library(eefAnalytics)
Package: eefAnalytics
Title: Robust Analytical Methods for Evaluating Educational Interventions using Randomised Controlled Trials Designs
Version: 1.1.0
Author: Germaine Uwimpuhwe, Akansha Singh, Dimitris Vallis, Steve Higgins, ZhiMin Xiao, Ewoud De Troyer and Adetayo Kasim
Maintainer: Dimitris Vallis <dimitris.vallis@durham.ac.uk>
Description: Analysing data from evaluations of educational interventions using a randomised controlled trial design. Various analytical tools to perform sensitivity analysis using different methods are supported (e.g. frequentist models with bootstrapping and permutations options, Bayesian models). The included commands can be used for simple randomised trials, cluster randomised trials and multisite trials. The methods can also be used more widely beyond education trials. This package can be used to evaluate other intervention designs using Frequentist and Bayesian multilevel models.
Imports: lme4, mvtnorm, graphics, stats, rstanarm, ggplot2, methods
License: GPL (>= 3)
Encoding: UTF-8
Roxygen: list(markdown = TRUE)
RoxygenNote: 7.2.0
Suggests: knitr, rmarkdown, testthat
VignetteBuilder: knitr
LazyData: true
URL: https://github.com/dimitris-90/eefanalytics
BugReports: https://github.com/dimitris-90/eefanalytics/issues
ComparePlot
: A plot function to compare different
eefAnalytics S3 objects from the eefAnalytics package.It generates bar plot that compares the effect size from eefAnalytics’ methods.
ComparePlot(
eefAnalyticsList,
group,Conditional = TRUE,
ES_Total = TRUE,
modelNames )
Argument | Description |
---|---|
eefAnalyticsList |
A list of eefAnalytics S3 objects from eefAnalytics package. |
group |
a string/scalar value indicating which intervention to plot. This must be one of the values of intervention variable excluding the control group. For a two arm trial, the maximum number of values to consider is 1 and 2 for three arm trial. |
Conditional |
a logical value to indicate whether to plot conditional effect size. The default is Conditional=TRUE, otherwise Conditional=FALSE should be specified for plot based on unconditional effect size. Conditional variance is total or residual variance a multilevel model with fixed effects, whilst unconditional variance is total variance or residual variance from a multilevel model with only intercept as fixed effect. |
ES_Total |
A logical value indicating whether to plot the effect size based on total variance or within school variance. The default is ES_Total=TRUE, to plot effect size using total variance. ES_Total=FALSE should be specified for effect size based on within school or residuals variance. |
modelNames |
a string factor containing the names of model to compare. See examples below. |
ComparePlot
produces a bar plot which compares the
effect sizes and the associated confidence intervals from the different
models. For a multilevel model, it shows the effect size based on
residual variance and total variance.
Returns a bar plot to compare the different methods. The returned
figure can be further modified as any ggplot
data(mstData)
###############
##### SRT #####
###############
<- srtFREQ(Posttest~ Intervention + Prettest,
outputSRT intervention = "Intervention", data = mstData)
<- srtFREQ(Posttest~ Intervention + Prettest,
outputSRTBoot intervention = "Intervention",nBoot=1000, data = mstData)
###############
##### MST #####
###############
<- mstFREQ(Posttest~ Intervention + Prettest,
outputMST random = "School", intervention = "Intervention", data = mstData)
<- mstFREQ(Posttest~ Intervention + Prettest,
outputMSTBoot random = "School", intervention = "Intervention",
nBoot = 1000, data = mstData)
##################
#### Bayesian ####
##################
<- srtBayes(Posttest~ Intervention + Prettest,
outputSRTbayes intervention = "Intervention",
nSim = 2000, data = mstData)
## comparing different results
ComparePlot(list(outputSRT,outputSRTBoot,outputMST,outputMSTBoot,outputSRTbayes),
modelNames =c("ols", "olsBoot","MLM","MLMBoot","OLSBayes"),group=1)
crtBayes
: Bayesian analysis of cluster randomised
education trials using Vague Priors.crtBayes
performs analysis of cluster randomised
education trials using a multilevel model under a Bayesian setting,
assuming vague priors.
crtBayes(
formula,
random,
intervention,
baseln,
adaptD,
condopt,
uncopt,nsim = 2000,
data,threshold = 1:10/10,
... )
Argument | Description |
---|---|
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. |
random |
a string variable specifying the “clustering variable” as contained in the data. See example below. |
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_lmer
to be passed only to the conditional model specification (for example,
defining priors only for the conditional model, etc.). |
uncopt |
additional arguments of stan_lmer
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_lmer
to be passed both to the conditional and unconditional model
specifications. |
S3 object; a list consisting of
Beta
: Estimates and credible intervals for
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.
covParm
: A vector of variance decomposition into
between cluster variance (Schools) and within cluster variance (Pupils).
