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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263 views

How to compare ordered logistic nested models?

Let's say that I have a full and a restricted model that looks like this: ...
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2answers
624 views

Are any pairs of these four structural models nested in another?

Are any pairs of these four structural models nested in another? I think the second-order single factor model is nested in the second-order two factor model (second order single factor model is when ...
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3answers
799 views

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 ...
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1answer
122 views

Are these glm models nested?

I am not able to tell if these two glm models are nested within one another. This is from the "mack" dataset in the R library "gamair". ...
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0answers
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AIC and nested models [duplicate]

There is a related question here but two highly upvoted answers there don't seem to agree with each other, and in any case I wanted to take a different tack. Is AIC useful for comparing: non-nested ...
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1answer
255 views

Why is this nested?

Is it fair to compare two models one with one of the predictors treated as a continuous variable and in the other, you treat it as categorical variable using ANOVA? Can we call the first model nested ...
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0answers
40 views

Comparisons across non-nested regressions

I am interested in two non-nested regressions for the same response, \begin{eqnarray} Y = \beta_{1}x_{1} + \beta_{2}x_{2} + \beta_{3}(x_{1}\times x_{2}) + \epsilon\\ Y = \beta_{1}’x_{1} + \beta_{...
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247 views

Multilevel and clustering with non nested groups

I work on health data. I want to estimate the probability for a patient to have an intervention. I control hospital effects by random effects and patient residence effects by errors clustering. I ...
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0answers
169 views

BIC difference for model selection when models have different (and correlated) predictors

I have a binomial dependent variable Y and two main IVs: A is categorical (5 non ordered levels) and B is continuous. A and B are collinear (I tested the effect of A on B with a linear model, and it ...
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0answers
49 views

Non-nested model with uniquely identifying groups

I'm testing various specifications of linear mixed effects models with lmer() in R. The data are fiscal year firm-level, so ...
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1answer
151 views

Are these models nested?

Are a standard Gaussian and a skew Gaussian nested? I'd say yes, because when we set the skewness parameter $\alpha=0$ in the skew normal we get the standard Gaussian. Also, are the normal/skew ...
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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-...
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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 ...
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1answer
749 views

Is a model nested within itself before collapsing categorical variables?

If I have a model with a categorical variable $X_1=\{0,1,2,3\}$ and a continuous variable $X_2$, and I have a regression model that includes an interaction between $X_1$ and $X_2$, then I decide I ...
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2answers
3k views

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 ...
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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-...
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1answer
210 views

The test statistic in the likelihood ratio test for nested linear models

Imagine that we have a family of probability disributions with p.d.f $f_{\theta}(z)$ where $\theta \in \Theta$. We also know that there is a linear dependence between parameters. As a consequence we ...
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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 ...
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0answers
246 views

Is this a nested model?

I have a dataset with explanatory variable $X$ and response variable $Y$. Besides, there is a two-level factor $S_{j}, j=1,2$. The random error variance might be different between these two strata. I ...
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1answer
320 views

Is this a nested model and can I use the likelihood ratio test?

I have a data set, total_data and I applied a model to it. For instance, the model has one parameter $\beta$, and I calculated the log-likelihood of the fitted model (using maximum likelihood method). ...
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147 views

Non-nested model verification

My questions are two fold: Is there a generally accepted statistic used to compare non-nested, nonlinear models with different numbers of parameters? I'm thinking RMSE, but wondering what other ...
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1answer
444 views

Nested Models for Likelihood Test

If I have a logistic regression model with 3 predictors, $x_1$, $x_2$, $x_3$, and then I remove $x_3$ from my model (left with only $x_1$ and $x_2$), are those models nested? And therefore I can use ...
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0answers
454 views

Davidson-MacKinnon J test vs Cox test for comparing two non-nested models

In library "lmtest" The jtest and coxtest functions are used to see if two non-nested models are equivalent. According to the help function: ...
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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: ...
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0answers
742 views

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 ...
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1answer
1k views

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: ...
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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 ...
13
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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 ...
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6answers
106k 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 ...