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Let's say we have two nested models. The smaller one (corresponds to $H_0$) has $p_0$ parameters, so its AIC is given by $$AIC_0=-2\log L_0+2p_0$$

The larger model has $p_1:=p_0+d$ parameters of which $d$ parameters are given by $H_0$. For the AIC we have $$AIC_1=-2\log L_1+2p_1$$

$H_0$ is accepted if $AIC_0<AIC_1$ which is equal to $2(\log L_1-\log L_0)<2(p_1-p_0)$. How can I determine the significance level of this test if $p_1-p_0=20$ for example?

user826130
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  • See the answer by glen_b [here](https://stats.stackexchange.com/questions/97257/stepwise-regression-in-r-critical-p-value) – Robert Long Jun 04 '21 at 15:04
  • @RobertLong Thanks. In the answer there he deals with the case $p_1-p_0=1$. He chooses $\chi_1^2$. I have $p_1-p_0=20$. Do I have to pick $20$ degrees of freedom and find out at what percentile $2\cdot20$ lies of a $\chi_{20}^{2}$? – user826130 Jun 04 '21 at 15:17
  • Yes. See [Wikipedia](https://en.wikipedia.org/wiki/Likelihood-ratio_test#General). – Richard Hardy Jun 05 '21 at 17:18

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