simulating a linear random intercept model with exogeneity assumption

dear ir. Thierry Onkelinx

thank you for your advise , my program code is as follows:

## The code of the program

# yj[i] = b0j+ b1*xj[i]+ej[i]
# b0j = b0 + u0j, u0j ~ N(0,1)              random intercept
# b1                                                    fixed slope
# -- load the used package
library(lme4)

set.seed(1)

    n=200000                                ##  the total size of the
simulated population
    grp=100                                   ##  the number of groups of
the simulated population
    nindiv=2000                            ##  the number of observations
in each group
    b0=2                                       ##  intercept
    b1=0.2                                    ##  slope of X
    u = rnorm(grp,0,0.05)
    e = rnorm(nindiv*grp,1)
    M.x=rnorm(grp,3,0.05)
    sigma<-diag(grp)                   ## identity matrix
    require(MASS)
    x=mvrnorm(nindiv,M.x,sigma)
    X=as.vector(x)
    data.set = data.frame(group.id = rep(1:grp, each=nindiv),
                  u = rep(u, each=nindiv),
                  M.x = rep(M.x, each=nindiv),
                  indiv.id = 1:(nindiv*grp),
                  X = X,
                  e = e)
    data.set$Y = b0 + b1*data.set$X + b2*data.set$mean.X+ data.set$u +
data.set$e

    indiv<- data.frame(data.set$group.id,data.set$X,data.set$Y)
    names(indiv)<-c("group.id","X","Y")

my problem is i do not know how can i write the command of the
independence between X and the error terms of the two levels of the model
(e and u ) in my program code.

and i appreciate your help

thanks mervat

On Wednesday, July 12, 2017, 9:46:10 AM GMT+2, Thierry Onkelinx <
thierry.onkelinx at inbo.be> wrote:


Dear Mervat,

This the r-sig-mixed-models mailing list. Not the write-code-for-me
mailing list. Please show us what you have tried. This can easily be solved
using expand.grid() and rnorm().

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2017-07-11 13:28 GMT+02:00 mervat mohamed via R-sig-mixed-models <
r-sig-mixed-models at r-project.org>:




----- Forwarded Message -----From: mervat mohamed <
mervat_moh2006 at yahoo.com>To: mailman-owner at r-project.org <
mailman-owner at r-project.org> Sent: Sunday, July 2, 2017, 5:39:42 AM
GMT+2Subject: Fw: [R-sig-ME] Fw: simulating a linear random intercept model
with exogeneity assumption


     On Wednesday, June 21, 2017 8:27 PM, mervat mohamed via
R-sig-mixed-models <r-sig-mixed-models at r-project. org
<r-sig-mixed-models at r-project.org>> wrote:




  Show original message    On Monday, June 19, 2017 1:36 PM, mervat
mohamed via R-sig-mixed-models <r-sig-mixed-models at r-project. org
<r-sig-mixed-models at r-project.org>> wrote:


 Hi r-sig group
I want to know how to write the code of simulating a linear random
intercept model with following assumptions using R programing:
the model:
yij=b.+b1 xij + u.j + eij,  where j refer to the group number and i refer
to the observation number in the j group
model assumptions:
  1- xij ~ N (3,1.5)  2- u.j ~ N (0,1)  3 - eij ~ N (0,1)  4 - cov (xij ,
u.j)=0  5 - cov (xij , eij)=0
  6- cov (u.j , eij)= 0
thnx for help
mervat
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