# Questions tagged [aic]

AIC stands for the Akaike Information Criterion, which is one technique used to select the best model from a class of models using a penalized likelihood. A smaller AIC implies a better model.

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### BMA formula with BIC

I am interested in using Bayesian modele averaging as a selection creteria (BMA) vs AIC. I read that BMA is widely implemented in clustering models. Suppose that we need to fit M models to a data and ...
18 views

### AIC-BIC in mixed models

I was reading about mixed models and I am confused about AIC and BIC criteria. My first question is can I use this types to calculate them? AIC=2d-2ln(l) BIC=dln(n)-2ln(l) where d: is the numbers of ...
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### Reporting AIC values for model fits with multiple runs - report the min or the average?

I have a model that I fit with NLL minimization. I fit that model n times with random starting values, to try to avoid local minima. When reporting the results, it seems reasonable to me to report the ...
27 views

### Model comparsion for robust linear mixed models (robustlmm)

I'm currently working on a project where I've fitted 4 robust linear mixed models. However, I've hit a bit of a roadblock when it comes to model selection. I've been using the AIC (Akaike Information ...
1 vote
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### Using step() and car::vif(): order matters?

When fitting linear models and coming up with a plausible one, AIC and VIF are often used. However, I notice that the order in which the methods are used makes a difference on the final model. Should ...
1 vote
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### Is it possible average an information criterion across models?

Is it possible to take the average of information criterion like the AIC? For my model comparison, I have 24 different models. I use 4 different GARCH models each with 6 different distributions for ...
31 views

### Use linear mixed model or linear quantile mixed model for non-normal residuals?

I started with this initial model: m1 <- lmer(response ~ treatment + (1|subjectID), data = data) However, the residuals of the model are heavy-tailed (presumably enough to violate the normality ...
279 views

### Does information criteria (AIC, BIC and DIC...) imply "causality"?

I am interested in finding out the graphical causal structure. Causal Discovery algorithms (e.g., DAG learning) are used to identify potential causal graphs. In score-based causal discovery methods, ...
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### How to manually calculate dAIC (survey design-based AIC) in R survey package

In preparation for fitting some more complicated distributions to survey-weighted data, I am trying to reproduce the $d\text{AIC}$ by hand for a simpler distribution (binomial in this case). I am ...
1 vote
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### Residuals and AIC

AIC is normally calculated using the maximum likelihood, so you must have some probability distribution to work with. But I saw some formulas using the sum of squared residuals or the mean absolute ...
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### What is the correct calculation for AIC corrected (AICc) for a bagged random forest model using the Boston Housing data set? [duplicate]

This question of calculating AIC was answered for a specific linear model here: Calculating AIC “by hand” in R The problem and solution for a linear model are as follows: ...
1 vote
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### Which evaluation metric should I choose? AIC or MSE?

I am currently at a total loss, so I hope someone can point me in the right direction regarding my model selection. The situation I want to create a linear model that best forecasts my data. I am ...
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### Should I calculate a value for the AIC based on a test set or a training set?

I am aware that a question very similar to mine has already been asked here (Should AIC be reported on training or test data?), but some points remain unclear to me. The accepted answer states: On ...
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### Rejection of ADF-test for log returns and AIC selected ARIMA(0,0,0) and ARIMA (0,0,0) with a drift?

I use monthly log returns for some stock portfolios and rejects the null of the ADF-test for both. Hereafter I use AIC to select best fitting models using auto.arima in R. The selected models are ...
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### AIC and BIC Manual Calculations Are a Bit Off From Statsmodels Estimates in Python

I ran a multiple regression using statsmodels. I wanted to verify my understanding of calculations for log-likelihood (ll), AIC and BIC. So I attempted to manually calculate the ll, AIC and BIC for ...
54 views

### Is AIC scale invariant for problems concerning the number of data points in regression?

I am trying to use Akaike Information Criterion with the small sample correction (AICc) as method for determining how many data points to use in a linear approximation of a non-linear function; the ...
1 vote
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### General question on model weighting and averaging

I've had a stats related question I've been wondering for a while, but for which I have yet to find good sources on. I'm aware of things like the Akaike Information Criterion for weighting candidate ...
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### Difference between AICc delta<2 and AICc delta<4 in model.average

I am running a PGLS (Phylogenetic Generalized Least Squares) model selection using the library 'MuMIn' and its functions, see below the code: ...
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### Model Comparison for Overlapping Models (Choosing between the different measurements of the same skill)

I have a large dataset with 15 independent variables. I am interested in investigating the potential interactions between certain independent variables; however, some independent variables measure the ...
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### If I have T observations from a binomial(n,p), how to consistently estimate n and p?

Suppose I have a dataset $\{S_t\}_{t=1}^T$, where $S_t\overset{i.i.d.}{\sim}Binomial(n,p)$, how to consistently estimate $n$ and $p$ using this dataset? It would be great if you could provide a method ...
46 views

### AIC and Adjusted R squared for fixed number of parameters in sequential selection

Suppose we fix the number of parameters used, why do AIC and adjusted R squared give the same combination of variables? Observed from the R leaps package that regsubsets gives only one combination of ...
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### Do AIC improvements make multicollinearity 'worth it'? (and an analagous question about GAM concurvity and fREML)

To what extent is it the case that I can ignore multicollinearity if adding in those terms improves my AIC? Frankly I'm a little rusty on my theory, but I've seen some people suggesting that AIC is a ... 95 views

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### Why is BIC considered consistent (though AIC is mostly used) for large number of observation?

AIC, BIC are the famous criteria for model selection. But many times they show different results. I read in several places that BIC is consistent while AIC is not. And AIC can achieve minimax rate but ... 