inla: Bayesian analysis of structured additive models

In inbo/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

Description

inla performs a full Bayesian analysis of additive models using Integrated Nested Laplace approximation

Usage

inla(
    formula,
    family = "gaussian", 
    contrasts = NULL,
    data,
    quantiles=c(0.025, 0.5, 0.975),
    E = NULL,
    offset=NULL,
    scale = NULL,
    weights = NULL,
    Ntrials = NULL,
    strata = NULL,
    link.covariates = NULL,
    verbose = FALSE,
    lincomb = NULL,
    control.compute = list(),
    control.predictor = list(),
    control.family = list(),
    control.inla = list(),
    control.results = list(),
    control.fixed = list(),
    control.mode = list(),
    control.expert = list(),
    control.hazard = list(),
    control.lincomb = list(),
    control.update = list(), 
    only.hyperparam = FALSE,
    inla.call = inla.getOption("inla.call"),
    inla.arg = inla.getOption("inla.arg"),
    num.threads = inla.getOption("num.threads"),
    blas.num.threads = inla.getOption("blas.num.threads"),
    keep = inla.getOption("keep"),
    working.directory = inla.getOption("working.directory"),
    silent = inla.getOption("silent"),
    debug = inla.getOption("debug"), 
    .parent.frame = parent.frame()
    )

 

Arguments

formula	A inla formula like y ~1 + z + f(ind, model="iid") + f(ind2, weights, model="ar1") This is much like the formula for a glm except that smooth or spatial terms can be added to the right hand side of the formula. See f for full details and the web site www.r-inla.org for several worked out examples. Each smooth or spatial term specified through f should correspond to separate column of the data frame data. The response variable, y can be a univariate response variable, a list or the output of the function inla.surf for survival analysis models.
family	A string indicating the likelihood family. The default is gaussian with identity link. See names(inla.models()$likelihood) for a list of possible alternatives and use inla.doc for detailed docs for individual families.
contrasts	Optional contrasts for the fixed effects; see ?lm or ?glm for details.
data	A data frame or list containing the variables in the model. The data frame MUST be provided
quantiles	A vector of quantiles, p(0), p(1),… to compute for each posterior marginal. The function returns, for each posterior marginal, the values x(0), x(1),… such that Prob(X<x)=p
E	Known component in the mean for the Poisson likelihoods defined as E exp(eta) where eta is the linear predictor. If not provided it is set to rep(1, n.data).
offset	This argument is used to specify an a-priori known and fixed component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length either one or equal to the number of cases. One or more offset() terms can be included in the formula instead or as well, and if both are used, they are combined into a common offset. If the A-matrix is used in the linear predictor statement control.predictor, then the offset given in this argument is added to eta*, the linear predictor related to the observations, as eta* = A eta + offset, whereas an offset in the formula is added to eta, the linear predictor related to the formula, as eta = ... + offset.formula. So in this case, the offset defined here and in the formula has a different meaning and usage.
scale	Fixed (optional) scale parameters of the precision for Gaussian and Student-T response models. Default value is rep(1, n.data).
weights	Fixed (optional) weights parameters of the likelihood, so the log-likelihood[i] is changed into weights[i]*log-likelihood[i]. Default value is rep(1, n.data). Due to the danger of mis-interpreting the results (see below), this option is DISABLED by default. You can enable this option for the rest of your R session, doing inla.setOption(enable.inla.argument.weights=TRUE). WARNING: The normalizing constant for the likelihood is NOT recomputed, so ALL marginals (and the marginal likelihood) must be interpreted with great care. Possibly, you may want to set the prior for the hyperparameters to "uniform" and the integration strategy to "eb" to mimic a maximum-likelihood approach.
Ntrials	A vector containing the number of trials for the binomial likelihood and variantes, or the number of required successes for the nbinomial2 likelihood. Default value is rep(1, n.data).
strata	Fixed (optional) strata indicators for tstrata likelihood model.
link.covariates	A vector or matrix with covariates for link functions
verbose	Boolean indicating if the inla-program should run in a verbose mode (default FALSE).
lincomb	Used to define linear combination of nodes in the latent field. The posterior distribution of such linear combination is computed by the inla function. See www.r-inla.org/faq for examples of how to define such linear combinations.
control.compute	See ?control.compute
control.predictor	See ?control.predictor
control.family	See ?control.family
control.inla	See ?control.inla
control.results	See ?control.result
control.fixed	See ?control.fixed
control.mode	See ?control.mode
control.expert	See ?control.expert
control.hazard	See ?control.hazard
control.lincomb	See ?control.lincomb
control.update	See ?control.update
only.hyperparam	A boolean variable saying if only the hyperparameters should be computed. This option is mainly used internally. (TODO: This option should not be located here, change it!)
inla.call	The path to, or the name of, the inla-program. This is program is installed together with the R-package, but, for example, a native compiled version can be used instead to improve the performance.
inla.arg	A string indicating ALL arguments to the 'inla' program and do not include default arguments. (OOPS: This is an expert option!)
num.threads	Maximum number of threads the inla-program will use
blas.num.threads	The absolute value of blas.num.threads is the maximum number of threads the the openblas/mklblas will use (if available). If blas.num.threads > 0, then the environment variables OPENBLAS_NUM_THREADS and MKL_NUM_THREADS will be assigned. If blas.num.threads < 0, then the environment variables OPENBLAS_NUM_THREADS and MKL_NUM_THREADS will be assigned unless they are already defined. If blas.num.threads = 0, then variables OPENBLAS_NUM_THREADS and MKL_NUM_THREADS will be removed.
keep	A boolean variable indicating that the working files (ini file, data files and results files) should be kept. If TRUE and no working.directory is specified the working files are stored in a directory called "inla".
working.directory	A string giving the name of an non-existing directory where to store the working files.
silent	If equal to 1L or TRUE, then the inla-program would be “silent”. If equal to 2L, then supress also error messages from the inla-program.
debug	If TRUE, then enable some debug output.
.parent.frame	Internal use only

