Last week I presented visualisations of theoretical distributions that predict ice cream sales statistics based on linear and generalised linear models, which I introduced in an earlier post.
Theoretical distributionsToday I will take a closer look at the log-transformed linear model and use Stan/rstan, not only to model the sales statistics, but also to generate samples from the posterior predictive distribution. The posterior predictive distribution is what I am most interested in.

Two weeks ago I discussed various linear and generalised linear models in R using ice cream sales statistics. The data showed not surprisingly that more ice cream was sold at higher temperatures.
icecream <- data.frame(
temp=c(11.9, 14.2, 15.2, 16.4, 17.2, 18.1, 18.5, 19.4, 22.1, 22.6, 23.4, 25.1),
units=c(185L, 215L, 332L, 325L, 408L, 421L, 406L, 412L, 522L, 445L, 544L, 614L)
)I used a linear model, a log-transformed linear model, a Poisson and Binomial generalised linear model to predict sales within and outside the range of data available.

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.

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