mstFREQ {eefAnalytics}

Analysis of Multisite Randomised Education Trials using Multilevel Model under a Frequentist Setting.

Description

mstFREQ performs analysis of multisite randomised education trials using a multilevel model under a frequentist setting.

Usage

mstFREQ(
  formula,
  random,
  intervention,
  baseln,
  nPerm,
  data,
  type,
  ci,
  seed,
  nBoot
)

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 permutated p-value.

data

data frame containing the data to be analysed.

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.

nBoot

number of bootstraps required to generate bootstrap confidence intervals.

Value

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). "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(mstData)

###############################################
## MLM analysis of multisite trials + 1.96SE ##
###############################################

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


### 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 multisite trials             ##
## with residual bootstrap confidence intervals ##
##################################################

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

tp <- output2$Bootstrap
### Effect size

ES2 <- output2$ES
ES2

### plot bootstrapped values

plot(output2, group=1)

#######################################################################
## MLM analysis of mutltisite trials with permutation p-value##
#######################################################################

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

ES3 <- output3$ES
ES3

#### plot permutated values

plot(output3, group=1)
}