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Helper functions for simulating data

sim_helpers.Rd

The rlkj function is for generating random LKJ correlation matrices and the rgampois function generates random draws from the Stan's alternative parameterisation of the negative binomial distribution.

Usage

rgampois(n, mu, scale)

rlkj(n, eta = 1, cholesky = FALSE)

rinvgamma(n, shape, scale)

rstudentt(n, df, mu, sigma)

Arguments

n

The number of samples to create/dimension of correlation matrix

mu

The mean used within the negative binomial parameterisation and the Student T distribution

scale

The phi parameter that controls overdispersion of the negative binomial distribution (see details for description), or the scale parameter used within the inverse gamma distribution (see stats::rgamma())

eta

The shape parameter of the LKJ distribution

cholesky

Whether the correlation matrix should be returned as the Cholesky decomposition, by default FALSE

shape

The shape parameter of the inverse gamma distribution (see stats::rgamma())

df

The degrees of freedom parameter within the Student T distribution (see details)

sigma

The scale of the Student T distribution (see details)

Details

The Lewandowski-Kurowicka-Joe (LKJ) distribution is a prior distribution for correlation matrices, with the shape parameter eta. If eta is 1 then the density is uniform over the correlation matrix, ith eta > 1 then the the probability concentrates around the identity matrix while is 0 < eta < 1 the probability concentrates away from the identity matrix.

The alternative parameterisation of the negative binomial distribution is:

$$NegBinomial2(y | mu, scale) = binom(y+scale-1,y) (mu/mu+scale)^y (scale/mu + scale)^scale$$

Where the mean of the distribution is mu and the variance is \(mu + (mu^2/scale)\)

The rlkj function are sourced from Ben Goodrich's response on the Stan google mailing list. (see link https://groups.google.com/g/stan-users/c/3gDvAs_qwN8/m/Xpgi2rPlx68J)). The rgampois function is sourced from the rethinking package by Richard McElreath.

The alternative parameterisation of the Student T distribution is by mean (mu) and scale (sigma) to be consistent with the Stan parameterisation rather than the parameterisation in stats::rt().