What are my options for modeling correlated observations that aren’t normal? The situation is I have observations y_{ij} where I’ve made I measurements each time observing J things. I can build a model for each J that works fine. So like I could do: y_{i1} \sim \text{log_normal}(...) \\ y_{i2} \…

My first idea would be to use J observation-level latent variables, model those as multivariate normal, and plug them into the formulae that generate the parameters for your J responses. So: L \sim N_j(0,\Sigma) Where L has i rows and j columns, and \Sigma is a J \times J correlation matrix. Addi…

A toy example in cmdstanr. I had to put a pretty strong prior on sigma1 to keep it from getting stuck at zero, since in this toy example the residuals and random effects aren’t well identified otherwise. data { int<lower=1> N; int<lower=1> J; real y1[N]; int y2[N]; } parameters { // vari…

Copulas! See https://www.github.com/spinkney/helpful_stan_functions/tree/main/examples%2Fcopula%2Fstan%2Fmulti_normal_copula_example.stan I show an example where I have 4 RV, normal, gumbel, weibull, and lognormal all correlated with each other. The R code to simulate and run everything is also in…

This is really cool! Do you have a favourite reference/resource for copulas? Seems like they’d pretty handy in a lot of situations

Here’s an excellent review paper on the topic. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1974297 The idea for Gaussian copulas is basically there’s a latent variables Z that is multivariate normal with mean 0 and and a correlation matrix. Each margin in Z is then transformed to (0,1) by …

Excellent thanks for that, will get to reading

Something that would be really useful is to add functors that take in distributions. Right now the mixed case is written for poisson and bernoulli discrete marginals. However, it would be cool to have a kernel like functor that takes in the distribution and handles everything knowing that the margin…

Thanks for the responses and example code all! I looked at copulas yesterday but wasn’t understanding how they worked. That example model makes it a lot clearer how they’re used so maybe I can dig into the Math papers now. @spinkney what’s the link to the mixed continuous/discrete code?

[image] Feature request: copulas for multivariate responses of mixed types brms @tarheel did most of the heavy lifting. I just packaged it up with a bow. Here’s the discrete-continuous multi-variate gaussian case. It uses the truncated MVN to derive the bounds from the lat…

Correlated observations that aren't normal

Modeling

spinkney April 19, 2021, 8:53pm 10

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Correlated observations that aren't normal

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