bfa_sp | R Documentation |
bfa_sp
is a Markov chain Monte Carlo (MCMC) sampler for a Bayesian spatial factor analysis model. The spatial component is
introduced using a Probit stick-breaking process prior on the factor loadings. The model is implemented using a Bayesian hierarchical framework.
bfa_sp( formula, data, dist, time, K, L = Inf, trials = NULL, family = "normal", temporal.structure = "exponential", spatial.structure = "discrete", starting = NULL, hypers = NULL, tuning = NULL, mcmc = NULL, seed = 54, gamma.shrinkage = TRUE, include.space = TRUE, clustering = TRUE )
formula |
A |
data |
A required |
dist |
A |
time |
A |
K |
A scalar that indicates the dimension (i.e., quantity) of latent factors. |
L |
The number of latent clusters. If finite, a scalar indicating the number of clusters for each column of the factor loadings matrix. By default |
trials |
A variable in |
family |
Character string indicating the distribution of the observed data. Options
include: |
temporal.structure |
Character string indicating the temporal kernel. Options include:
|
spatial.structure |
Character string indicating the type of spatial process. Options include:
|
starting |
Either When |
hypers |
Either When
|
tuning |
Either When |
mcmc |
Either
|
seed |
An integer value used to set the seed for the random number generator (default = 54). |
gamma.shrinkage |
A logical indicating whether a gamma shrinkage process prior is used for the variances of the factor loadings columns. If FALSE, the hyperparameters (A1 and A2) indicate the shape and rate for a gamma prior on the precisions. Default is TRUE. |
include.space |
A logical indicating whether a spatial process should be included. Default is TRUE, however if FALSE the spatial correlation matrix
is fixed as an identity matrix. This specification overrides the |
clustering |
A logical indicating whether the Bayesian non-parametric process should be used, default is TRUE. If FALSE is specified each column is instead modeled with an independent spatial process. |
Details of the underlying statistical model proposed by Berchuck et al. 2019. are forthcoming.
bfa_sp
returns a list containing the following objects
lambda
NKeep x (M x O x K)
matrix
of posterior samples for factor loadings matrix lambda
.
The labels for each column are Lambda_O_M_K.
eta
NKeep x (Nu x K)
matrix
of posterior samples for the latent factors eta
.
The labels for each column are Eta_Nu_K.
beta
NKeep x P
matrix
of posterior samples for beta
.
sigma2
NKeep x (M * (O - C))
matrix
of posterior samples for the variances sigma2
.
The labels for each column are Sigma2_O_M.
kappa
NKeep x ((O * (O + 1)) / 2)
matrix
of posterior samples for kappa
. The
columns have names that describe the samples within them. The row is listed first, e.g.,
Kappa3_2
refers to the entry in row 3
, column 2
.
delta
NKeep x K
matrix
of posterior samples for delta
.
tau
NKeep x K
matrix
of posterior samples for tau
.
upsilon
NKeep x ((K * (K + 1)) / 2)
matrix
of posterior samples for Upsilon
. The
columns have names that describe the samples within them. The row is listed first, e.g.,
Upsilon3_2
refers to the entry in row 3
, column 2
.
psi
NKeep x 1
matrix
of posterior samples for psi
.
xi
NKeep x (M x O x K)
matrix
of posterior samples for factor loadings cluster labels xi
.
The labels for each column are Xi_O_M_K.
rho
NKeep x 1
matrix
of posterior samples for rho
.
metropolis
2 (or 1) x 3
matrix
of metropolis
acceptance rates, updated tuners, and original tuners that result from the pilot
adaptation.
runtime
A character
string giving the runtime of the MCMC sampler.
datobj
A list
of data objects that are used in future bfa_sp
functions
and should be ignored by the user.
dataug
A list
of data augmentation objects that are used in future
bfa_sp
functions and should be ignored by the user.
Reference for Berchuck et al. 2019 is forthcoming.
###Load womblR for example visual field data library(womblR) ###Format data for MCMC sampler blind_spot <- c(26, 35) # define blind spot VFSeries <- VFSeries[order(VFSeries$Location), ] # sort by location VFSeries <- VFSeries[order(VFSeries$Visit), ] # sort by visit VFSeries <- VFSeries[!VFSeries$Location %in% blind_spot, ] # remove blind spot locations dat <- data.frame(Y = VFSeries$DLS / 10) # create data frame with scaled data Time <- unique(VFSeries$Time) / 365 # years since baseline visit W <- HFAII_Queen[-blind_spot, -blind_spot] # visual field adjacency matrix (data object from womblR) M <- dim(W)[1] # number of locations ###Prior bounds for psi TimeDist <- as.matrix(dist(Time)) BPsi <- log(0.025) / -min(TimeDist[TimeDist > 0]) APsi <- log(0.975) / -max(TimeDist) ###MCMC options K <- 10 # number of latent factors O <- 1 # number of spatial observation types Hypers <- list(Sigma2 = list(A = 0.001, B = 0.001), Kappa = list(SmallUpsilon = O + 1, BigTheta = diag(O)), Delta = list(A1 = 1, A2 = 20), Psi = list(APsi = APsi, BPsi = BPsi), Upsilon = list(Zeta = K + 1, Omega = diag(K))) Starting <- list(Sigma2 = 1, Kappa = diag(O), Delta = 2 * (1:K), Psi = (APsi + BPsi) / 2, Upsilon = diag(K)) Tuning <- list(Psi = 1) MCMC <- list(NBurn = 1000, NSims = 1000, NThin = 2, NPilot = 5) ###Fit MCMC Sampler reg.bfa_sp <- bfa_sp(Y ~ 0, data = dat, dist = W, time = Time, K = 10, starting = Starting, hypers = Hypers, tuning = Tuning, mcmc = MCMC, L = Inf, family = "tobit", trials = NULL, temporal.structure = "exponential", spatial.structure = "discrete", seed = 54, gamma.shrinkage = TRUE, include.space = TRUE, clustering = TRUE) ###Note that this code produces the pre-computed data object "reg.bfa_sp" ###More details can be found in the vignette.
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