In mlysy/losmix: Inference for Gaussian Location-Scale Mixed-Effects Models

source("format.R")

`r section("Typical Usage")`

Here are some functions we might need:

Let's assume that dat is a data frame with columns id, y, x1, x2, ..., xp.
losmix_marg: Posterior sampling from $p(\pph \mid \YY, \XX)$.
losmix_cond: Posterior sampling from $p(\tth_i \mid \YY_i, \XX_i, \pph)$.

Then for mixed effect models, we'll need the following C++ things to be called from user's TMB code:

mnix: A class for the mNIX distribution. Will contain methods to get/set sufficient statistics, hyperparameters of the conjugate prior/posterior.
nix: Same thing, but specialized for covariate-free case.
mnix_zeta and nix_zeta: Normalizing constants for mnix and nix.

How about from the R side?

# 1.  TMB object for marginal distribution
lp_obj <- TMB::MakeADFun(data = c(list(method = "lpmarg"), lp_data),
                         parameters = lp_pars,
                         DLL = "MyModel", silent = TRUE)

# 2.  Sample from marginal distribution

# 2a. Fit normal approximation
psi_mean <- optim(par = lp_obj$par, fn = lp_obj$fn, gr = lp_obj$gr,
                  method = "BFGS")
psi_var <- losmix_mvar(obj, psi_mean, type = "numDeriv")

# 2b. Sample from it
nsamples <- 1e4
Psi <- rmvn(nsamples, psi_mean, psi_var)

# 3.  Sample from posterior random-effects distribution for a
#     particular observation.
sim_obj <- TMB::MakeADFun(data = c(list(method = "simcond"), sim_data),
                          parameters = list(Psi = Psi),
                          DLL = "MyModel", silent = TRUE)
Theta <- sim_obj$simulate()

`r subsection("Tests")`

Might also want to define some utility functions on the R side, if only for testing the TMB code more easily.

*_suff: Extract sufficient statistics from data, where * = {mnix, nix}. This is really for testing purposes, so may not want to increase size of package due to compiled C++ code...
*_post: Posterior parameters from data + prior.
*_marg: Marginal hyperparameter distribution with default prior.
*_sim: Random draws.