I am trying to understand avnoa
on two logistic regression models. I noticed that the chisq (Chisq
) test and likelihood ratio test (LRT
) are returning the exact same results in this following toy example. Why?
> fit1=glm(am~mpg+hp,mtcars, family = binomial())
> fit2=glm(am~mpg+hp+wt,mtcars, family = binomial())
> anova(fit1,fit2, test="Chisq")
Analysis of Deviance Table
Model 1: am ~ mpg + hp
Model 2: am ~ mpg + hp + wt
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 29 19.2326
2 28 8.7661 1 10.466 0.001216 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> anova(fit1,fit2, test="LRT")
Analysis of Deviance Table
Model 1: am ~ mpg + hp
Model 2: am ~ mpg + hp + wt
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 29 19.2326
2 28 8.7661 1 10.466 0.001216 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Best Answer
The likelihood ratio test is a (type of) Chi-square test.
The documentation for
?anova.glm
says:Plainly, it is just a poor choice of notation. "Chisq" test is more succinctly said to be a likelihood ratio test.