It also contains intra-cluster correlation (ICC).
SchEffects
: A vector of the estimated deviation of
each school from the intercept.
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, covParm and ProbES obtained based on between and within cluster
variances from the unconditional model (model with only the intercept as
a fixed effect).
data(crtData)
########################################################
## Bayesian analysis of cluster randomised trials ##
########################################################
<- crtBayes(Posttest~ Intervention+Prettest,random="School",
output intervention="Intervention",nsim=2000,data=crtData)
### Fixed effects
<- output$Beta
beta
beta
### Effect size
<- output$ES
ES1
ES1
## Covariance matrix
<- output$covParm
covParm
covParm
### plot random effects for schools
plot(output)
### plot posterior probability of an effect size to be bigger than a pre-specified threshold
plot(output,group=1)
###########################################################################################
## Bayesian analysis of cluster randomised trials using informative priors for treatment ##
###########################################################################################
### define priors for explanatory variables
<- normal(location = c(0,6), scale = c(10,1))
my_prior
### specify the priors for the conditional model only
<- crtBayes(Posttest~ Prettest+Intervention,random="School",
output2 intervention="Intervention",nsim=2000,data=crtData,
condopt=list(prior=my_prior))
### Fixed effects
<- output2$Beta
beta2
beta2
### Effect size
<- output2$ES
ES2
ES2
crtData
: Cluster Randomised Trial Data.A cluster randomised trial dataset containing 22 schools. The data contains a random sample of test data of pupils and not actual trial data.
A data frame with 265 rows and 5 variables
Posttest: posttest scores
Prettest: prettest scores
Intervention: the indicator for intervention groups in a two arm trial, coded as 1 for intervention group and 0 for control group.
Intervention2: a simulated indicator for intervention groups in a three arm trial.
School: numeric school identifier
crtFREQ
: Analysis of Cluster Randomised Education
Trials using Multilevel Model under a Frequentist Setting.crtFREQ
performs analysis of cluster randomised
education trials using a multilevel model under a frequentist
setting.
crtFREQ(formula, random, intervention, baseln, nPerm, nBoot, seed, data)
Argument | Description |
---|---|
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. |
random |
a string variable specifying the “clustering variable” as contained in the data. See example below. |
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. |
nPerm |
number of permutations required to generate a permutated p-value. |
nBoot |
number of bootstraps required to generate bootstrap confidence intervals. |
type |
method of bootstrapping including case re-sampling at student level “case(1)”, case re-sampling at school level “case(2)”, case re-sampling at both levels “case(1,2)” and residual bootstrapping using “residual”. If not provided, default will be case re-sampling at student level. |
ci |
method for bootstrap confidence interval calculations; options are the Basic (Hall’s) confidence interval “basic” or the simple percentile confidence interval “percentile”. If not provided default will be percentile. |
seed |
seed required for bootstrapping and permutation procedure, if not provided default seed will be used. |
data |
data frame containing the data to be analysed. |
S3 object; a list consisting of
Beta
: Estimates and confidence intervals for
variables specified in the model.
ES
: Conditional Hedges’ g effect size and its 95 %
confidence intervals. If nBoot is not specified, 95% confidence
intervals are based on standard errors. If nBoot is specified, they are
non-parametric bootstrapped confidence intervals.
covParm
: A vector of variance decomposition into
between cluster variance (Schools) and within cluster variance (Pupils).
It also contains intra-cluster correlation (ICC).
SchEffects
: A vector of the estimated deviation of
each school from the intercept.
Perm
: A “nPerm x 2w” matrix containing permutated
effect sizes using residual variance and total variance. “w” denotes
number of intervention. “w=1” for two arm trial and “w=2” for three arm
trial excluding the control group. It is produced only when
nPerm
is specified.
Bootstrap
: A “nBoot x 2w” matrix containing the
bootstrapped effect sizes using residual variance (Within) and total
variance (Total), where “w” denotes number of interventions excluding
the control group. For example, “w=1” for a two arm trial and “w=2” for
a three arm trial excluding the control group. It is only produced when
nBoot
is specified.
