**mages' blog**, and kindly contributed to R-bloggers)

This post will present the wonderful `pairs.panels`

function of the `psych`

package [1] that I discovered recently to visualise multivariate random numbers.

Here is a little example with a Gaussian copula and normal and log-normal marginal distributions. I use `pairs.panels`

to illustrate the steps along the way.

I start with standardised multivariate normal random numbers:

`library(psych)`

library(MASS)

Sig <- matrix(c(1, -0.7, -.5,

-0.7, 1, 0.6,

-0.5, 0.6, 1),

nrow=3)

X <- mvrnorm(1000, mu=rep(0,3), Sigma = Sig,

empirical = TRUE)

pairs.panels(X)

Next, I map the random figures into the interval [0,1] using the distribution function `pnorm`

, so I end up with multivariate uniform random numbers:

`U <- pnorm(X)`

pairs.panels(U)

Finally, I transform the uniform numbers into the desired marginals:

`Z <- cbind(`

A=qlnorm(U[,1], meanlog=-2.5, sdlog=0.25),

B=qnorm(U[,2], mean=1.70, sd=0.1),

C=qnorm(U[,3], mean=0.63,sd=0.08)

)

pairs.panels(Z)

Those steps can actually be shorten with functions of the `copula`

package [2].

Unfortunately, I struggled to install the `copula`

package on my local Mac, running Mavericks. No CRAN binaries are currently available and gfortran is playing up on my system to install it from source. Thus, I quickly fired up an Ubuntu virtual machine on Amazon’s EC2 Cloud and installed R. Within 15 minutes I was back in business – that is actually pretty amazing.

`library(copula)`

myCop=normalCopula(param=c(-0.7,-.5,0.6), dim = 3, dispstr = "un")

myMvd <- mvdc(copula=myCop, margins=c("lnorm", "norm", "norm"),

paramMargins=list(list(meanlog=-2.5, sdlog=0.25),

list(mean=1.70, sd=0.1),

list(mean=0.63,sd=0.08)) )

Z2 <- rmvdc(myMvd, 1000)

colnames(Z2) <- c("A", "B", "C")

pairs.panels(Z2)

### References

[1] Revelle, W. (2014) psych: Procedures for Personality and Psychological Research, Northwestern University, Evanston, Illinois, USA, http://CRAN.R-project.org/package=psych Version = 1.4.5.

[2] Marius Hofert, Ivan Kojadinovic, Martin Maechler and Jun Yan (2014). copula: Multivariate Dependence with Copulas. http://CRAN.R-project.org/package=copula Version = 0.999-10

### Session Info Local

`R version 3.1.0 (2014-04-10)`

Platform: x86_64-apple-darwin13.1.0 (64-bit)

locale:

[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:

[1] stats graphics grDevices utils datasets methods base

other attached packages:

[1] psych_1.4.5 MASS_7.3-31

loaded via a namespace (and not attached):

[1] tools_3.1.0

### Session Info EC2

`R version 3.0.2 (2013-09-25)`

Platform: x86_64-pc-linux-gnu (64-bit)

locale:

[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C

[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8

[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8

[7] LC_PAPER=en_US.UTF-8 LC_NAME=C

[9] LC_ADDRESS=C LC_TELEPHONE=C

[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:

[1] stats graphics grDevices utils datasets methods base

other attached packages:

[1] psych_1.4.5 copula_0.999-10

loaded via a namespace (and not attached):

[1] ADGofTest_0.3 grid_3.0.2 gsl_1.9-10 lattice_0.20-24

[5] Matrix_1.1-2 mvtnorm_0.9-99992 pspline_1.0-16 stabledist_0.6-6

[9] stats4_3.0.2

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**mages' blog**.

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