crtFREQ function

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,
  type,
  ci,
  seed,
  data
)

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.
• 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.

Returns

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). "w" denotes number of intervention. "w=1" for two arm trial and "w=2" for 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).

Examples

if(interactive()){

data(crtData)

########################################################
## MLM analysis of cluster randomised trials + 1.96SE ##
########################################################

output1 <- crtFREQ(Posttest~ Intervention+Prettest,random="School",
                intervention="Intervention",data=crtData)

### Fixed effects
beta <- output1$Beta
beta

### Effect size
ES1 <- output1$ES
ES1

## Covariance matrix
covParm <- output1$covParm
covParm

### plot random effects for schools

plot(output1)

##################################################
## MLM analysis of cluster randomised trials    ##
## with residual bootstrap confidence intervals ##
##################################################

output2 <- crtFREQ(Posttest~ Intervention+Prettest,random="School",
                intervention="Intervention",nBoot=1000,type="residual",data=crtData)

### Effect size

ES2 <- output2$ES
ES2

### plot bootstrapped values

plot(output2, group=1)

#######################################################################
## MLM analysis of cluster randomised trials with permutation p-value##
#######################################################################

output3 <- crtFREQ(Posttest~ Intervention+Prettest,random="School",
                intervention="Intervention",nPerm=1000,data=crtData)

### Effect size

ES3 <- output3$ES
ES3

### plot permutated values

plot(output3, group=1)
}