bootGOF

Bootstrap based goodness-of-fit tests for (linear) models. Assume you have fitted a statistical model, e.g. classical linear model or generalized linear model or a model that follows Y = m(β^⊤X) + ϵ. This package allows to perform a rigorous statistical test to check if the chosen model family is correct.

Example

First we generate a data-set in order to apply the package.

set.seed(1)
N <- 100
X1 <- rnorm(N)
X2 <- rnorm(N)
d <- data.frame(
  y = rpois(n = N, lambda = exp(4 + X1 * 2 + X2 * 6)),
  x1 = X1,
  x2 = X2)

Note that both covariates influence the dependent variable Y. Taking only one of the covariates into account obviously leads to a model family that is not correct and the GOF-test should reveal that:

fit <- glm(y ~ x1, data = d, family = poisson())

library(bootGOF)
mt <- GOF_model(
  model = fit,
  data = d,
  nmb_boot_samples = 100,
  simulator_type = "parametric",
  y_name = "y",
  Rn1_statistic = Rn1_KS$new())
mt$get_pvalue()
#> [1] 0

On the other hand assuming the correct model family should in general not be rejected by the GOF-test:

fit <- glm(y ~ x1 + x2, data = d, family = poisson())
mt <- GOF_model(
  model = fit,
  data = d,
  nmb_boot_samples = 100,
  simulator_type = "parametric",
  y_name = "y",
  Rn1_statistic = Rn1_KS$new())
mt$get_pvalue()
#> [1] 0.61

…

Installation

You can install it from CRAN

install.packages("bootGOF")

or github

devtools::install_github("MarselScheer/bootGOF")

Tests

After installing the package you can execute the unit tests of the package in your environment by calling:

library(tinytest)
tinytest::test_package("bootGOF")

sessionInfo

sessionInfo()
#> R Under development (unstable) (2025-08-19 r88650)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.2 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices datasets  utils     methods   base     
#> 
#> other attached packages:
#> [1] bootGOF_0.1.1
#> 
#> loaded via a namespace (and not attached):
#>  [1] digest_0.6.37     desc_1.4.3        backports_1.5.0   R6_2.6.1         
#>  [5] fastmap_1.2.0     xfun_0.53         knitr_1.50        htmltools_0.5.8.1
#>  [9] rmarkdown_2.29    cli_3.6.5         renv_1.1.5        withr_3.0.2      
#> [13] pkgload_1.4.0     compiler_4.6.0    rprojroot_2.1.0   tools_4.6.0      
#> [17] pkgbuild_1.4.8    checkmate_2.3.3   evaluate_1.0.4    yaml_2.3.10      
#> [21] rlang_1.1.6