Compute Z-residuals for Poisson brms models

Computes Z-residuals for fitted Bayesian Poisson models. Z-residuals are useful for model diagnostics, including checking fit and overdispersion, and can be calculated using posterior or cross-validated predictive p-values.

This is an internal workhorse for Zresidual.poisson.brms() and is not intended to be called directly by end users.

Usage

Zresidual_poisson_brms(fit, method = "iscv", n.rep = 1, ...)

Arguments

fit

A fitted brms model object for a Poisson outcome.

method

Character string specifying the residual calculation method: "iscv" for importance-sampled cross-validated randomized predictive p-values, "rpost" for posterior predictive p-values, or "mpost" for marginal posterior predictive p-values. Default is "iscv".

n.rep

Integer; the number of replicated Z-residual sets to generate. Default is 1.

...

Further arguments passed to lower-level helper functions.

Value

A numeric matrix of Z-residuals with attributes such as:

• zero_id: Indices of zero outcomes.

• log_pmf: Log-probability mass function values.

• log_cdf: Log-cumulative distribution function values.

• covariates: Model covariates.

• linear.pred: Linear predictor values from the fitted model.

The S3 wrapper Zresidual.poisson.brms() will additionally attach the class "zresid" to the returned object.

Details

The function typically performs the following steps:

1. Extracts the observed response vector from the model data.

2. Computes the log-PMF and log-CDF for the Poisson model using log_pred_dist_pois.

3. Generates randomized or posterior predictive p-values according to the specified method.

4. Converts the p-values to Z-residuals via the negative quantile of the standard normal distribution.

The output is a matrix of Z-residuals with one column per replication.

See also

log_pred_dist_pois, post_logrpp, iscv_logrpp, and the S3 wrapper Zresidual.poisson.brms().

Examples

if (FALSE) { # \dontrun{
  # Compute Z-residuals for a Poisson model
  zres_pois <- Zresidual_poisson_brms(
    fit    = fit_pois,
    method = "iscv"
  )

  # Compute Z-residuals with 2 replicates using posterior predictive p-values
  zres_pois_post <- Zresidual_poisson_brms(
    fit    = fit_pois,
    method = "rpost",
    n.rep  = 2
  )
} # }