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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
[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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