Easy Problem: Large N And Half The Variables Are Unrelated
library(GlmSimulatoR)
library(ggplot2)
library(MASS)
#Creating data to work with
set.seed(1)
simdata <- simulate_inverse_gaussian(N = 100000, link = "1/mu^2",
weights = c(1, 2, 3), unrelated = 3)
#Y looks like an inverse gaussian distribution.
ggplot(simdata, aes(x=Y)) +
geom_histogram(bins = 30)
#Setting the simplest model and the most complex model.
scopeArg <- list(
lower = Y ~ 1,
upper = Y ~ X1 + X2 + X3 + Unrelated1 + Unrelated2 + Unrelated3
)
#Run search
startingModel <- glm(Y ~ 1, data = simdata, family = inverse.gaussian(link = "1/mu^2"))
glmSearch <- stepAIC(startingModel, scopeArg)
#> Start: AIC=-209832
#> Y ~ 1
#>
#> Df Deviance AIC
#> + X3 1 33541 -211190
#> + X2 1 33792 -210458
#> + X1 1 33956 -209982
#> <none> 34008 -209832
#> + Unrelated3 1 34008 -209830
#> + Unrelated1 1 34008 -209830
#> + Unrelated2 1 34008 -209830
#>
#> Step: AIC=-211211.7
#> Y ~ X3
#>
#> Df Deviance AIC
#> + X2 1 33327 -211844
#> + X1 1 33489 -211366
#> <none> 33541 -211212
#> + Unrelated3 1 33541 -211210
#> + Unrelated1 1 33541 -211210
#> + Unrelated2 1 33541 -211210
#> - X3 1 34008 -209830
#>
#> Step: AIC=-211849.4
#> Y ~ X3 + X2
#>
#> Df Deviance AIC
#> + X1 1 33273 -212009
#> <none> 33327 -211849
#> + Unrelated3 1 33327 -211848
#> + Unrelated1 1 33327 -211847
#> + Unrelated2 1 33327 -211847
#> - X2 1 33541 -211212
#> - X3 1 33792 -210460
#>
#> Step: AIC=-212009.4
#> Y ~ X3 + X2 + X1
#>
#> Df Deviance AIC
#> <none> 33273 -212009
#> + Unrelated3 1 33273 -212008
#> + Unrelated1 1 33273 -212008
#> + Unrelated2 1 33273 -212007
#> - X1 1 33327 -211850
#> - X2 1 33489 -211367
#> - X3 1 33739 -210616
summary(glmSearch)
#>
#> Call:
#> glm(formula = Y ~ X3 + X2 + X1, family = inverse.gaussian(link = "1/mu^2"),
#> data = simdata)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -2.6856 -0.4742 -0.0887 0.2979 2.3616
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.81192 0.20843 13.49 <2e-16 ***
#> X3 3.03191 0.08116 37.36 <2e-16 ***
#> X2 2.05731 0.08101 25.40 <2e-16 ***
#> X1 1.02594 0.08067 12.72 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for inverse.gaussian family taken to be 0.3335926)
#>
#> Null deviance: 34008 on 99999 degrees of freedom
#> Residual deviance: 33273 on 99996 degrees of freedom
#> AIC: -212009
#>
#> Number of Fisher Scoring iterations: 5
rm(simdata, scopeArg, glmSearch, startingModel)Looking at the summary, the correct model was found. Stepwise search worked perfectly!
