This function is intended to be used on the right hand side of the formula argument to
create_sampler or generate_data.
gen(
formula = ~1,
factor = NULL,
remove.redundant = FALSE,
drop.empty.levels = FALSE,
X = NULL,
var = NULL,
prior = NULL,
Q0 = NULL,
PX = NULL,
priorA = NULL,
strucA = GMRF_structure(),
R0 = NULL,
RA = NULL,
constr = NULL,
S0 = NULL,
SA = NULL,
formula.gl = NULL,
a = 1000,
name = "",
sparse = NULL,
control = gen_control(),
debug = FALSE
)An object with precomputed quantities and functions for sampling from prior or conditional posterior distributions for this model component. Intended for internal use by other package functions.
a model formula specifying the effects that vary over the levels of
the factor variable(s) specified by argument factor. Defaults to ~1,
corresponding to random intercepts. If X is specified formula is ignored.
Variable names are looked up in the data frame passed as data argument to
create_sampler or generate_data, or in environment(formula).
a formula with factors by which the effects specified in the formula
argument vary. Often only one such factor is needed but multiple factors are allowed so that
interaction terms can be modeled conveniently. The formula must take the form
~ f1(fac1, ...) * f2(fac2, ...) ..., where
fac1, fac2 are factor variables and f1, f2 determine the
correlation structure assumed between levels of each factor, and the ... indicate
that for some correlation types further arguments can be passed. Correlation structures
currently supported include iid for independent identically distributed effects,
RW1 and RW2 for random walks of first or second order over the factor levels,
AR1 for first-order autoregressive effects, season for seasonal effects,
spatial for spatial (CAR) effects and custom for supplying a custom
precision matrix corresponding to the levels of the factor. For further details about
the correlation structures, and further arguments that can be passed, see
correlation. Argument factor is ignored if X is specified.
The factor variables are looked up in the data frame passed as data argument to
create_sampler or generate_data, or in environment(formula).
whether redundant columns should be removed from the model matrix
associated with formula. Default is FALSE.
whether to remove factor levels without observations.
A (possibly sparse) design matrix. If X is specified, formula and factor
are only used to derive the random effects' structured precision matrix.
the (co)variance structure among the varying effects defined by formula
over the levels of the factors defined by factor.
The default is "unstructured", meaning that a full covariance matrix
parametrization is used. For uncorrelated effects with unequal variances use
var="diagonal". For uncorrelated effects with equal variances use var="scalar".
In the case of a single varying effect there is no difference between these choices.
the prior specification for the variance parameters of the random effects.
These can currently be specified by a call to pr_invwishart in case
var="unstructured" or by a call to pr_invchisq otherwise.
See the documentation of those prior specification functions for more details.
precision matrix associated with formula. This can only be used in
combination with var="scalar".
whether parameter expansion should be used. Default is TRUE, which
applies parameter expansion with default options. The only exception is that for
gamma sampling distributions the default is FALSE, i.e. no parameter expansion.
Alternative options can be specified
by supplying a list with one or more of the following components:
prior for the multiplicative expansion parameter. Defaults to a
normal prior with mean 0 and standard deviation 1, unless the sampling
distribution is gamma in which case the default is a Multivariate Log
inverse Gamma prior. The default parameters can be changed using functions
pr_normal or pr_MLiG.
whether a redundant multiplicative expansion parameter is used for each varying effect
specified by formula. The default is TRUE except when var="scalar".
If FALSE a single redundant multiplicative parameter is used.
whether the data level scale is used as a variance factor for the expansion
parameters. Default is TRUE.
prior distribution for scale factors at the variance scale associated with QA.
In case of IGMRF models the scale factors correspond to the innovations.
The default NULL means not to use any local scale factors.
A prior can currently be specified using pr_invchisq or pr_exp.
this option can be used to modify the default structure encoded by
factor to a 'bym2' or 'leroux' structure. See GMRF_structure
for details.
an optional equality restriction matrix acting on the coefficients defined by formula, for each
level defined by factor. If c is the number of restrictions, R0 is a
q0 x c matrix where q0 is the number of columns of the design matrix derived
from formula. Together with RA it defines the set of equality constraints
to be imposed on the vector of coefficients. Only allowed in combination with var="scalar".
an optional equality restriction matrix acting on the coefficients defined by factor,
for each effect defined by formula. If c is the number of restrictions, RA is a
l x c matrix where l is the number of levels defined by factor.
Together with R0 this defines the set of equality constraints to be imposed on the vector
of coefficients.
If constr=TRUE, additional constraints are imposed, corresponding to the
null-vectors of the singular precision matrix in case of an intrinsic Gaussian Markov Random Field.
whether constraints corresponding to the null-vectors of the precision matrix
are to be imposed on the vector of coefficients. By default this is TRUE for
improper or intrinsic GMRF model components, i.e. components with a singular precision matrix
such as random walks or CAR spatial components.
an optional inequality restriction matrix acting on the coefficients defined by formula, for each
level defined by factor. If c is the number of restrictions, S0 is a
q0 x c matrix where q0 is the number of columns of the design matrix derived
from formula. Together with SA it defines the set of inequality constraints
to be imposed on the vector of coefficients.
an optional inequality restriction matrix acting on the coefficients defined by factor,
for each effect defined by formula. If c is the number of restrictions, SA is a
l x c matrix where l is the number of levels defined by factor.
Together with S0 this defines the set of constraints to be imposed on the vector
of coefficients.
a formula of the form ~ glreg(...) for group-level predictors
around which the random effect component is hierarchically centered.
See glreg for details.
only used in case the effects are MLiG distributed, as
assumed in case of a gamma sampling distribution, or for
gaussian variance modelling. In those cases a controls how close
the effects' prior is to a normal prior, see pr_MLiG.
the name of the model component. This name is used in the output of the MCMC simulation
function MCMCsim. By default the name will be 'gen' with the number of the model term attached.
whether the model matrix associated with formula should be sparse.
The default is based on a simple heuristic based on storage size.
a list with further computational options. These options can
be specified using function gen_control.
if TRUE a breakpoint is set at the beginning of the posterior
draw function associated with this model component. Mainly intended for developers.
J. Besag and C. Kooperberg (1995). On Conditional and Intrinsic Autoregression. Biometrika 82(4), 733-746.
C.M. Carvalho, N.G. Polson and J.G. Scott (2010). The horseshoe estimator for sparse signals. Biometrika 97(2), 465-480.
L. Fahrmeir, T. Kneib and S. Lang (2004). Penalized Structured Additive Regression for Space-Time Data: a Bayesian Perspective. Statistica Sinica 14, 731-761.
A. Gelman (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1(3), 515-533.
A. Gelman, D.A. Van Dyk, Z. Huang and W.J. Boscardin (2008). Using Redundant Parameterizations to Fit Hierarchical Models. Journal of Computational and Graphical Statistics 17(1), 95-122.
T. Park and G. Casella (2008). The Bayesian Lasso. Journal of the American Statistical Association 103(482), 681-686.
H. Rue and L. Held (2005). Gaussian Markov Random Fields. Chapman & Hall/CRC.