The goal of holi is to provide web applications for higher order likelihood inference.
You can install the released version of ‘holi’ from CRAN:
install.packages("holi")You can install the development version of holi from GitHub with:
# install.packages("devtools")
devtools::install_github("mightymetrika/holi")This is a basic example which shows you how to compare the p-value from stats::glm() and the r* p-value from holi::rstar_glm() when analyzing ‘mtcars’. The holi::rstar_glm() function relies on likelihoodAsy::rstar().
library(holi)
# Fit model
rs_linear <- rstar_glm(mpg ~ wt + hp, .data = mtcars, .model = "linear")
#> get mle .... get mle under the null....
#> start Monte Carlo computation
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
# See results from stats::glm()
rs_linear$fit_glm |> summary()
#>
#> Call:
#> stats::glm(formula = .formula, family = stats::gaussian, data = .data)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 37.22727 1.59879 23.285 < 2e-16 ***
#> wt -3.87783 0.63273 -6.129 1.12e-06 ***
#> hp -0.03177 0.00903 -3.519 0.00145 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 6.725785)
#>
#> Null deviance: 1126.05 on 31 degrees of freedom
#> Residual deviance: 195.05 on 29 degrees of freedom
#> AIC: 156.65
#>
#> Number of Fisher Scoring iterations: 2
# See r* results
rs_linear$fit_glm |> summary()
#>
#> Call:
#> stats::glm(formula = .formula, family = stats::gaussian, data = .data)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 37.22727 1.59879 23.285 < 2e-16 ***
#> wt -3.87783 0.63273 -6.129 1.12e-06 ***
#> hp -0.03177 0.00903 -3.519 0.00145 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 6.725785)
#>
#> Null deviance: 1126.05 on 31 degrees of freedom
#> Residual deviance: 195.05 on 29 degrees of freedom
#> AIC: 156.65
#>
#> Number of Fisher Scoring iterations: 2In this example, the p-value for r* (5.556e-07) is smaller than the p-value for stats::glm() (1.12e-06).
Pierce, D. A., & Bellio, R. (2017). Modern Likelihood-Frequentist Inference. International Statistical Review / Revue Internationale de Statistique, 85(3), 519–541. doi:10.1111/insr.12232