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Residuals from an hbb_fit

Source: R/methods.R
residuals.hbb_fit.Rd

Computes residuals for the hurdle Beta-Binomial model. Two types are supported:

Usage

# S3 method for class 'hbb_fit'
residuals(object, type = c("response", "pearson"), ...)

Arguments

object

An object of class "hbb_fit" returned by hbb.

type

Character string: "response" (default) or "pearson".

...

Currently unused; included for S3 method consistency.

Value

Numeric vector of length \(N\).

Details

"response"

Raw residuals on the proportion scale: \(r_i = y_i / n_i - \hat{q}_i \hat{\mu}_i\).

"pearson"

Pearson residuals standardised by the model-implied standard deviation (count scale): $$ r_i^P = \frac{y_i - n_i \hat{q}_i \hat{\mu}_i} {\sqrt{\widehat{\mathrm{Var}}(Y_i)}}, $$ where \(\widehat{\mathrm{Var}}(Y_i)\) is computed via hurdle_variance using \((n_i, \hat{q}_i, \hat\mu_i, \hat\kappa)\). Under correct model specification, Pearson residuals have approximately mean zero and variance one.

Numerical stability (Pearson residuals)

Several guards are applied to prevent division by zero or NaN:

  • \(\hat\mu_i\) is clamped to \((\varepsilon,\; 1 - \varepsilon)\) where \(\varepsilon = \sqrt{\mathtt{.Machine\$double.eps}}\) (\(\approx 1.49 \times 10^{-8}\)).

  • \(\hat{q}_i\) is clamped to \([\varepsilon,\; 1]\). (\(q = 0\) yields \(\mathrm{Var}[Y] = 0\), making Pearson undefined.)

  • \(\hat{\kappa}\) is clamped to \(\le 10^{15}\).

  • The hurdle variance is floored at .Machine$double.eps to prevent division by zero.

  • Non-finite residuals are replaced with NA and a warning is issued.

See also

fitted.hbb_fit, hurdle_variance

Examples

if (FALSE) { # \dontrun{
fit <- hbb(y | trials(n_trial) ~ poverty + urban, data = my_data)
r_raw     <- residuals(fit)
r_pearson <- residuals(fit, type = "pearson")
hist(r_pearson, breaks = 50)
} # }