inla

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

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

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.surv() 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, $p(0), p(1),\dots$ to compute for each posterior marginal. The function returns, for each posterior marginal, the values $x(0), x(1),\dots$ such that $$\mbox{Prob}(X<x(p))=p$$
E: Known component in the mean for the Poisson likelihoods defined as $$E_i\exp(\eta_i)$$ where $$\eta_i$$ 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). WARNING: The normalizing constant for the likelihood is NOT recomputed, so ALL marginals (and the marginal likelihood) must be interpreted with great care.
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 and similar. The documentation for each likelihood will inform if this argument is required.
lp.scale: A vector with same length as the predictor going into the likelihood with either NA's or indices indexing the scaling coefficients. NA or a index less or equal to 0 means no scaling. The priors and properties of the scaling coefficients are set in control.lp.scale. Note that only the non-offset part of the linear predictor is scaled. This is an EXPERIMENTAL option.
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 inla.getOption("verbose"))
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 vignette Short tutorials from old www-page for information on how to define such linear combinations.
selection: This is a similar argument to the one in inla.posterior.sample and follow the same format. This argument allows to define a subset of the latent field for which to compute an approximated joint distribution. It will appear in result$selection. See also ?inla.rjmarginal and the approriate vignette.
control.compute: See ?control.compute
control.predictor: See ?control.predictor
control.family: See ?control.family
control.inla: See ?control.inla
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
control.lp.scale: See ?control.lp.scale
control.pardiso: See ?control.pardiso
control.stiles: See ?control.stiles
control.taucs: See ?control.taucs
control.numa: See ?control.numa
only.hyperparam: If TRUE, then only the hyperparameters are computed.
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. (This is an expert option and not intended for normal usage.)
num.threads: Maximum number of threads the inla-program will use, or as 'A:B' defining the number threads in the outer (A) and inner (B) layer for nested parallelism. If B is set to -1, then one can force some single function evaluations to be perfored in parallel, so num.threads=4:-1 will locally behave like num.threads=4:1 (if considered to be more efficient). If B > 1 then num.threads=A:B and num.threads=A:-B are equivalent.
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 model-files are stored in the current directory called "inla.model" or "inla.model-NUMBER".
working.directory: A string giving the name of an non-existing directory where to store the model-files. Sometimes this argument is required if the temporary directory returned with tempdir() not writeable or has an encoding that is not supported.
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.
inla.mode: Run inla in compact-mode, or the classic-mode. Default is to use the mode set by inla.getOption("inla.mode") which is default compact-mode.
safe: If TRUE, then enable possible restarts to improve initial values and Hessian if needed.
debug: If TRUE, print 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: 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 $\eta$ in the model
marginals.linear.predictor: If compute=TRUE in control.predictor, a list containing the posterior marginals of the linear predictors $\eta$ in the model.
summary.fitted.values: A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the fitted values $g^{-1}(\eta)$ 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 $g^{-1}(\eta)$ 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.
selection: Provide the approximated joint distribution for the selection
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$po are the values of the predictive ordinate (CPO) (pi(yi|y))
residuals: If residuals=TRUE in control.compute, a list of standardized residuals are provided, see ?control.compute for details
waic: If waic=TRUE in control.compute, a list of two elements: waic$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 hyperparameters.
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

Havard Rue hrue@r-inla.org and Sara Martino

Arguments

Value

See also

Author