Unconditional
: A list of unconditional effect
sizes, covParm, Perm and Bootstrap obtained based on variances from the
unconditional model (model with only the intercept as a fixed
effect).
data(crtData)
########################################################
## MLM analysis of cluster randomised trials + 1.96SE ##
########################################################
<- crtFREQ(Posttest~ Intervention+Prettest,random="School",
output1 intervention="Intervention",data=crtData)
### Fixed effects
<- output1$Beta
beta
beta
### Effect size
<- output1$ES
ES1
ES1
## Covariance matrix
<- output1$covParm
covParm
covParm
### plot random effects for schools
plot(output1)
##################################################
## MLM analysis of cluster randomised trials ##
## with residual bootstrap confidence intervals ##
##################################################
<- crtFREQ(Posttest~ Intervention+Prettest,random="School",
output2 intervention="Intervention",nBoot=1000,type="residual",data=crtData)
### Effect size
<- output2$ES
ES2
ES2
### plot bootstrapped values
plot(output2, group=1)
#######################################################################
## MLM analysis of cluster randomised trials with permutation p-value##
#######################################################################
<- crtFREQ(Posttest~ Intervention+Prettest,random="School",
output3 intervention="Intervention",nPerm=1000,data=crtData)
### Effect size
<- output3$ES
ES3
ES3
### plot permutated values
plot(output3, group=1)
eefAnalytics-defunct
: Defunct functions in
eefAnalyticsThese functions are marked as defunct and have been removed from eefAnalytics.
These functions are marked as defunct and have been removed from eefAnalytics.
These functions are marked as defunct and have been removed from eefAnalytics.
These functions are marked as defunct and have been removed from eefAnalytics.
mlmbayes(...)
caceMSTBoot(...)
caceCRTBoot(...)
caceSRTBoot(...)
mstBayes
: Bayesian analysis of Multisite Randomised
Education Trials using Vague Priors.mstBayes
performs analysis of multisite randomised
education trials using a multilevel model under a Bayesian setting
assuming vague priors.
mstBayes(
formula,
random,
intervention,
baseln,
adaptD,nsim = 2000,
condopt,
uncopt,
data,threshold = 1:10/10,
... )
Argument | Description |
---|---|
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. |
random |
a string variable specifying the “clustering variable” as contained in the data. See example below. |
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_lmer
to be passed only to the conditional model specification (for example,
defining priors only for the conditional model, etc.). |
uncopt |
additional arguments of stan_lmer
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 that the observed effect size is greater than or equal to the threshold(s). |
... |
additional arguments of stan_lmer
to be passed both to the conditional and unconditional model
specifications. |
S3 object; a list consisting of
Beta
: Estimates and credible intervals for
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.
covParm
: A list of variance decomposition into
between cluster variance-covariance matrix (schools and school by
intervention) and within cluster variance (Pupils). It also contains
intra-cluster correlation (ICC).
SchEffects
: A vector of the estimated deviation of
each school from the intercept and intervention slope.
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, covParm and ProbES obtained based on between and within cluster
variances from the unconditional model (model with only the intercept as
a fixed effect).
data(mstData)
########################################################
## Bayesian analysis of multisite randomised trials ##
########################################################
<- mstBayes(Posttest~ Intervention+Prettest,random="School",
output intervention="Intervention",nsim=2000,data=mstData)
### Fixed effects
<- output$Beta
beta
beta
### Effect size
<- output$ES
ES1
ES1
## Covariance matrix
<- output$covParm
covParm
covParm
### plot random effects for schools
plot(output)
### plot posterior probability of an effect size to be bigger than a pre-specified threshold
plot(output,group=1)
#############################################################################################
## Bayesian analysis of multisite randomised trials using informative priors for treatment ##
#############################################################################################
### define priors for explanatory variables
<- normal(location = c(0,6), scale = c(10,1))
my_prior
### specify the priors for the conditional model only
<- mstBayes(Posttest~ Prettest+Intervention,random="School",
output2 intervention="Intervention",nsim=2000,data=mstData,
condopt=list(prior=my_prior))
### Fixed effects
<- output2$Beta
beta2
beta2
### Effect size
<- output2$ES
ES2
ES2
mstData
: Multisite Trial Data.A multisite trial dataset containing 54 schools. This data contains a random sample of test data of pupils and not actual trial data.
A data frame with 210 rows and 5 variables
Posttest: posttest scores
Prettest: prettest scores
Intervention: the indicator for the intervention groups in a two arm trial, coded as 1 for intervention group and 0 for control group.
