# How to create (simulate) a clustered (multilevel) panel data set in R

How can I simulate a clustered panel data set, that includes 2 levels in R?

An example would be student test scores in a classroom.

I am searching for an efficient and easy way to construct the following equation:

$Y_{igt} = \alpha_i + \gamma_g + \tau_t + \beta_{0}\,t + \beta_{1}\,D_{gt} + \beta_2\,X_{it} + \varepsilon_{igt}$

where $Y_{igt}$ is the Outcome of individual $i$ in group $g$ at time $t$, $D_{gt}$ is a treatment dummy at the group level, $X_it$ is a random variable, $\alpha_i$, $\gamma_g$, $\tau_t$ are individual, group and time fixed effects. $\varepsilon_{igt}$ is the idiosyncratic error.

I have tried it in a quite complicated way (see below), though I am sure there must exist easier ways. Furthermore at a later stage it should be able to include additional correlated explanatory predictors with and without trends.

###overall mean
d.const<-data.frame(
const=20
)

##individuals
N<-300
x<-data.frame(
id=1:N,
alpha.i=rnorm(N,0,1)
)
d.indiv<-x

##groups
G=20
d.group<-data.frame(
gid=1:G,
D.g=rbinom(G,1,0.5),
tstart=sample(1:T,G,replace=T),
gamma.g=rnorm(G,10,5)
)
d.group

##time fixed effect
T<-5
d.tfix<-data.frame(
year=1:T,
tau.t=rnorm(T,0,5)
)
d.tfix

##panel data structure set
d.panel<-data.frame(
id=rep(1:N,each=T),
gid=sample(1:G,N,replace=T),
year=rep(1:T,N)
)
d.panel

###merged
d<-d.panel
d<-merge(d,d.indiv,by="id")
d<-merge(d,d.group,by="gid")
d<-merge(d,d.tfix,by="year")
d<-d[order(d$gid,d$id,d$year),] d #predictors d$x.it<-rnorm(nrow(d),10,20)
d$D.gi<-ifelse(d$D.g==1 & d$year==d$tstart,1,0)
#error
d$epsilon<-rnorm(nrow(d),0,1) #outcome d$y<-with(d,const+alpha.i+gamma.g+tau.t+2*year+3*alpha.i*D.gi+5*x.it+epsilon)