Interface to fit orthus models

This function is largely a more user friendly wrapper around optimPibbleCollapsed and uncollapsePibble for fitting orthus models. See details for model specification. Notation: N is number of samples, P is the number of dimensions of observations in the second dataset, 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)

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

Arguments

Y

D x N matrix of counts (if NULL uses priors only)

Z

P x N matrix of counts (if NULL uses priors only - must be present/absent if Y is present/absent)

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+P) x Q matrix of prior mean for regression parameters (default: matrix(0, D-1+P, Q))

Gamma

QxQ prior covariance matrix (default: diag(Q))

Xi

(D-1+P)x(D-1+P) 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

Value

an object of class pibblefit

Details

the full model is given by: $$Y_j \sim Multinomial(Pi_j)$$ $$Pi_j = Phi^{-1}(Eta_j)$$ $$cbind(Eta, Z) \sim MN_{D-1+P x N}(Lambda*X, Sigma, I_N)$$ $$Lambda \sim MN_{D-1+P x Q}(Theta, Sigma, Gamma)$$ $$Sigma \sim InvWish(upsilon, Xi)$$ Where Gamma is a Q x Q covariance matrix, and Phi^-1 is ALRInv_D transform. That is, the orthus model models the latent multinomial log-ratios (Eta) and the observations of the second dataset jointly as a linear model. This allows Sigma to also describe the covariation between the two datasets.

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

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

fido_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

Examples

sim <- orthus_sim()
fit <- orthus(sim$Y, sim$Z, sim$X)