Expected Values of the Posterior Predictive Distribution

Compute posterior draws of the expected value of the posterior predictive distribution of a brmsfit model in the brmcoda object. Can be performed for the data used to fit the model (posterior predictive checks) or for new data. By definition, these predictions have smaller variance than the posterior predictions performed by the predict.brmcoda method. This is because only the uncertainty in the expected value of the posterior predictive distribution is incorporated in the draws computed by fitted while the residual error is ignored there. However, the estimated means of both methods averaged across draws should be very similar.

Usage

# S3 method for class 'brmcoda'
fitted(object, scale = c("linear", "response"), summary = TRUE, ...)

Arguments

object

An object of class brmcoda.

scale

Specifically for models with compositional responses, either "response" or "linear". If "linear", results are returned on the log-ratio scale. If "response", results are returned on the compositional scale of the response variable.

summary

Should summary statistics be returned instead of the raw values? Default is TRUE.

...

Further arguments passed to fitted.brmsfit that control additional aspects of prediction.

Value

An array of predicted mean response values. If summary = FALSE the output resembles those of posterior_epred.brmsfit.

If summary = TRUE the output depends on the family: For categorical and ordinal families, the output is an N x E x C array, where N is the number of observations, E is the number of summary statistics, and C is the number of categories. For all other families, the output is an N x E matrix. The number of summary statistics E is equal to 2 + length(probs): The Estimate column contains point estimates (either mean or median depending on argument robust), while the Est.Error column contains uncertainty estimates (either standard deviation or median absolute deviation depending on argument robust). The remaining columns starting with Q contain quantile estimates as specified via argument probs.

In multivariate models, an additional dimension is added to the output which indexes along the different response variables.

See also

fitted.brmsfit

Examples

# \donttest{
## fit a model
if(requireNamespace("cmdstanr")){
  ## compute composition and ilr coordinates
  cilr <- complr(data = mcompd, sbp = sbp,
                 parts = c("TST", "WAKE", "MVPA", "LPA", "SB"),
                 idvar = "ID", total = 1440)
  
  ## fit a model
  m1 <- brmcoda(complr = cilr,
                formula = Stress ~ bilr1 + bilr2 + bilr3 + bilr4 +
                  wilr1 + wilr2 + wilr3 + wilr4 + (1 | ID),
                chain = 1, iter = 500,
                backend = "cmdstanr")
  
  ## compute expected predictions
  epred <- fitted(m1)
  head(epred)
  
  ## fit a model with compositional outcome
  m2 <- brmcoda(complr = cilr,
                formula = mvbind(ilr1, ilr2, ilr3, ilr4) ~ Stress + Female + (1 | ID),
                chain = 1, iter = 500,
                backend = "cmdstanr")
  
  ## expected predictions on compositional scale
  epredcomp <- fitted(m2, scale = "response")
  head(epredcomp)
}# }
#> Error: CmdStan path has not been set yet. See ?set_cmdstan_path.