informative-hypotheses.sites.uu.nl/software/bain/

### References

See the vignette for additional references.

Hoijtink, H., Mulder, J., van Lissa, C., and Gu, X. (2018). A tutorial on testing hypotheses using the Bayes factor. Psychological Methods. DOI: 10.1037/met0000201

### Examples

    # USING BAIN WITH A LM OBJECT: Bayesian ANOVA
    # make a factor of variable site
    sesamesim$site <- as.factor(sesamesim$site)
    # execute an analysis of variance using lm() which, due to the -1, returns
    # estimates of the means per group
    anov <- lm(postnumb~site-1,sesamesim)
    # take a look at the estimated means and their names
    coef(anov)
    # set a seed value
    set.seed(100)
    # use the names to formulate and test hypotheses with bain
    results <- bain(anov, "site1=site2=site3=site4=site5; site2>site5>site1>
    site3>site4")
    #
    # USING BAIN WITH A NAMED VECTOR: Bayesian ANOVA

    # make a factor of variable site
    sesamesim$site <- as.factor(sesamesim$site)
    # execute an analysis of variance using lm() which, due to the -1, returns
    # estimates of the means per group
    anov <- lm(postnumb~site-1,sesamesim)
    # collect the estimates means in a vector
    estimate <- coef(anov)
    # give names to the estimates in anov
    names(estimate) <- c("site1", "site2", "site3","site4","site5")
    # create a vector containing the sample sizes of each group
    ngroup <- table(sesamesim$site)
    # compute the variance of the means and collect them in a list
    var <- summary(anov)$sigma**2
    cov1 <- matrix(var/ngroup[1], nrow=1, ncol=1)
    cov2 <- matrix(var/ngroup[2], nrow=1, ncol=1)
    cov3 <- matrix(var/ngroup[3], nrow=1, ncol=1)
    cov4 <- matrix(var/ngroup[4], nrow=1, ncol=1)
    cov5 <- matrix(var/ngroup[5], nrow=1, ncol=1)
    covlist <- list(cov1, cov2, cov3, cov4,cov5)
    # set a seed value
    set.seed(100)
    # test hypotheses with bain. Note that there are multiple groups
    # characterized by one mean, therefore group_parameters=1. Note that
    # there are no joint parameters, therefore, joint_parameters=0.
    results <- bain(estimate,
    "site1=site2=site3=site4=site5; site2>site5>site1>site3>site4",
    n=ngroup,Sigma=covlist,group_parameters=1,joint_parameters = 0)

    # SEE THE TUTORIAL AND VIGNETTE FOR MANY ADDITIONAL EXAMPLES

[Package bain version 0.2.6 Index]