Value

inla returns an object of class "inla". This is a list containing at least the following arguments:

summary.fixed	Matrix containing the mean and standard deviation (plus, possibly quantiles and cdf) of the the fixed effects of the model.
marginals.fixed	A list containing the posterior marginal densities of the fixed effects of the model.
summary.random	List of matrices containing the mean and standard deviation (plus, possibly quantiles and cdf) of the the smooth or spatial effects defined through f().
marginals.random	If return.marginals.random=TRUE in control.results (default), a list containing the posterior marginal densities of the random effects defined through f.
summary.hyperpar	A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the hyperparameters of the model
marginals.hyperpar	A list containing the posterior marginal densities of the hyperparameters of the model.
summary.linear.predictor	A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the linear predictors η in the model
marginals.linear.predictor	If compute=TRUE in control.predictor, a list containing the posterior marginals of the linear predictors η in the model.
summary.fitted.values	A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the fitted values g^{-1}(η) obtained by transforming the linear predictors by the inverse of the link function. This quantity is only computed if marginals.fitted.values is computed. Note that if an observation is NA then the identity link is used. You can manually transform a marginal using inla.marginal.transform() or set the argument link in the control.predictor-list; see ?control.predictor
marginals.fitted.values	If compute=TRUE in control.predictor, a list containing the posterior marginals of the fitted values g^{-1}(η) obtained by transforming the linear predictors by the inverse of the link function. Note that if an observation is NA then the identity link is used. You can manually transform a marginal using inla.marginal.transform() or set the argument link in the control.predictor-list; see ?control.predictor
summary.lincomb	If lincomb != NULL a list of matrices containing the mean and sd (plus, possibly quantiles and cdf) of all linear combinations defined.
marginals.lincomb	If lincomb != NULL a list of posterior marginals of all linear combinations defined.
joint.hyper	A matrix containing the joint density of the hyperparameters (in the internal scale)
dic	If dic=TRUE in control.compute, the deviance information criteria and effective number of parameters, otherwise NULL
cpo	If cpo=TRUE in control.compute, a list of three elements: cpo$cpo are the values of the conditional predictive ordinate (CPO), cpo$pit are the values of the probability integral transform (PIT) and cpo$failure indicates whether some assumptions are violated. In short, if cpo$failure[i] > 0 then some assumption is violated, the higher the value (maximum 1) the more seriously.
po	If po=TRUE in control.compute, a list of one elements: po$po are the values of the predictive ordinate (CPO) (pi(yi|y))
waic	If waic=TRUE in control.compute, a list of two elements: waic$waic is the Watanabe-Akaike information criteria, and waic$p.eff is the estimated effective number of parameters
mlik	If mlik=TRUE in control.compute, the log marginal likelihood of the model (using two different estimates), otherwise NULL
neffp	Expected effective number of parameters in the model. The standard deviation of the expected number of parameters and the number of replicas for parameter are also returned
mode	A list of two elements: mode$theta is the computed mode of the hyperparameters and mode$x is the mode of the latent field given the modal value of the hyperparamters.
call	The matched call.
formula	The formula supplied
nhyper	The number of hyperparameters in the model
cpu.used	The cpu time used by the inla function

Author(s)

Havard Rue [e-mail] and Sara Martino

References

Rue, H. and Martino, S. and Chopin, N. (2009) Approximate Bayesian Inference for latent Gaussian models using Integrated Nested Laplace Approximations, JRSS-series B (with discussion), vol 71, no 2, pp 319-392. Rue, H and Held, L. (2005) Gaussian Markov Random Fields - Theory and Applications Chapman and Hall

See Also

f, inla.hyperpar

Examples

## Not run: 
##See the web page \url{www.r-inla.org} for a series of worked out examples

## End(Not run)

inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.