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Interface to fit basset models

Source: R/fit_basset.R
basset_fit.Rd

Basset (A Lazy Learner) - non-linear regression models in fido

Usage

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

# S3 method for class 'bassetfit'
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 (cannot be NULL)

upsilon

dof for inverse wishart prior (numeric must be > D) (default: D+3)

Theta

A function from dimensions dim(X) -> (D-1)xN (prior mean of gaussian process). For an additive GP model, can be a list of functions from dimensions dim(X) -> (D-1)xN + a (optional) matrix of size (D-1)xQ for the prior of a linear component if desired.

Gamma

A function from dimension dim(X) -> NxN (kernel matrix of gaussian process). For an additive GP model, can be a list of functions from dimension dim(X) -> NxN + a QxQ prior covariance matrix if a linear component is specified. It is assumed that the order matches the order of Theta.

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)

linear

A vector denoting which rows of X should be used if a linear component is specified. Default is all rows.

init

(D-1) x Q initialization for Eta for optimization

pars

character vector of posterior parameters to return

newdata

Default is NULL. If non-null, newdata is used in the uncollapse sampler in place of X.

...

other arguments passed to pibble (which is used internally to fit the basset model)

m

object of class bassetfit

Value

an object of class bassetfit

Details

the full model is given by: $$Y_j \sim Multinomial(Pi_j)$$ $$Pi_j = Phi^{-1}(Eta_j)$$ $$Eta \sim MN_{D-1 \times N}(Lambda, Sigma, I_N)$$ $$Lambda \sim GP_{D-1 \times Q}(Theta(X), Sigma, Gamma(X))$$ $$Sigma \sim InvWish(upsilon, Xi)$$ Where Gamma(X) is short hand for the Gram matrix of the Kernel function.

Alternatively can be used to fit an additive GP of the form: $$Y_j \sim Multinomial(Pi_j)$$ $$Pi_j = Phi^{-1}(Eta_j)$$ $$Eta \sim MN_{D-1 \times N}(Lambda, Sigma, I_N)$$ $$Lambda = Lambda_1 + ... + Lambda_p + Beta X$$ $$Lambda_1 \sim GP_{D-1 \times Q}(Theta_1(X), Sigma, Gamma_p(X))$$ ... $$Lambda_p \sim GP_{D-1 \times Q}(Theta_1(X), Sigma, Gamma_1(X))$$ $$Beta \sim MN(Theta_B, Sigma, Gamma_B)$$ $$Sigma \sim InvWish(upsilon, Xi)$$ Where Gamma(X) is short hand for the Gram matrix of the Kernel function.

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