Intervention2: a simulated indicator for intervention groups in a three arm trial.
School: numeric school identifier
mstFREQ
: Analysis of Multisite Randomised Education
Trials using Multilevel Model under a Frequentist Setting.mstFREQ
performs analysis of multisite randomised
education trials using a multilevel model under a frequentist
setting.
mstFREQ(formula, random, intervention, baseln, nPerm, data, seed, nBoot)
Argument | Description |
---|---|
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. |
random |
a string variable specifying the “clustering variable” as contained in the data. See example below. |
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. |
nPerm |
number of permutations required to generate permutated p-value. |
data |
data frame containing the data to be analysed. |
seed |
seed required for bootstrapping and permutation procedure, if not provided default seed will be used. |
nBoot |
number of bootstraps required to generate bootstrap confidence intervals. |
type |
method of bootstrapping including case re-sampling at student level “case(1)”, case re-sampling at school level “case(2)”, case re-sampling at both levels “case(1,2)” and residual bootstrapping using “residual”. If not provided, default will be case re-sampling at student level. |
ci |
method for bootstrap confidence interval calculations; options are the Basic (Hall’s) confidence interval “basic” or the simple percentile confidence interval “percentile”. If not provided default will be percentile. |
S3 object; a list consisting of
Beta
: Estimates and confidence intervals for
variables specified in the model.
ES
: Conditional Hedge’s g effect size (ES) and its
95 % confidence intervals. If nBoot is not specified, 95% confidence
intervals are based on standard errors. If nBoot is specified, they are
non-parametric bootstrapped confidence intervals.
covParm
: A list of variance decomposition into
between cluster variance-covariance matrix (schools and school by
intervention) and within cluster variance (Pupils). It also contains
intra-cluster correlation (ICC).
SchEffects
: A vector of the estimated deviation of
each school from the intercept and intervention slope.
Perm
: A “nPerm x 2w” matrix containing permutated
effect sizes using residual variance and total variance. “w” denotes
number of intervention. “w=1” for two arm trial and “w=2” for three arm
trial excluding the control group. It is produced only when
nPerm
is specified.
Bootstrap
: A “nBoot x 2w” matrix containing the
bootstrapped effect sizes using residual variance (Within) and total
variance (Total), where “w” denotes number of interventions excluding
the control group. For example, “w=1” for a two arm trial and “w=2” for
a three arm trial excluding the control group. It is only produced when
nBoot
is specified.
Unconditional
: A list of unconditional effect
sizes, covParm, Perm and Bootstrap obtained based on variances from the
unconditional model (model with only the intercept as a fixed
effect).
data(mstData)
###############################################
## MLM analysis of multisite trials + 1.96SE ##
###############################################
<- mstFREQ(Posttest~ Intervention+Prettest,random="School",
output1 intervention="Intervention",data=mstData)
### Fixed effects
<- output1$Beta
beta
beta
### Effect size
<- output1$ES
ES1
ES1
## Covariance matrix
<- output1$covParm
covParm
covParm
### plot random effects for schools
plot(output1)
###############################################
## MLM analysis of multisite trials ##
## with bootstrap confidence intervals ##
###############################################
<- mstFREQ(Posttest~ Intervention+Prettest,random="School",
output2 intervention="Intervention",nBoot=1000,data=mstData)
<- output2$Bootstrap
tp ### Effect size
<- output2$ES
ES2
ES2
### plot bootstrapped values
plot(output2, group=1)
################################################################
## MLM analysis of mutltisite trials with permutation p-value ##
################################################################
<- mstFREQ(Posttest~ Intervention+Prettest,random="School",
output3 intervention="Intervention",nPerm=1000,data=mstData)
<- output3$ES
ES3
ES3
#### plot permutated values
plot(output3, group=1)
plot.eefAnalytics
: A plot method for an eefAnalytics S3
object obtained from the eefAnalytics package.Plots different figures based on output from eefAnalytics package.
list(list("plot"), list("eefAnalytics"))(x, group, Conditional = TRUE, ES_Total = TRUE, slope = FALSE, ...)
