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Questions tagged [nested-models]

One model is "nested" in another if it is a constrained version of it. Nested models can be compared with a likelihood-ratio test. Use this tag for questions about comparing non-nested models too.

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25
votes
3answers
14k views

Prerequisites for AIC model comparison

What are exactly the prerequisites, that need to be fulfilled for AIC model comparison to work? I just came around this question when I did comparison like this: ...
19
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3answers
14k views

Comparing non nested models with AIC

Say we have to GLMMs mod1 <- glmer(y ~ x + A + (1|g), data = dat) mod2 <- glmer(y ~ x + B + (1|g), data = dat) These models are not nested in the usual ...
13
votes
2answers
10k views

Non-nested model selection

Both the likelihood ratio test and the AIC are tools for choosing between two models and both are based on the log-likelihood. But, why the likelihood ratio test can't be used to choose between two ...
4
votes
1answer
2k views

Comparison of log-likelihood of two non-nested models

I know I can only use the log-likelihoods of two models as selection criterion if they are nested. However, I don't understand this completely. Why isn't it possible to apply this reasoning to non-...
3
votes
1answer
329 views

Can one give an example(s) of when non-nested AIC model comparison is not useful for model selection?

Note: The question here is not the same as this one. Indeed, as an answer to that question the answer below was closed as unrelated, together with the suggestion (credit @gung) to ask a separate ...
61
votes
6answers
108k views

What is the difference between a “nested” and a “non-nested” model?

In the literature on hierarchical/multilevel models I have often read about "nested models" and "non-nested models", but what does this mean? Could anyone maybe give me some examples or tell me about ...
14
votes
1answer
6k views

Likelihood ratio test - lmer R - Non-nested models

I am currently reviewing some work and have come across the following, which seems wrong to me. Two mixed models are fitted (in R) using lmer. The models are non-nested and are compared by likelihood-...
2
votes
1answer
375 views

Tests of Forecast Accuracy for Nested Models

Can anyone explain why "classic" tests of forecast accuracy, (i.e. Diebold-Mariano test, Meese-Rogoff test and Morgan-Granger-Newbold test) are not suited for nested models? I could not find a good ...
12
votes
1answer
3k views

AIC for non-nested models: normalizing constant

The AIC is defined as $AIC=-2 \log(L(\hat\theta))+2p$, where $\hat\theta$ is the maximum likelihood estimator and $p$ is the dimension of the parameter space. For the estimation of $\theta$, one ...
12
votes
2answers
2k views

Why can't likelihood ratio tests be used for non-nested models?

More specifically, why do the likelihood ratio tests have asymptotically a $\chi^2$ distribution if the models are nested, but this is no longer the case for the not-nested models? I understand that ...
1
vote
1answer
187 views

How do you deal with “nested” variables in a regression model? in R

A conceptual solution for this scenario has been posted in: How do you deal with "nested" variables in a regression model? Problem is I am having trouble using this solution in R - glm() ...
3
votes
1answer
152 views

Exact equivalence of LR and Wald in linear regression under known error variance

Is it true that the LR statistic and the Wald statistic are numerically equivalent when testing a nested hypothesis in a linear regression when the error variance is known? Hence, is a squared t-...