mstBayes function

Bayesian analysis of Multisite Randomised Education Trials (MST) using Vague Priors

mstBayes performs Bayesian multilevel analysis of multisite randomised education trials, utilising vague priors and JAGS language to fit the model. It assumes hierarchical clustering, such as students within schools, and estimates treatment effects while accounting for this structure and assuming that all random effects are independent.

mstBayes(
  formula,
  random,
  intervention,
  baseln,
  nsim = 10000,
  data,
  alpha = 0.05,
  digits = 3,
  threshold = c(0, 0.05, seq(0.1, 1, 0.1)),
  condopt,
  uncopt,
  ...
)

Arguments

• formula: The model to be analysed. It should be of the form y ~ x1 + x2 + ..., where y is the outcome variable and Xs are the predictors.
• random: A string specifying the "clustering variable" (e.g., schools or sites) as found in the dataset.
• intervention: A string specifying the "intervention variable" as it appears in the formula.
• baseln: A string specifying the reference category for the intervention variable. If not provided, the first level will be used as the reference (e.g., baseln = "0" for an intervention with levels 0 and 1).
• nsim: Number of MCMC iterations to be performed. A minimum of 10,000 is recommended to ensure convergence.
• data: A data frame containing the variables referenced in the formula, including predictors, the clustering variable, and the intervention.
• alpha: significant level, default alpha = 0.05.
• digits: number of decimal places, by default digits=3
• threshold: a scalar or vector of pre-specified threshold(s) for estimating Bayesian posterior probability such that the observed effect size is greater than or equal to the threshold(s).
• condopt: additional arguments of jags to be passed exclusively to the conditional model (e.g., defining n.chains only for the conditional model, etc.).
• uncopt: additional arguments of jags to be passed exclusively to the unconditional model (e.g., defining n.chains only for the unconditional model, etc.).
• ...: Common additional arguments of jags to be passed to both the conditional and unconditional model specifications

Returns

S3 object; a list consisting of:

• Beta: Estimates and credible intervals for the predictors specified in the model (posterior distributions).
• ES: Hedges' g effect size for the intervention(s). If bootstrapping is not used, 95% credible intervals are computed based on MCMC sampling.
• covParm: Variance components broken down into between-cluster variance (e.g., between schools), within-cluster variance (e.g., within pupils), and intra-cluster correlation (ICC).
• randomEffects: Posterior estimates of random intercepts for each cluster (e.g., schools).
• ProbES: A matrix showing the probability of observing an effect size larger than various thresholds (0, 0.05, 0.10, ...).
• Model: A model object from jags and an MCMCsummary object containing only the mean and credible intervals (CIs) as columns.
• Unconditional: A list containing the unconditional effect size and variance decomposition.

Details

The function provides posterior estimates for fixed effects (predictors) and random effects (clustering) under a Bayesian framework. Effect sizes are computed using Hedges' g, and variance components are decomposed into between-cluster and within-cluster variances.

Examples

if(interactive()){

  data(mstData)

  ########################################################
  ## Bayesian analysis of multisite randomised trials   ##
  ########################################################

  output <- mstBayes(formula = Posttest ~ Prettest + Intervention,
                     random = "School",
                     intervention = "Intervention",
                     alpha = 0.05,
                     digits = 3,
                     nsim = 10000,
                     data = mstData)
  output

  ### Fixed effects
  beta <- output$Beta
  beta

  ### Effect size
  ES1 <- output$ES
  ES1

  ## Covariance matrix
  covParm <- output$covParm
  covParm

  ## Prob ES
  ProbES <- output$ProbES
  ProbES

  ## Unconditional
  Unconditional <- output$Unconditional
  Unconditional

  ## Random Effect
  randomEffects <- output$SchEffects
  randomEffects

  ### plot random effects for schools

  plot(output)

  ### plot posterior probability of an effect size to be bigger than a pre-specified threshold

  plot(output,group=1)

}