srtBayes function

Bayesian Analysis of Simple Randomised Education Trials (SRT) using Bayesian Linear Regression Model with Vague Priors.

srtBayes performs Bayesian multilevel analysis of Simple Randomised Education Trials (SRT), utilising vague priors and JAGS language to fit the model. This can also be used with schools as fixed effects.

srtBayes(
  formula,
  intervention,
  baseln,
  nsim = 2000,
  data,
  alpha = 0.05,
  digits = 3,
  threshold = 1:10/10,
  condopt,
  uncopt,
  ...
)

Arguments

• formula: The model to be analysed is of the form y~x1+x2+.... Where y is the outcome variable and Xs are the independent variables.
• intervention: A string variable specifying the "intervention variable" as appearing in the formula and the data. See example below.
• baseln: A string variable allowing the user to specify the reference category for intervention variable. When not specified, the first level will be used as a reference.
• nsim: number of MCMC iterations per chain. Default is 2000.
• data: Data frame containing the data to be analysed.
• 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 only to the conditional model specification (for example, defining priors only for the conditional model, etc.).
• uncopt: additional arguments of jags to be passed only to the unconditional model specification (for example, defining priors 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 variables specified in the model. Use summary.eefAnalytics to get Rhat and effective sample size for each estimate.
• ES: Conditional Hedges' g effect size and its 95% credible intervals.
• sigma2: Residual variance.
• ProbES: A matrix of Bayesian posterior probabilities such that the observed effect size is greater than or equal to a pre-specified threshold(s).
• Model: A model object from jags and an MCMCsummary object containing only the mean and credible intervals (CIs) as columns.
• Unconditional: A list of unconditional effect sizes, sigma2 and ProbES obtained based on residual variance from the unconditional model (model with only the intercept as a fixed effect).

Examples

if(interactive()){

  data(mstData)

  ########################################################
  ## Bayesian analysis of simple randomised trials      ##
  ########################################################

  output <- srtBayes(Posttest~ Intervention+Prettest,
                     alpha = 0.2,
                     digits=4,
                     intervention="Intervention",
                     nsim=10000,
                     data=mstData)

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

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

  ### Effect size
  ES2 <- output$Unconditional$ES
  ES2

  ## Covariance matrix
  covParm1 <- output$sigma2
  covParm1

  ## Unconditional Covariance matrix
  covParm2 <- output$Unconditional$sigma2
  covParm2

  ## Prob ES
  ProbES1 <- output$ProbES
  ProbES1

  ## Prob  based on Unconditional ES
  ProbES2 <- output$Unconditional$ProbES
  ProbES2

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

  plot(output,group=1)

}