Argument | Description |
---|---|
x |
an output object from the eefAnalytics package. |
group |
a string/scalar value indicating which intervention to plot. This must be one of the values of intervention variable excluding the control group. For a two arm trial, the maximum number of values to consider is 1 and 2 for three arm trial. |
Conditional |
a logical value to indicate whether to plot the conditional effect size. The default is Conditional=TRUE, otherwise Conditional=FALSE should be specified for plot based on the unconditional effect size. Conditional variance is total or residual variance from a multilevel model with fixed effects, whilst unconditional variance is total variance or residual variance from a multilevel model with only intercept as fixed effect. |
ES_Total |
A logical value indicating whether to plot the effect size based on total variance or within school variance. The default is ES_Total=TRUE, to plot the effect size using total variance. ES_Total=FALSE should be specified for the effect size based on within school or residuals variance. |
slope |
A logical value indicating whether to return the plot of random intercept (default is slope=FALSE). return other school-by-intervention interaction random slope (s) is slope=TRUE. This argument is suitable only for mstBayes and mstFREQ functions. |
... |
arguments passed to plot.default |
Plot produces a graphical visualisation depending on which model is fitted:
For srtFREQ()
, plot can only be used when
nBoot
or nPerm
is specified to visualise the
distribution of bootstrapped or permutated values.
For crtFREQ()
or mstFREQ()
, plot shows
the distribution of random intercepts when group=NULL
. It
produces histogram of permutated or bootstrapped values when
group
is specified and either nBoot
or
nPerm
is also specified.
Returns relevant plots for each model.
#### read data
data(mstData)
data(crtData)
###############
##### SRT #####
###############
##### Bootstrapped
<- srtFREQ(Posttest~ Intervention + Prettest,
outputSRTBoot intervention = "Intervention",nBoot=1000, data = mstData)
plot(outputSRTBoot,group=1)
##### Permutation
<- srtFREQ(Posttest~ Intervention + Prettest,
outputSRTPerm intervention = "Intervention",nPerm=1000, data = mstData)
plot(outputSRTPerm,group=1)
###############
##### MST #####
###############
#### Random intercepts
<- mstFREQ(Posttest~ Intervention + Prettest,
outputMST random = "School", intervention = "Intervention", data = mstData)
plot(outputMST)
#### Bootstrapped
<- mstFREQ(Posttest~ Intervention + Prettest,
outputMSTBoot random = "School", intervention = "Intervention",
nBoot = 1000, data = mstData)
plot(outputMSTBoot)
plot(outputMSTBoot,group=1)
#### Permutation
<- mstFREQ(Posttest~ Intervention + Prettest,
outputMSTPerm random = "School", intervention = "Intervention",
nPerm = 1000, data = mstData)
plot(outputMSTPerm)
plot(outputMSTPerm,group=1)
###############
##### CRT #####
###############
#### Random intercepts
<- crtFREQ(Posttest~ Intervention + Prettest, random = "School",
outputCRT intervention = "Intervention", data = crtData)
plot(outputCRT)
## Bootstrapped
<- crtFREQ(Posttest~ Intervention + Prettest, random = "School",
outputCRTBoot intervention = "Intervention", nBoot = 1000, data = crtData)
plot(outputCRTBoot,group=1)
##Permutation
<- crtFREQ(Posttest~ Intervention + Prettest, random = "School",
outputCRTPerm intervention = "Intervention", nPerm = 1000, data = crtData)
plot(outputCRTPerm,group=1)
print.eefAnalytics
: Print for a fitted model
represented by an eefAnalytics
object.Print for a fitted model represented by an eefAnalytics
object.
list(list("print"), list("eefAnalytics"))(x, ...)
Argument | Description |
---|---|
x |
Object of class eefAnalytics |
... |
Additional arguments of print |
Print conditional and unconditional effect sizes.
srtBayes
: Analysis of Simple Randomised Education
Trials using Bayesian Linear Regression Model with Vague Priors.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.
srtBayes(
formula,
intervention,
baseln,
adaptD,nsim = 2000,
condopt,
uncopt,
data,threshold = 1:10/10,
... )
Argument | Description |
---|---|
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 |
A number of MCMC iterations per chain. Default is 2000. |
condopt |
additional arguments of stan_lmer
to be passed only to the conditional model specification (for example,
defining priors only for the conditional model, etc.). |
uncopt |
additional arguments of stan_lmer
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_lmer
to be passed both to the conditional and unconditional model
specifications. |
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).
