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
)
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 N 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.- ...
arguments passed to
optimPibbleCollapsed
anduncollapsePibble
- m
object of class pibblefit
Details
the full model is given by: $$Y_j \sim Multinomial(Pi_j)$$ $$Pi_j = Phi^{-1}(Eta_j)$$ $$Eta \sim MN_{D-1 \times N}(Lambda*X, Sigma, I_N)$$ $$Lambda \sim MN_{D-1 \times Q}(Theta, Sigma, Gamma)$$ $$Sigma \sim InvWish(upsilon, Xi)$$ Where Gamma is a Q x Q covariance matrix, and \(Phi^{-1}\) is ALRInv_D transform.
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
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)