Draw fitted values from the posterior distribution

Expectations (fitted values) of the response drawn from the posterior distribution of fitted model using a Gaussian approximation to the posterior or a simple Metropolis Hastings sampler.

Usage

fitted_samples(model, ...)

# S3 method for class 'gam'
fitted_samples(
  model,
  n = 1,
  data = newdata,
  seed = NULL,
  scale = c("response", "linear_predictor"),
  method = c("gaussian", "mh", "inla", "user"),
  n_cores = 1,
  burnin = 1000,
  thin = 1,
  t_df = 40,
  rw_scale = 0.25,
  freq = FALSE,
  unconditional = FALSE,
  draws = NULL,
  mvn_method = c("mvnfast", "mgcv"),
  ...,
  newdata = NULL,
  ncores = NULL
)

# S3 method for class 'scam'
fitted_samples(
  model,
  n = 1,
  data = NULL,
  seed = NULL,
  scale = c("response", "linear_predictor"),
  method = c("gaussian", "mh", "inla", "user"),
  n_cores = 1,
  burnin = 1000,
  thin = 1,
  t_df = 40,
  rw_scale = 0.25,
  freq = FALSE,
  unconditional = FALSE,
  draws = NULL,
  mvn_method = c("mvnfast", "mgcv"),
  ...
)

Arguments

model: a fitted model of the supported types
...: arguments passed to other methods. For fitted_samples(), these are passed on to mgcv::predict.gam(). For posterior_samples() these are passed on to fitted_samples(). For predicted_samples() these are passed on to the relevant simulate() method.
n: numeric; the number of posterior samples to return.
data: data frame; new observations at which the posterior draws from the model should be evaluated. If not supplied, the data used to fit the model will be used for data, if available in model.
seed: numeric; a random seed for the simulations.
scale: character; what scale should the fitted values be returned on? "linear predictor" is a synonym for "link" if you prefer that terminology.
method: character; which method should be used to draw samples from the posterior distribution. "gaussian" uses a Gaussian (Laplace) approximation to the posterior. "mh" uses a Metropolis Hastings sampler that alternates t proposals with proposals based on a shrunken version of the posterior covariance matrix. "inla" uses a variant of Integrated Nested Laplace Approximation due to Wood (2019), (currently not implemented). "user" allows for user-supplied posterior draws (currently not implemented).
n_cores: number of cores for generating random variables from a multivariate normal distribution. Passed to mvnfast::rmvn(). Parallelization will take place only if OpenMP is supported (but appears to work on Windows with current R).
burnin: numeric; number of samples to discard as the burnin draws. Only used with method = "mh".
thin: numeric; the number of samples to skip when taking n draws. Results in thin * n draws from the posterior being taken. Only used with method = "mh".
t_df: numeric; degrees of freedom for t distribution proposals. Only used with method = "mh".
rw_scale: numeric; Factor by which to scale posterior covariance matrix when generating random walk proposals. Negative or non finite to skip the random walk step. Only used with method = "mh".
freq: logical; TRUE to use the frequentist covariance matrix of the parameter estimators, FALSE to use the Bayesian posterior covariance matrix of the parameters.
unconditional: logical; if TRUE (and freq == FALSE) then the Bayesian smoothing parameter uncertainty corrected covariance matrix is used, if available.
draws: matrix; user supplied posterior draws to be used when method = "user".
mvn_method: character; one of "mvnfast" or "mgcv". The default is uses mvnfast::rmvn(), which can be considerably faster at generate large numbers of MVN random values than mgcv::rmvn(), but which might not work for some marginal fits, such as those where the covariance matrix is close to singular.
newdata: Deprecated: use data instead.
ncores: Deprecated; use n_cores instead. The number of cores for generating random variables from a multivariate normal distribution. Passed to mvnfast::rmvn(). Parallelization will take place only if OpenMP is supported (but appears to work on Windows with current R).

Value

A tibble (data frame) with 3 columns containing the posterior predicted values in long format. The columns are

row (integer) the row of data that each posterior draw relates to,
draw (integer) an index, in range 1:n, indicating which draw each row relates to,
response (numeric) the predicted response for the indicated row of data.

Note

Models with offset terms supplied via the offset argument to mgcv::gam() etc. are ignored by mgcv::predict.gam(). As such, this kind of offset term is also ignored by posterior_samples(). Offset terms that are included in the model formula supplied to mgcv::gam() etc are not ignored and the posterior samples produced will reflect those offset term values. This has the side effect of requiring any new data values provided to posterior_samples() via the data argument must include the offset variable.

References

Wood, S.N., (2020). Simplified integrated nested Laplace approximation. Biometrika 107, 223–230. doi:10.1093/biomet/asz044

Author

Gavin L. Simpson

Examples

load_mgcv()
dat <- data_sim("eg1", n = 1000, dist = "normal", scale = 2, seed = 2)
m1 <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = dat, method = "REML")

fs <- fitted_samples(m1, n = 5, seed = 42)
# \donttest{
fs
#> # A tibble: 5,000 x 4
#>     .row .draw .parameter .fitted
#>    <int> <int> <chr>        <dbl>
#>  1     1     1 location      6.34
#>  2     2     1 location      5.08
#>  3     3     1 location      6.84
#>  4     4     1 location      7.71
#>  5     5     1 location      9.23
#>  6     6     1 location      8.03
#>  7     7     1 location      6.19
#>  8     8     1 location      7.28
#>  9     9     1 location     14.0 
#> 10    10     1 location     12.7 
#> # i 4,990 more rows
# }

# can generate own set of draws and use them
drws <- generate_draws(m1, n = 2, seed = 24)
fs2 <- fitted_samples(m1, method = "user", draws = drws)
# \donttest{
fs2
#> # A tibble: 2,000 x 4
#>     .row .draw .parameter .fitted
#>    <int> <int> <chr>        <dbl>
#>  1     1     1 location      6.30
#>  2     2     1 location      5.12
#>  3     3     1 location      7.40
#>  4     4     1 location      7.42
#>  5     5     1 location      9.40
#>  6     6     1 location      8.04
#>  7     7     1 location      5.83
#>  8     8     1 location      7.30
#>  9     9     1 location     14.3 
#> 10    10     1 location     13.1 
#> # i 1,990 more rows
# }