# 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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### AIC vs. p-values for coefficients of an ARIMA model

Do the p values associated with ARIMA coefficients have any significance attached to them? For example, can it happen that for an ARIMA(2,0,0) model the lag 2 coefficient is significant as indicated ...
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### Explain asymptotic optimality property of AIC (Akaike information criterion)

I am trying to use AIC in my research, I know how to apply it and how to interpret its value, but I do not understand the asymptotic optimality property in general and why AIC has this property. Can ...
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### Can I do model selection comparing model computed using aov and lmer?

I am interested in model selection and wonder if it is appropriate to compare an anova (generated using aov) to a linear mixed model (generated using lmer) using AIC?
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### How to compare nonlinear regression vs piecewise linear regression?

We have time series of plant growth (length vs time) and we can reasonably model these with two approaches: With a nonlinear model length(time)=length0*exp(r*time) where length0 is lenght at initial ...
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### Should I compare two models using AIC?

I calculated duration (IV) in seconds using two different ranges (0 to 5s and 0 to 10s). The aim was to find out which range contributes to higher word learning outcomes (dichotomous DV). I ...
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### Minimizing AIC for VAR Model Results in Many Insignificant Lags

I have a pair of cointegrated ETF's. Both ETF's track the exact same underlying. SPY and IVV. I am using the vars package in R to build a VAR model and eventually a VECM. When I select the lags ...
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### Dealing with a statistically insignificant variable while AIC decreases when introduced in the survival analysis model selection?

I am new to survival analysis and currently very confused regarding a model selection process (forward stepwise) in cox proportional hazard model. What happens is basically the following step by ...
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### Akaike Information Criterion (AIC) derivation

I am trying to understand the Akaike Information Criterion (AIC) derivation and this resource explains quite well although there are some mysteries for me. First of all it considers $\hat{\theta}$ as ...
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### when selecting an arima model, shouldn't we consider the characteristic roots as well as the AIC?

the Hyndman-Khandakar algorithm for automatic ARIMA modelling searches the model space and looks only on the AICc as its criteria for finding the best model. Shouldn't it also look at the ...
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### Is there an AIC and BIC equivalent for MAP?

I would like to know if there is an AIC or BIC equivalent for maximum a posterior estimation. I'm trying to compare several different models that have been fit using MAP, but I am unsure of the best ...
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### Why can't algorithms avoid overfitting themselves?

So, I understand overfitting (bonus question: precise statistical definition of overfitting?). You don't want to match the noise in your sample. What I don't understand is why this requires a ...
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### Is the final model of backward elimination with AIC ​always​ the same as the final model of forward elimination with AIC?

I have a question: is the final model of backward elimination with AIC ​always​ the same as the final model of forward elimination with AIC? I assume that it is the same result
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### Using AIC/BIC within cross-validation for likelihood based loss functions

For a course I am teaching, I am having my students fit a Gaussian mixture model using MLEs via the EM algorithm to a bivariate dataset. I have asked the students to use use cross-validation to choose ...
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### Regularization via model averaging?

Say you have the model $$\Phi^{-1} \left(y\right)=\beta_0 + \beta_1 x$$ I am interested in adding some regularization, specifically concerning the parameter $\beta_1$, to introduce some "skepticism" ...
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### Calculating Likelihood from misfit?

I am performing a geophysical inversion where the result is an ensemble of models (~400000) with their misfits. I want to calculate the likelihood of each model from the misfit values which is given ...
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### How is Akaike Information Criterion related to Information theory?

How is the Akaike Information Criterion (AIC) related to Information theory ? I mean from the equation (below), it is not at all intuitive how information theory comes into picture. Also is AIC ...
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### Optimal lag-selection in VAR-model in R

Having troubles with the lag specification of a VAR-model. The purpose of the model is to measure orthogonal impulse/response function of oil price shocks on macroeconomic variables, such as GDP-...
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### Estimate quasi AIC for GAM models in R

I am new to R with little statistical backround. I want to built a GAM model which consists of categorical and continuous variables and cross basis matrices(cb). I use dlnm and mgcv packages. So, I ...
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### Model selection Multivariate Regression

I have a question about the construction of a multivariate regression model. I have one major predictor (continuous: IV1) and 3 continuous dependent variables. As we are registering our study on OSF ...
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### Can AIC be used on out-of-sample data in cross-validation to select a model over another?

Following Gelman's 2017 publication entitled "Understanding predictive information criteria for Bayesian models" I understand cross-validation and information criteria (Bayesian information criterion ...
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### Can results for model selection with AIC be interpretable at the population level?

