ermvnorm function

Multivariate Normal Random Numbers with Exact Parameters

Random numbers of the multivariate normal distribution with EXACT mean vector, EXACT variance vector and approximate correlation matrix. This function is based on the function rmvnorm.

ermvnorm(n, mean, sd, corr = diag(rep(1, length(mean))), mnt = 10000)

Arguments

• n: a number of observations
• mean: a mean vector
• sd: a vector of standard deviations
• corr: a correlation matrix
• mnt: a maximum number of tries for the computation

Details

Unfortunately, it's very common to present only summary statistics in the literature when evaluating real data. This makes it hard to retrace or to verify the related statistical evaluation. Also, the use of such data as an example for other statistical tests is hardly possible. For that reason, ermvnorm allows to reproduce data by simulation. In contrast to rmvnorm, the function ermvnorm produces random numbers which have EXACTLY the same paramer values as specified by mean and sd. The correlation matrix corr is met only approximately.

The simple idea behind ermvnorm is to apply rmvnorm, but only for the first n-2 random numbers. The remaining 2 numbers are obtained by solving a quadratic equation to achieve the specified values for the mean vector and for the vector of standard deviations. Depending on the n-2 random numbers, the underlying quadratic equation can possibly have no solution. In this case, ermvnorm creates a new set of n-2 random numbers until a valid data set is obtained, or until the maximum number of tries mnt is reached.

Returns

A matrix of random numbers with dimension n * length(mean).

Note

This function is to be used only with caution. Usually, random numbers with exact mean and standard deviation are not intended to be used. For example, simulations concerning type I error or power of statistical tests cannot be based on ermvnorm. However, ermvnorm can strongly be recommended for meta-analyses or re-evaluations of results already published.

References

Hothorn, T. et al. (2001): On Multivariate t and Gauss Probabilities in R. R News 1, 27--29.

Author(s)

Gemechis Djira Dilba and Mario Hasler

See Also

rmvnorm, rcm

Examples

# Example 1:
# A dataset representing one endpoint.

set.seed(1234)
dataset1 <- ermvnorm(n=10,mean=100,sd=10)
dataset1
mean(dataset1)
sd(dataset1)

# Example 2:
# A dataset representing two correlated endpoints.

set.seed(5678)
dataset2 <- ermvnorm(n=10,mean=c(10,120),sd=c(1,10),corr=rbind(c(1,0.7),c(0.7,1)))
dataset2
mean(dataset2[,1]); mean(dataset2[,2])
sd(dataset2[,1]); sd(dataset2[,2])
round(cor(dataset2),3)
pairs(dataset2)

# Example 3:
# A dataset representing three uncorrelated endpoints.

set.seed(9101)
dataset3 <- ermvnorm(n=20,mean=c(1,12,150),sd=c(0.5,2,20))
dataset3
mean(dataset3[,1]); mean(dataset3[,2]); mean(dataset3[,3])
sd(dataset3[,1]); sd(dataset3[,2]); sd(dataset3[,3])
pairs(dataset3)

# Example 4:
# A dataset representing four randomly correlated endpoints.

set.seed(1121)
dataset4 <- ermvnorm(n=10,mean=c(2,10,50,120),sd=c(1,4,8,10),corr=rcm(ncol=4))
dataset4
mean(dataset4[,1]); mean(dataset4[,2]); mean(dataset4[,3]); mean(dataset4[,4])
sd(dataset4[,1]); sd(dataset4[,2]); sd(dataset4[,3]); sd(dataset4[,4])
round(cor(dataset4),3)
pairs(dataset4)