stan_gamm4: Bayesian generalized linear additive models with group-specific terms via Stan

Description

Bayesian inference for GAMMs with flexible priors.

Usage

stan_gamm4(formula, random = NULL, family = gaussian(), data = list(),
  weights = NULL, subset = NULL, na.action, knots = NULL,
  drop.unused.levels = TRUE, ..., prior = normal(),
  prior_intercept = normal(), prior_ops = prior_options(),
  prior_covariance = decov(), prior_PD = FALSE, algorithm = c("sampling",
  "meanfield", "fullrank"), adapt_delta = NULL, QR = FALSE)

Arguments

formula, random, family, data, knots, drop.unused.levels

Same as for gamm4.

subset, weights, na.action

Same as glm, but rarely specified.

...

Further arguments passed to sampling (e.g. iter, chains, cores, etc.) or to vb (if algorithm is

prior

Prior for coefficients. See priors for details. Set prior to NULL to omit a prior, i.e., use an (improper) uniform prior.

prior_intercept

Prior for intercept. See priors for details. Set prior_intercept to NULL to omit a prior, i.e., use an (improper) uniform prior. (Note: the prior distribution for

prior_ops

Additional options related to prior distributions. Can be NULL to omit a prior on the dispersion and see prior_options otherwise.

prior_covariance

Cannot be NULL; see decov for more information about the default arguments.

prior_PD

A logical scalar (defaulting to FALSE) indicating whether to draw from the prior predictive distribution instead of conditioning on the outcome.

algorithm

Character string (possibly abbreviated) indicating the estimation approach to use. Can be "sampling" for MCMC (the default), "optimizing" for optimization, "meanfield" for variational inference with independent norm

adapt_delta

Only relevant if algorithm="sampling". See adapt_delta for details.

A logical scalar (defaulting to FALSE) but if TRUE applies a scaled qr decomposition to the design matrix, $X = Q^\ast R^\ast$, where $Q^\ast = Q \sqrt{n-1}$ and $R^\ast = \frac{1}{\s

Value

A stanreg object is returned for stan_gamm4.

Details

The stan_gamm4 function is similar in syntax to gamm4, which accepts a syntax that is similar to (but not quite as extensive as) that for gamm and converts it internally into the syntax accepted by glmer. But rather than performing (restricted) maximum likelihood estimation, the stan_gamm4 function utilizes MCMC to perform Bayesian estimation. The Bayesian model adds independent priors on the common regression coefficients (in the same way as stan_glm) and priors on the terms of a decomposition of the covariance matrices of the group-specific parameters, including the smooths. Estimating these models via MCMC avoids the optimization issues that often crop up with GAMMs and provides better estimates for the uncertainty in the parameter estimates. See gamm4 for more information about the model specicification and priors for more information about the priors.

Examples

Run this code

# see example(gamm4, package = "gamm4") but prefix gamm4() calls with stan_