orthus_fit {fido} | R Documentation |
Interface to fit orthus models
Description
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
)
Usage
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 |
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 \times N}(\Lambda X, \Sigma, I_N)
\Lambda \sim MN_{D-1+P \times 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.
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
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)