Can you use AIC to compare non nested models?

In SEM context, you can use AIC and BIC to compare non-nested models. However, note that there is some disagreement in the literature over the use of AIC for comparing non-nested models, as the original theory by Akaike was worked out for nested models only.

What is the difference between nested and non nested models?

Broadly speaking, two models (or hypotheses) are said to be ‘non-nested’ if neither can be obtained from the other by the imposition of appropriate parametric restrictions or as a limit of a suitable approximation; otherwise they are said to be ‘nested’.

How can you tell if two models are nested?

Basically, if you can get one model by constraining parameters of another, those models are nested. For example, the set of normal distribution models contains an infinite number of nested models, including normal distributions with means of 0, 1, or 99.

When would you use a nested model?

We often use nested models in practice when we want to know if a model with a full set of predictor variables can fit a dataset better than a model with a subset of those predictor variables.

When can you not use AIC to compare models?

You can not compare the two models as they do not model the same variable (as you correctly recognise yourself). Nevertheless AIC should work when comparing both nested and nonnested models.

Can AIC be used to compare different models?

In statistics, AIC is used to compare different possible models and determine which one is the best fit for the data. AIC is calculated from: the number of independent variables used to build the model. the maximum likelihood estimate of the model (how well the model reproduces the data).

What is a nested model in SEM?

A nested model is a model that uses the same variables (and cases!) as another model but specifies at least one additional parameter to be estimated.

How is Vuong test calculated?

The Vuong test is compare the likelihood functions at the MLE between the two models, that is, ∑ i = 1 n [ log ( f 1 ( y i | θ 1 * ) ) − log ( f 2 ( y i | θ 2 * ) ) ] = ∑ i = 1 n [ log ( f 1 ( y i | θ 1 * ) f 2 ( y i | θ 2 * ) ) ] .

What is the difference between two way Anova and nested Anova?

The difference is that in a two-way anova, the values of each nominal variable are found in all combinations with the other nominal variable; in a nested anova, each value of one nominal variable (the subgroups) is found in combination with only one value of the other nominal variable (the groups).

What is nested analysis?

A nested ANOVA is a type of ANOVA (“analysis of variance”) in which at least one factor is nested inside another factor. Note: Sometimes a nested ANOVA is called a “hierarchical ANOVA.” These two terms are often used interchangeably.

What is the difference between two way anova and nested anova?

What are nested models in SEM?

What is the best way to compare two non-nested models?

I have 2 non-nested models which I would like to compare. Both models are based on the same dataset but use different predictors. I know there are multiple tests available to select the “best” method: 1) jtest (Davidson-MacKinnon J test) 2) coxtest (Cox test) 3) encomptest (Davidson & MacKinnon)

What is the best Test to compare two models?

Both models are based on the same dataset but use different predictors. I know there are multiple tests available to select the “best” method: 1) jtest (Davidson-MacKinnon J test) 2) coxtest (Cox test) 3) encomptest (Davidson & MacKinnon) All of the test are described in r for the comparison of non-nested models. However, which test is prefered?

How do you find the difference between restricted and unrestricted models?

The unrestricted model is the one with the additional parameters, in our case, model D. For both models, we calculate the maximized log-likelihood, subtract the one for the unrestricted model from the one for the restricted model and take negative 2 times the difference as the statistic.

How to select between the constrained and the unconstrained models?

If the models are nested in the manner described above, tests such as the F-test for regression analysis and the Likelihood Ratio test can be used to select between the constrained and the unconstrained models.