# [R] Simulation Questions

From: Shane Phillips <SPhillips_at_Lexington1.net>
Date: Sun, 01 May 2011 00:33:41 -0400
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?

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)

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