maltipoo_fit: Interface to fit maltipoo models

In jsilve24/mongrel: Bayesian Multinomial Logistic Normal Regression

Description

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

Usage

maltipoo(Y = NULL, X = NULL, upsilon = NULL, Theta = NULL,
  U = NULL, Xi = NULL, init = NULL, ellinit = NULL,
  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))
U	a PQ x Q matrix of stacked variance components (each of dimension Q x 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
ellinit	P vector initialization values for ell for optimization
pars	character vector of posterior parameters to return
...	arguments passed to optimPibbleCollapsed and uncollapsePibble

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)

Gamma = e^{ell_1} U_1 + ... + e^{ell_P} U_P

Sigma \sim InvWish(upsilon, Xi)

Where A = (I_N + X * Gamma * X')^-1, K^-1 = Xi is a (D-1)x(D-1) covariance matrix, U_1 is a Q x Q covariance matrix (a variance component), e^ell_i is a scale for that variance component and Phi^-1 is ALRInv_D transform.

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

Parameters ell are treated as fixed and estimated by MAP estimation.

Value

an object of class maltipoofit

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