Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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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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 the mathematical implications of this phrasing?
llama
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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: > uu0 = lm(log(usili) ~ rok) > uu1 = lm(usili ~ rok) > AIC(uu0) [1] 3192.14 >…
Tomas
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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 sense of: a <- glmer(y ~ x + A + (1|g), data = dat) b <- glmer(y ~ x + A + B + (1|g), data =…
user1322296
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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 non-nested models while AIC can?
user7064
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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-ratio tests. In short, here is a reproducible…
user38193
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4 answers

What is the relationship between ANOVA to compare means of several groups and ANOVA to compare nested models?

I've so far seen ANOVA used in two ways: First, in my introductory statistics text, ANOVA was introduced as a way to compare means of three or more groups, as an improvement over pairwise comparison, in order to determine if one of the means has a…
Austin
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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 this follows from the Wilks' theorem, but…
January
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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 usually neglects the constant factor of the density.…
Kawabata
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Does likelihood ratio test control for overfitting?

I have two nested logistic regression models, A and B. A is nested under B. Let's say B has $K$ more features than A. B has a higher log likelihood than A. However the improved likelihood of B is due to the fact that the $K$ features easily overfit…
czxttkl
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Biased estimates when intercept is included in a linear regression

I am simulating 10000 data-sets, each of length 20, that follow an autoregressive model with lag 1, using the following code: set.seed(1) N = 20 n.reps <- 10000 burn.in = 50 total <- N + burn.in x <- matrix(NA, n.reps, total) x[ , 1] <- 0.1 noise…
Matteo Fasiolo
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How the Error() term in aov() decides what goes in which stratum?

I am trying to understand how the principles of nested anova in R, but I am having extreme difficulty with the error term. Imagining the simplest case. I measured plant growth in two places, A and B. Inside place A, I applied treatment w to five…
JMenezes
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What are some of the robustness checks for the likelihood ratio test?

In the application of statistical methods in social science, one usually does a lot of robustness checks. If I got some publishable findings using LRT test by discrimination two theoretical models, what robustness checks can I do? I found this paper…
High GPA
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Linear regression - are my models nested or non-nested?

I’ve got two main groups, which I am comparing, a) rats and b) rabbits. Each group consists of two subgroups – breed 1 and breed 2. Using linear regression, I would need to find out, does a model taking into account the subgroups account for more…
Ina
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Lmer model syntax for a combination of crossed and nested random effects

I'm trying to use the lmer() function in R to specify a particular random effects structure for a model that has four levels: each measurement on a students occurs in one or more groups, and each group occurs in one of several districts. The…
user2363777
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When to use likelihood ratio test vs. incremental F-test in nested nonlinear model selection?

I have two nested nonlinear models and I want to know which provides a better fit to some data. I see descriptions of both the likelihood ratio test and of the incremental F-test (also called the nested F-test or the extra sum-of-squares F-test) but…
Ken Miller
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