Generate INLA-compatible Model Formulas

Description

This function streamlines the creation of INLA-compatible model formulas by automatically structuring fixed effects, random effects, and interactions. It accepts a list of covariate sets and produces a corresponding set of model formulas that share a common random effect structure.

write_inla_formulas(
  outcome,
  covariates = NULL,
  baseline = TRUE,
  re1 = list(id = NULL, model = NULL, replicate = NULL, group = NULL, graph = NULL,
    cyclic = FALSE, scale.model = FALSE, constr = FALSE, adjust.for.con.comp = FALSE,
    hyper = NULL),
  re2 = NULL,
  re3 = NULL,
  re4 = NULL,
  re5 = NULL
)

Arguments

  • outcome: Character string specifying the name of the outcome variable.
  • covariates: A list of character vectors, where each vector contains covariate names to be included in the model. If a single vector is provided, a single model formula is generated.
  • baseline: Logical; If TRUE, a baseline formula without covariates is included. If no random effects are specified, this will be an intercept-only model. If random effects are specified, the baseline formula will include random effects but not covariates. This formula will be the first in the list. Default is TRUE.
  • re1: A list defining a random effect structure. Up to five such lists (re1 through re5) can be passed.
  • re2: Additional random effect definitions, as described for re1.
  • re3: Additional random effect definitions, as described for re1.
  • re4: Additional random effect definitions, as described for re1.
  • re5: Additional random effect definitions, as described for re1.

Details

The write_inla_formulas() function simplifies the creation of multiple INLA models by automatically structuring fixed effects, random effects, and interactions. The function ensures that all models have a consistent structure, making them easier to analyze and modify.

If baseline = TRUE, a null formula (without covariates) is included as the first element of the list.

The number of formulas generated depends on the length of the covariates list.

Random effects can be added using re1, ..., re5, where each effect must be a named list (e.g. re1 = list(id = “year_id”, model = “rw1”)). In the list the following fields are strictly necessary:

  • id (character): the variable name that indexes the random effect (e.g., “year”, “region”).

  • model (character): the type of random effect. Supported values include: "iid", "rw1", "rw2", "bym", and "bym2".

  • The following optional fields can be provided in the random effect list:

    • replicate (character): defines an additional variable used to replicate the random effect structure across groups (e.g., spatial units for repeated time-series).
    • group (character): used to model group-specific effects or nested structures.
    • graph (character): required for "bym" and "bym2" models; refers to the name of an object in the environment that holds the spatial adjacency matrix.
    • cyclic (logical): indicates whether the random walk ("rw1" or "rw2") is cyclic. Default is FALSE. Use for periodic structures (e.g., months).
    • scale.model (logical): if TRUE, scales structured random effects (like rw1, rw2, bym) so the generalized variance is 1. For bym2 INLA automatically applies scale.model = TRUE internally.
    • constr (logical): If TRUE, a sum to zero constrain is introduced. This ‘constr’ option is applied only to ‘iid’ random effects. For rw, ar, bym, bym2 INLA automatically applies scale.model = TRUE internally.
    • adjust.for.con.comp (logical): if TRUE, accounts for disconnected components in spatial graphs. Recommended for "bym" and "bym2". Default is FALSE.
    • hyper (character): the name of an object in the environment that contains the hyperprior specification for the random effect’s precision or other parameters.

For more information on random effects in R-INLA, see Bayesian inference with INLA: Mixed-effects Models.

Returns

A character vector of INLA model formulas.

See Also

as_GHRformulas for transforming model formulas into structured objects.

Examples

# Define covariates of interest
covs <- c("tmin.l1", "tmin.l2", "pdsi.l1", "pdsi.l2", "urban_level")

# Combine covariate names using a pattern-matching functionality
combined_covariates <- cov_multi(
  covariates = covs,
  pattern    = c("tmin", "pdsi", "urban_level")
)

# Define hyperprior specifications for random effects
prior_re1 <- list(prec = list(prior = "loggamma", param = c(0.01, 0.01)))
prior_re2 <- list(prec = list(prior = "loggamma", param = c(0.01, 0.01)))
prior_re3 <- list(
  prec = list(prior = "pc.prec", param = c(0.5 / 0.31, 0.01)),
  phi  = list(prior = "pc",      param = c(0.5, 2 / 3))
)

# Write a set of INLA-compatible model formulas
inla_formulas <- write_inla_formulas(
  outcome    = "dengue_cases",
  covariates = combined_covariates,
  re1 = list(
    id        = "month_id",
    model        = "rw1",
    cyclic    = TRUE,
    hyper     = "prior_re1",
    replicate = "spat_meso_id"
  ),
  re2 = list(
    id    = "year_id",
    model    = "rw1",
    hyper = "prior_re2"
  ),
  re3 = list(
    id    = "spat_id",
    model    = "iid",
    hyper = "prior_re3"
  ),
  baseline = TRUE
)