data(mstData)
########################################################
## Bayesian analysis of simple randomised trials ##
########################################################
<- srtBayes(Posttest~ Intervention+Prettest,
output intervention="Intervention",nsim=2000,data=mstData)
### Fixed effects
<- output$Beta
beta
beta
### Effect size
<- output$ES
ES1
ES1
## Covariance matrix
<- output$covParm
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
<- normal(location = c(0,6), scale = c(10,1))
my_prior
### specify the priors for the conditional model only
<- srtBayes(Posttest~ Prettest+Intervention,
output2 intervention="Intervention",
nsim=2000,data=mstData,
condopt=list(prior=my_prior))
### Fixed effects
<- output2$Beta
beta2
beta2
### Effect size
<- output2$ES
ES2 ES2
srtFREQ
: Analysis of Simple Randomised Education Trial
using Linear Regression Model.srtFREQ
performs analysis of educational trials under
the assumption of independent errors among pupils. This can also be used
with schools as fixed effects.
srtFREQ(formula, intervention, baseln, nBoot, nPerm, seed, data)
Argument | Description |
---|---|
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. |
nBoot |
number of bootstraps required to generate bootstrap confidence intervals. |
nPerm |
number of permutations required to generate permutated p-value. |
seed |
seed required for bootstrapping and permutation procedure, if not provided default seed will be used. |
ci |
method for bootstrap confidence interval calculations; options are the Basic (Hall’s) confidence interval “basic” or the simple percentile confidence interval “percentile”. If not provided default will be percentile. |
data |
data frame containing the data to be analysed. |
S3 object; a list consisting of
Beta
: Estimates and confidence intervals for the
variables specified in the model.
ES
: Conditional Hedges’g effect size and its 95 %
confidence intervals. If nBoot is not specified, 95% confidence
intervals are based on standard errors. If nBoot is specified, they are
non-parametric bootstrapped confidence intervals.
sigma2
: Residual variance.
Perm
: A “nPerm x w” matrix containing permutated
effect sizes using residual variance. “w” denotes number of
intervention. “w=1” for two arm trial and “w=2” for three arm trial
excluding the control group. It is produced only if nPerm
is specified.
Bootstrap
: A “nBoot x w” matrix containing the
bootstrapped effect sizes using residual variance. “w” denotes number of
intervention. “w=1” for two arm trial and “w=2” for three arm trial
excluding the control group. It is produced only if nBoot
is specified.
Unconditional
: A list of unconditional effect size,
sigma2, Perm and Bootstrap obtained based on variances from the
unconditional model (model with only intercept as fixed
effect).
data(mstData)
###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
###################################################################
<- srtFREQ(Posttest~ Intervention+Prettest,
output1 intervention="Intervention",data=mstData )
<- output1$ES
ES1
ES1
###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
## with Permutation p-value ##
###################################################################
<- srtFREQ(Posttest~ Intervention+Prettest,
output2 intervention="Intervention",nPerm=1000,data=mstData )
<- output2$ES
ES2
ES2
#### plot permutated values
plot(output2, group=1)
###################################################################
## Analysis of simple randomised trials using Hedges Effect Size ##
## with non-parametric Basic bootstrap confidence intervals ##
###################################################################
<- srtFREQ(Posttest~ Intervention+Prettest,
output3 intervention="Intervention",nBoot=1000,ci="basic",data=mstData)
<- output3$ES
ES3
ES3
### plot bootstrapped values
plot(output3, group=1)
####################################################################
## Analysis of simple randomised trials using Hedges' effect size ##
## with schools as fixed effects ##
####################################################################
<- srtFREQ(Posttest~ Intervention+Prettest+as.factor(School),
output4 intervention="Intervention",data=mstData )
<- output4$ES
ES4
ES4
####################################################################
## Analysis of simple randomised trials using Hedges' effect size ##
## with schools as fixed effects and with permutation p-value ##
####################################################################
<- srtFREQ(Posttest~ Intervention+Prettest+as.factor(School),
output5 intervention="Intervention",nPerm=1000,data=mstData )
<- output5$ES
ES5
ES5
#### plot permutated values
plot(output5, group=1)
####################################################################
## Analysis of simple randomised trials using Hedges' effect size ##
## with schools as fixed effects and with permutation p-value ##
####################################################################
<- srtFREQ(Posttest~ Intervention+Prettest+as.factor(School),
output6 intervention="Intervention",nBoot=1000,data=mstData)
<- output6$ES
ES6
ES6
### plot bootstrapped values
plot(output6, group=1)
summary.eefAnalytics
: Summary for a fitted model
represented by an eefAnalytics
object.Summary for a fitted model represented by an
eefAnalytics
object.
list(list("summary"), list("eefAnalytics"))(object, ...)
Argument | Description |
---|---|
object |
Object of class eefAnalytics |
... |
Additional arguments of summary |
Returns relevant summary including Rhat and effective sample sizes.