I have created two different models that include the same variables but not the same relations between them.

form=status~(A1+A2+  B1 + ... + B10 +  (1 | C))

Mod <- glmer(form, data = dadosesc, family = binomial) 

form1=status~(A1+A2+  B1 + ... +   (B10 | C))

Mod1 <- glmer(form, data = dadosesc, family = binomial) 

A Gaussian log-likelihood is given by

$$ \log(L(\theta)) =-\frac{|D|}{2}\log(2\pi) -\frac{1}{2} \log(|K|) -\frac{1}{2}(x-\mu)^T K^{-1} (x-\mu), $$

$K$ being the covariance structure of your model, $|D|$ the number of points in your datasets, $\mu$ the mean response and $x$ your dependent variable.

We now that AIC is calculated to be equal to $2k - 2 \log(L)$, where $k$ is the number of fixed effects in your model and $L$ your likelihood function.

So to bring it all together the obvious things to remember when using AIC are three :

  1. You can not use it to compare models of different data sets.

  2. You should use the same response variables for all the candidate models.

  3. You should have $|D| >> k$, because otherwise you do not get good asymptotic consistency.

In this case I quoted, could I compare mod1 and mod with AIC or BIC?

If negative, could suggest me any way?



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