[R] Simulation Questions

[Shane Phillips]

I have the following script for generating a dataset.  It works like a champ except for a couple of things.

1.  I need the variables "itbs" and  "map" to be negatively correlated with the binomial variable "lunch"  (around -0.21 and -0.24, respectively). The binomial variable  "lunch" needs to remain unchanged.
2.  While my generated variables do come out with the desired means and correlations, the distribution is very narrow and only represents a small portion of the possible scores.  Can I force it to encompass a wider range of scores, while maintaining my desired parameters and correlations?

Please help...

Shane

Script follows...



#Number the subjects
subject=1:1000
#Assign a treatment condition from a binomial distribution with a probability of 0.13
treat=rbinom(1*1000,1,.13)
#Assign a lunch status condition froma binomial distribution with a probability of 0.35
lunch=rbinom(1*1000,1,.35)
#Generate age in months from a random normal distribution with mean of 87 and sd of 2
age=rnorm(1000,87,2)
#invoke the MASS package
require(MASS)
#Establish the covariance matrix for MAP, ITBS and CogAT scores
sigma <- matrix(c(1, 0.84, 0.59, 0.84, 1, 0.56, 0.59, 0.56, 1), ncol = 3)
#Establish MAP as a random normal variable with mean of 200 and sd of 9
map   <- rnorm(1000, 200, 9)
#Establish ITBS as a random normal variable with mean of 175 and sd of 15
itbs <- rnorm(1000, 175, 15)
#Establish CogAT as a random normal variable with mean of 100 and sd of 16
cogat<-rnorm(1000,100,16)
#Create a dataframe of MAP, ITBS, and CogAT
data <- data.frame(map, itbs, cogat)
#Draw from the multivariate distribution defined by MAP, ITBS, and CogAT means and the covariance matrix
sim <- mvrnorm(1000, mu=mean(data), sigma, empirical=FALSE)
#Set growth at 0
growth=0
#Combine elements into a single dataset
simtest=data.frame (subject=subject, treat=treat,lunch, age=round(age,0),round(sim,0),growth)
#Set mean growth by treatment condition with treatd subjects having a mean growth of 1.5 and non-treated having a mean growth of 0.1
simtest<-transform(simtest, growth=rnorm(1000,m=ifelse(treat==0,0.1,1.5),s=1))
simtest
cor (simtest)