srtBayes: Analysis of Simple Randomised Education Trials using Bayesian...

In eefAnalytics: Robust Analytical Methods for Evaluating Educational Interventions using Randomised Controlled Trials Designs

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

Description

srtBayes performs analysis of educational trials under the assumption of independent errors among pupils using Bayesian framework with Stan. This can also be used with schools as fixed effects.

Usage

srtBayes(
  formula,
  intervention,
  baseln,
  adaptD,
  nsim = 2000,
  condopt,
  uncopt,
  data,
  threshold = 1:10/10,
  ...
)

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.
adaptD	As this function uses rstanarm, this term provides the target average proposal acceptance probability during Stan’s adaptation period. Default is NULL.
nsim	number of MCMC iterations per chain. Default is 2000.
condopt	additional arguments of stan_glm to be passed only to the conditional model specification (for example, defining priors only for the conditional model, etc.).
uncopt	additional arguments of stan_glm to be passed only to the unconditional model specification (for example, defining priors only for the unconditional model, etc.).
data	Data frame containing the data to be analysed.
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).
...	Additional arguments of stan_glm to be passed both to the conditional and unconditional model specifications.

Value

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 stan_glm object used in ES computation, this object can be used for convergence diagnostic.

• 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,
		intervention="Intervention",nsim=2000,data=mstData)

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

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

## Covariance matrix
covParm <- output$covParm
covParm

### 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)

###########################################################################################
## Bayesian analysis of simple randomised trials using informative priors for treatment  ##
###########################################################################################

### define priors for explanatory variables

my_prior <- normal(location = c(0,6), scale = c(10,1))

### specify the priors for the conditional model only

output2 <- srtBayes(Posttest~ Prettest+Intervention,
                    intervention="Intervention",
                    nsim=2000,data=mstData,
                    condopt=list(prior=my_prior))

### Fixed effects
beta2 <- output2$Beta
beta2

### Effect size
ES2 <- output2$ES
ES2
}

eefAnalytics documentation built on May 31, 2023, 9:24 p.m.