Estimate a Robust Bayesian T-Test

RoBTT is used to estimate a robust Bayesian t-test or truncated Bayesian t-test (if truncation is used). The input either requires the vector of observations for each group, x1, x2, or the summary statistics (only if the normal likelihood models are used).

RoBTT(
  x1 = NULL,
  x2 = NULL,
  mean1 = NULL,
  mean2 = NULL,
  sd1 = NULL,
  sd2 = NULL,
  N1 = NULL,
  N2 = NULL,
  truncation = NULL,
  prior_delta = prior(distribution = "cauchy", parameters = list(location = 0, scale =
    sqrt(2)/2)),
  prior_rho = prior(distribution = "beta", parameters = list(alpha = 1, beta = 1)),
  prior_nu = if (is.null(truncation)) prior(distribution = "exp", parameters = list(rate
    = 1)),
  prior_delta_null = prior(distribution = "spike", parameters = list(location = 0)),
  prior_rho_null = prior(distribution = "spike", parameters = list(location = 0.5)),
  prior_nu_null = prior_none(),
  prior_mu = NULL,
  prior_sigma2 = NULL,
  chains = 4,
  iter = 10000,
  warmup = 5000,
  thin = 1,
  parallel = FALSE,
  control = set_control(),
  convergence_checks = set_convergence_checks(),
  save = "all",
  seed = NULL,
  silent = TRUE,
  ...
)

Arguments

x1

vector of observations of the first group

x2

vector of observations of the second group

mean1

mean of the first group

mean2

mean of the first group

sd1

standard deviation of the first group

sd2

standard deviation of the first group

N1

sample size of the first group

N2

sample size of the first group

truncation

an optional list specifying truncation applied to the data. Defaults to NULL, i.e., no truncation was applied and the full likelihood is applied. Alternative the truncation can be specified via a named list with:

"x": where x is a vector of two values specifying the lower and upper truncation points common across the groups
"x1" and "x2": where x1 is a vector of two values specifying the lower and upper truncation points for the first group and x2 is a vector of two values specifying the lower and upper truncation points for the second group.
"sigma": where sigma corresponds to the number of standard deviations from the common mean where the truncation points should be set.
"sigma1" and "sigma2": where sigma1 corresponds to the number of standard deviations from the mean of the first group where the truncation points should be set and sigma2 corresponds to the number of standard deviations from the mean of the second group where the truncation points should be set.

prior_delta

prior distributions for the effect size delta parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "Cauchy", parameters = list(location = 0, scale = sqrt(2)/2)).

prior_rho

prior distributions for the precision allocation rho parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "beta", parameters = list(alpha = 1, beta = 1)).

prior_nu

prior distribution for the degrees of freedom + 2 nu parameter that will be treated as belonging to the alternative hypothesis. Defaults to prior(distribution = "exp", parameters = list(rate = 1)) if no truncation is specified. If truncation is specified, the default is NULL (i.e., use only normal likelihood).

prior_delta_null

prior distribution for the delta parameter that will be treated as belonging to the null hypothesis. Defaults to point distribution with location at 0 ( prior(distribution = "point", parameters = list(location = 0))).

prior_rho_null

prior distribution for the rho parameter that will be treated as belonging to the null hypothesis. Defaults to point distribution with location at 0.5 ( prior(distribution = "point", parameters = list(location = 0.5))).

prior_nu_null

prior distribution for the nu parameter that will be treated as belonging to the null hypothesis. Defaults to prior_none ( (i.e., normal likelihood)).

prior_mu

prior distribution for the grand mean parameter. Defaults to NULL which sets Jeffreys prior for the grand mean in case of no truncation or an unit Cauchy prior distributions for the grand mean in case of truncation (which greatly improves sampling efficiency).

prior_sigma2

prior distribution for the grand variance parameter. Defaults to NULL which sets Jeffreys prior for the variance in case of no truncation or an exponential prior distribution for the variance in case of truncation (which greatly improves sampling efficiency).

chains

a number of chains of the MCMC algorithm.

iter

a number of sampling iterations of the MCMC algorithm. Defaults to 10000, with a minimum of 4000.

warmup

a number of warmup iterations of the MCMC algorithm. Defaults to 5000.

thin

a thinning of the chains of the MCMC algorithm. Defaults to 1.

parallel

whether the individual models should be fitted in parallel. Defaults to FALSE. The implementation is not completely stable and might cause a connection error.

control

allows to pass control settings with the set_control() function. See ?set_control for options and default settings.

convergence_checks

automatic convergence checks to assess the fitted models, passed with set_convergence_checks() function. See ?set_convergence_checks for options and default settings.

save

whether all models posterior distributions should be kept after obtaining a model-averaged result. Defaults to "all" which does not remove anything. Set to "min" to significantly reduce the size of final object, however, some model diagnostics and further manipulation with the object will not be possible.

seed

a seed to be set before model fitting, marginal likelihood computation, and posterior mixing for reproducibility of results. Defaults to NULL - no seed is set.

silent

whether all print messages regarding the fitting process should be suppressed. Defaults to TRUE. Note that parallel = TRUE also suppresses all messages.

...

additional arguments.

Value

RoBTT returns an object of class

"RoBTT".

Details

See Maier et al. (2022) for more details regarding the robust Bayesian t-test methodology and the corresponding vignette (vignette("Introduction_to_RoBTT", package = "RoBTT")).

See Godmann et al. (2024) for more details regarding the truncated Bayesian t-test methodology and the corresponding vignette (vignette("Truncated_t_test", package = "RoBTT")).

Generic summary.RoBTT(), print.RoBTT(), and plot.RoBTT() functions are provided to facilitate manipulation with the ensemble.

References

Godmann HR, Bartoš F, Wagenmakers E (2024). “A truncated t-test: Excluding outliers without biasing the Bayes factor.” PsyArxiv Preprint.

Maier M, Bartoš F, Quintana DS, van den Bergh D, Marsman M, Ly A, Wagenmakers E (2022). “Model-averaged Bayesian t-tests.” doi:10.31234/osf.io/d5zwc , PsyArxiv Preprint.

Examples