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 version 4.1.0 (2021-05-18)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.2 LTS
#> 
#> Matrix products: default
#> BLAS/LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.8.so
#> 
#> 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=C             
#>  [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       
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices datasets  utils     methods   base     
#> 
#> other attached packages:
#> [1] bootGOF_0.1.0.9000
#> 
#> loaded via a namespace (and not attached):
#>  [1] knitr_1.29        magrittr_1.5      pkgload_1.1.0     R6_2.4.1         
#>  [5] rlang_0.4.10      fansi_0.4.1       stringr_1.4.0     tools_4.1.0      
#>  [9] pkgbuild_1.0.8    checkmate_2.0.0   xfun_0.15         cli_2.0.2        
#> [13] withr_2.4.1       htmltools_0.5.0   yaml_2.2.1        assertthat_0.2.1 
#> [17] rprojroot_1.3-2   digest_0.6.25     crayon_1.3.4      processx_3.4.3   
#> [21] callr_3.4.3       ps_1.3.3          testthat_2.3.2    glue_1.4.1       
#> [25] evaluate_0.14     rmarkdown_2.3     stringi_1.4.6     compiler_4.1.0   
#> [29] desc_1.2.0        backports_1.1.8   prettyunits_1.1.1 renv_0.14.0