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Goodness-of-fit test for GLM

Source: R/gof.R
gof_test.glm.Rd

Debiased score test for goodness of fit of GLM.

Usage

# S3 method for class 'glm'
gof_test(
  object,
  hunt.style = "optimal",
  hunt.method = "grf",
  hunt_fun = NULL,
  trim.outlier.hunt = TRUE,
  X.cols.exclude = NULL,
  splits = c(0.5, 0.5),
  arg.hunt_fun = NULL,
  predict_fun_alt = NULL,
  verbose = FALSE,
  ...
)

Arguments

object

Fitted glm object.

hunt.style

Hunting algorithm with the following options.

  • 'optimal': optimal hunting (default). See hunt_optimal.

  • 'wls': a simpler hunting using weighted least squares, which can be less powerful. See hunt_wls.

  • 'vanilla': a basic hunting; not recommended unless unable to fit an alternative model with weighted least squares. See hunt_vanilla.

hunt.method

Built-in method for hunting. Currently available:

  • 'grf': regression forest from package grf.

When this is set to any other value, arguments hunt_fun, arg.hunt_fun and predict_fun_alt are used to specify a customized hunting method.

hunt_fun

Default NULL. When hunt.method is not set to a built-in method, this is a customized function for hunting. When hunt.style is 'optimal' or 'wls', this function must have signature hunt_fun(y, X, w, ...) that returns a fitted alternative model \(\hat{g} \in \mathcal{G}\) via weighted least squares, i.e., by minimizing \(\sum_i w_i (y_i - g(x_i))^2\); otherwise, for 'vanilla' hunting, this function must have signature hunt_fun(y, X, ...) that returns an alternative model fitted in any fashion. The returned object g must support predict_fun_alt(g, X) for evaluation.

trim.outlier.hunt

If TRUE (default), extreme values produced by the hunted function will be trimmed using Tukey's IQR rule.

X.cols.exclude

Columns in stats::model.matrix(object) to be excluded when hunting for alternative signal. Default NULL.

splits

Numeric vector of length 2 or 3 giving the relative sizes of the sample splits; rescaled internally to sum to one. Default is c(0.5, 0.5), which splits data into two halves for hunt and test respectively. Though typically unnecessary in practice, one can also specify a 3-way split for hunt, debiasing and test respectively.

arg.hunt_fun

Extra arguments (default NULL) passed to the customized hunt.fun.

predict_fun_alt

When a customized hunt.fun is used, this is a function with signature predict_fun_alt(fit, X) returning a numeric vector of predictions from a fitted alternative model produced by hunt_fun().

verbose

Default FALSE; information is printed if set to TRUE.

...

Unused; present for S3 generic/method consistency.

Examples

 set.seed(42)
 n <- 500
 X <- matrix(rnorm(n * 3), nrow = n)
 # log(E[y]) ~ X well-specified
 y0 <- 5 * exp(X[,1] + X[,3]) + rnorm(n) * 3
 fit.0 <- glm(y0 ~ X, family = gaussian(link = "log"), start=rep(1,4))
 gof_test(fit.0)
#> Debiased score test: 
#> y ~ X, with X consists of (Intercept), X1, X2, X3.
#> (hunt.style = optimal, hunt.method = grf)
#> n = 500, two-way split: hunt = 250, debias & test = 250
#> 
#> T = -0.2426, p-value = 0.595837
 # log(E[y]) ~ X misspecified
 y1 <- y0 + exp(6 * cos(X[,1]/6)^2) / sqrt(n)
 fit.1 <- glm(y1 ~ X, family = gaussian(link = "log"), start=rep(1,4))
 gof_test(fit.1)
#> Debiased score test: 
#> y ~ X, with X consists of (Intercept), X1, X2, X3.
#> (hunt.style = optimal, hunt.method = grf)
#> n = 500, two-way split: hunt = 250, debias & test = 250
#> 
#> T = 9.0599, p-value = 6.53019e-20