Compute Z-residuals for hurdle or count Poisson brms models

Computes Z-residuals for fitted Bayesian hurdle or count models with a Poisson distribution using a brms model with family = hurdle_poisson(). Z-residuals can be calculated for zeros, counts, or the overall hurdle distribution, and can be used for model diagnostics.

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

Usage

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

Arguments

fit

A fitted brms model object for a hurdle or count Poisson outcome.

type

Character string specifying which part of the model to calculate Z-residuals for: "zero" for the hurdle/zero portion, "count" for the truncated Poisson counts, "hurdle" for the full hurdle-Poisson model.

method

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

n.rep

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

Value

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

• type: The requested model component.

• 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.hurdle_poisson.brms() will additionally attach the class "zresid" to the returned object.

Details

A typical implementation:

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

2. Computes the log-PMF and log-CDF for the specified part of the model using the corresponding log_pred_dist_* function, such as log_pred_dist_HP or log_pred_dist_TP.

3. Generates 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_HP, log_pred_dist_TP, post_logrpp, iscv_logrpp, and the S3 wrapper Zresidual.hurdle_poisson.brms().

Examples

if (FALSE) { # \dontrun{
  # Compute Z-residuals for counts
  zres_counts <- Zresidual_hurdle_poisson_brms(
    fit    = fit_hp,
    type   = "count",
    method = "iscv"
  )
} # }