pibble_fit: Interface to fit pibble models

In jsilve24/mongrel: Bayesian Multinomial Logistic Normal Regression

Description

This function is largely a more user friendly wrapper around optimPibbleCollapsed and uncollapsePibble. See details for model specification. Notation: N is number of samples, D is number of multinomial categories, Q is number of covariates, iter is the number of samples of eta (e.g., the parameter n_samples in the function optimPibbleCollapsed)

Usage

pibble(Y = NULL, X = NULL, upsilon = NULL, Theta = NULL,
  Gamma = NULL, Xi = NULL, init = NULL, pars = c("Eta", "Lambda",
  "Sigma"), ...)

## S3 method for class 'pibblefit'
refit(m, pars = c("Eta", "Lambda", "Sigma"), ...)

Arguments

Y	D x N matrix of counts (if NULL uses priors only)
X	Q x N matrix of covariates (design matrix) (if NULL uses priors only, must be present to sample Eta)
upsilon	dof for inverse wishart prior (numeric must be > D) (default: D+3)
Theta	(D-1) x Q matrix of prior mean for regression parameters (default: matrix(0, D-1, Q))
Gamma	QxQ prior covariance matrix (default: diag(Q))
Xi	(D-1)x(D-1) prior covariance matrix (default: ALR transform of diag(1)*(upsilon-D)/2 - this is essentially iid on "base scale" using Aitchison terminology)
init	(D-1) x Q initialization for Eta for optimization
pars	character vector of posterior parameters to return
...	arguments passed to optimPibbleCollapsed and uncollapsePibble
m	object of class pibblefit

Details

the full model is given by:

Y_j \sim Multinomial(Pi_j)

Pi_j = Phi^{-1}(Eta_j)

Eta \sim MN_{D-1 x N}(Lambda*X, Sigma, I_N)

Lambda \sim MN_{D-1 x Q}(Theta, Sigma, Gamma)

Sigma \sim InvWish(upsilon, Xi)

Where Gamma is a Q x Q covariance matrix, and Phi^-1 is ALRInv_D transform.

Default behavior is to use MAP estimate for uncollaping the LTP model if laplace approximation is not preformed.

Value

an object of class pibblefit

References

JD Silverman K Roche, ZC Holmes, LA David, S Mukherjee. Bayesian Multinomial Logistic Normal Models through Marginally Latent Matrix-T Processes. 2019, arXiv e-prints, arXiv:1903.11695

See Also

stray_transforms provide convenience methods for transforming the representation of pibblefit objects (e.g., conversion to proportions, alr, clr, or ilr coordinates.)

access_dims provides convenience methods for accessing dimensions of pibblefit object

Generic functions including summary, print, coef, as.list, predict, name, and sample_prior name_dims

Plotting functions provided by plot and ppc (posterior predictive checks)

Examples

sim <- pibble_sim()
fit <- pibble(sim$Y, sim$X)

jsilve24/mongrel documentation built on Jan. 27, 2022, 9:54 p.m.