To install this github version type (in R):
##if devtools is not installed yet:
## install.packages("devtools")
library(devtools)
install_github("livioivil/flipscores")J Hemerik, JJ Goeman and L Finos (2019) Robust testing in generalized linear models by sign-flipping score contributions. Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 82, Issue 3, July 2020, Pages 841–864.
https://doi.org/10.1111/rssb.12369
R De Santis, J Goeman, J Hemerik, L Finos (2022) Inference in generalized linear models with robustness to misspecified variances arXiv: 2209.13918.
https://arxiv.org/abs/2209.13918
library(flipscores)
set.seed(1)
dt=data.frame(X=rnorm(20),
Z=factor(rep(LETTERS[1:3],length.out=20)))
dt$Y=rpois(n=20,lambda=exp(dt$X))
mod=flipscores(Y~Z+X,data=dt,family="poisson",x=TRUE)
summary(mod)
#>
#> Call:
#> flipscores(formula = Y ~ Z + X, family = "poisson", data = dt,
#> x = TRUE)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -1.6910 -0.5792 0.1012 0.4900 1.0440
#>
#> Coefficients:
#> Estimate Score Std. Error z value Part. Cor Pr(>|z|)
#> (Intercept) -0.1026 -0.7229 2.7127 -0.2665 -0.088 0.7460
#> ZB -0.1501 -0.7125 2.1789 -0.3270 -0.104 0.6564
#> ZC 0.1633 0.8106 2.2232 0.3646 0.117 0.6924
#> X 0.9439 16.2062 4.7272 3.4283 0.671 0.0098 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for poisson family taken to be 1)
#>
#> Null deviance: 27.135 on 19 degrees of freedom
#> Residual deviance: 12.888 on 16 degrees of freedom
#> AIC: 57.459
#>
#> Number of Fisher Scoring iterations: 5
# Anova test
anova(mod)
#> Analysis of Deviance Table (Type III test)
#>
#> Model: poisson, link: log
#>
#> Inference is provided by FlipScores approach (5000 sign flips).
#>
#> Model: Y ~ Z + X
#> Df Score Pr(>Score)
#> Z 2 0.77184 0.6984
#> X 1 0.02977 0.0098 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# or
mod0=flipscores(Y~Z,data=dt,family="poisson",x=TRUE)
anova(mod0,mod)
#> Analysis of Deviance Table (Type III test)
#>
#> Model: poisson, link: log
#>
#> Inference is provided by FlipScores approach (5000 sign flips).
#>
#> Model 1: Y ~ Z
#> Model 2: Y ~ Z + X
#> Df Score Pr(>Score)
#> Model 2 vs Model 1 1 0.029586 0.0108 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# and
mod0=flipscores(Y~X,data=dt,family="poisson")
anova(mod0,mod)
#> Analysis of Deviance Table (Type III test)
#>
#> Model: poisson, link: log
#>
#> Inference is provided by FlipScores approach (5000 sign flips).
#>
#> Model 1: Y ~ X
#> Model 2: Y ~ Z + X
#> Df Score Pr(>Score)
#> Model 2 vs Model 1 2 1.4245 0.5244
set.seed(1)
D=data.frame(x=(1:40)/20, z=rnorm(40))
D$y=rnbinom(40,mu=exp(D$x),size=3)
library(MASS)
mod_par=glm.nb(y~x+z,data=D, link="log")
summary(mod_par)
#>
#> Call:
#> glm.nb(formula = y ~ x + z, data = D, link = "log", init.theta = 7.972747099)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -2.0746 -0.7748 -0.1086 0.4617 2.0435
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.15365 0.29358 -0.523 0.601
#> x 0.92089 0.21481 4.287 1.81e-05 ***
#> z -0.01282 0.13606 -0.094 0.925
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for Negative Binomial(7.9727) family taken to be 1)
#>
#> Null deviance: 61.217 on 39 degrees of freedom
#> Residual deviance: 41.312 on 37 degrees of freedom
#> AIC: 154.29
#>
#> Number of Fisher Scoring iterations: 1
#>
#>
#> Theta: 7.97
#> Std. Err.: 6.95
#>
#> 2 x log-likelihood: -146.286
mod=flipscores(y~x+z, data=D, family = "negbinom")
summary(mod)
#>
#> Call:
#> flipscores(formula = y ~ x + z, family = "negbinom", data = D)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -2.0746 -0.7748 -0.1086 0.4617 2.0435
#>
#> Coefficients:
#> Estimate Score Std. Error z value Part. Cor Pr(>|t|)
#> (Intercept) -0.15365 -1.84162 3.42399 -0.53786 -0.087 0.5808
#> x 0.92089 14.93128 4.42610 3.37346 0.547 0.0014 **
#> z -0.01282 -0.72457 7.24491 -0.10001 -0.016 0.9612
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for Negative Binomial(7.9727) family taken to be 0.9960228)
#>
#> Null deviance: 61.217 on 39 degrees of freedom
#> Residual deviance: 41.312 on 37 degrees of freedom
#> AIC: 154.29
#>
#> Number of Fisher Scoring iterations: 1