# Reporting from a likelihood ratio test

I don't know if this belongs here or in StackExchange, it is a mixed but probably pretty simple question. How do I normally report a Likelihood Ratio Test? I would love a good reference in your answer, I have searched but could not find any good answers.

> glmm0 <- glmer(yngel ~ (1|nest), data, family=poisson(link="log"))
> glmm <- glmer(yngel ~ age.level + (1|nest) + 0, data, family=poisson(link="log"))
> anova(glmm0, glmm)
Data: data
Models:
glmm0: yngel ~ (1 | nest)
glmm: yngel ~ age.level + (1 | nest) + 0
Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
glmm0  2 682.33 689.38 -339.16   678.33
glmm   3 672.37 682.95 -333.18   666.37 11.959      1   0.000544 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


My best guess so far is: I used likelihood ratio test to compare the model with the fixed effect to a model without it. The model including the fixed effect (age-level) was a better fit ($\chi^2(df=?)=11.96$, $p=0.00054$).

And I cannot actually figure out how many df to report from that. The there is 2 for one model and 3 for the other, and 1 between them.

Thank you for your help.

• Any guesses on what the "Chi Df" column is about? – John Feb 13 '14 at 21:13
• "How do I report a likelihood ratio test?" belongs here (though I am not sure where else you meant - here is part of stackexchange; were you referring to stackoverflow perhaps?). The df for the chi-square test is the "1" in the table that's right beside the p-value. – Glen_b Feb 13 '14 at 21:57

## 1 Answer

For a likelihood ratio test, the degrees of freedom are equal to the difference in number of parameters for the two models. In this case, df = 1, and so $\chi^2(1)=11.96$, $p=0.0005$.

• Thanks (+1). If I perform (for consitency) a LRT on linear models (lm) where do I find the χ2 value? Is it the value given under Sum of Sq? – bee guy Dec 22 '17 at 8:29
• You can compare two linear models using the anova() function, so anova(mod1, mod2). The X^2 value is under the "Chisq" column, much like the output in the original question – dmartin Dec 23 '17 at 17:39
• Hi dmartin, I don't obtain a X^2 value when I run anova(mod1, mod2) on linear models (without random effects). This returns an F-statistic. Even if I run anova(mod1, mod2, test = "Chisq"), I don't see a column Chisq, but a column Sum of sq. – bee guy Mar 12 '18 at 8:40
• Is the absolute value of this the difference in sum of squares the X^2 value? – bee guy Mar 12 '18 at 8:46
• I actually think I might have been mistaken, as anova for a chi-square seems to only work with models that return deviance (like glm). You might try something like lrtest for what you want to do: stats.stackexchange.com/questions/6505/… – dmartin Mar 12 '18 at 15:41