AIC results for model selection are dependent on the sample size. For example if I make this model with a sample size n=100: ...
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### Adding uncorrelated variables to glm increases AIC

I am trying to understand how AIC works. I am using data from this tutorial: https://www.jaredknowles.com/journal/2013/11/25/getting-started-with-mixed-effect-models-in-r ...
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### AIC and BIC values by auto.arima and manual ARIMA

A time series of yearly data, I want to compare the AIC and BIC values by auto.arima and manual ARIMA. ...
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### Is the AIC of an ARIMA model comparable with the AIC of a regression with ARIMA errors?

I already know that models from different "families" cannot be compared through AIC (or other information criteria such as BIC or HQIC), however, I'm not sure about the specific case of ARIMA and ...
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### Help with model averaged parameter estimates with aiccmodavg

I am trying to compute model averaged parameter estimates using modavg from AICcmodavg but I am getting an error I don't understand. Here is an example: ...
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### Optimality of AIC w.r.t. loss functions used for evaluation

Under certain conditions, AIC is an efficient model selection criterion. I understand this roughly as if AIC will tend to select the model that will yield the largest expected likelihood of a new data ...
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### Questions Tags Users Unanswered Connection of the critical value for KS distance and model complexity

I asked a similar question is math exchange, but here it seems to fit better. I wonder about a relationship of the critical value for the KS distance (with Lilliefor correction) and model complexity? ...
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### AIC / BIC for Model Seleciton in Copula Model

I'm trying to select the distributional model of 30 marginals (which are restricted to have the same distributional family) in a copula model. However, I therefore get 30 Likelihood/AIC/BIC values for ...
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### Calculating BIC based on number of parameters in neural network and loss

I have implemented a variational autoencoder. Now, I would like to calculate the Bayesian Information Criterion (BIC) based on the number of parameters in the network and the loss. For example, let's ...
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### Using a AIC ot LRT for a GLM and LMM

I am trying to compare 2 models (a GLMER with a random effect and a GLM with the random effect removed). However, I was told you can't use an AIC for GLM's but I thought you could!?
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### RNN architecture selection by AIC or other methods

I am using recurrent neural netword (RNN) to model a time series. However, I am not sure how should I do the cross-validation for hyper-parameter selection. For other dynamic model, I am using AIC (or ...
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### Can I compare the AIC of gamm models with s(x) and s(x,by=z) predictors?

I am fitting a set of generalized additive mixed models using gamm or gamm4 packages for R, and in particular want to compare the AIC of two models of these forms: mod1 <- gamm(y~s(x), random=~(1|...
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### Test all models possibles is a good manner to choose the “best” model?

I have programmed a function in python to test all possibles linear regression models that I can do with 5 variables. I choose the "best" model in base its AIC and BIC. These models are ...
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### A better (top ranked) model has a much higher deviance in AIC model selection

I have the same number of parameters for the top model but a much higher deviance for that model than some of the lower-ranked models. I don't have any missing values for any of my variables, no ...
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### Glmer Model selection [duplicate]

Bit stuck on how to choose between models. My goal is to evidence the direction of the regression slope (negative shows improvement in a metric, positive shows decline). Models ...
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### Negative AIC values [duplicate]

I have negative AIC values for comparing models and want to know which would suggest a model fits better. I know that smaller values indicate a better fitting model but unsure how this works for ...
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### Can I use the AIC to compare ordered logistic regression models based on different datasets?

I performed ordered logistic regression using the polr() command in R. I did this with the same independent and dependent variable (the X and Y are the same for every model), but the exact data in ...
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### MLE with higher order markov chain model

I am trying to estimate my Markov chain model. I understand that in a standard model, a higher order will lead to overfitting and higher likelihood. Hence, one can use AIC/BIC to find the order of the ...
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### Model selection: Two-Part Mixed Effects Model for Semi-Continuous Data

I have now been studying mixed models for about a month, I am still a pure beginner. I have zero inflated semi continuous dependent variable (yield of trees between two periods). Exploring ...
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### Averaging GLM's based on delta AIC < 2 and using the resulting coefficient estimates with their associated raster to build a predictive raster

I'm trying to construct a predictive spatial raster based on averaged GLM's Not the exact code but an example: mod1 <- glm(c~ x1 + x2 + x3, data=data) mod2 <- glm(c~ x1 + x2, data=data) mod3 &...
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### Code incorrectly determines that a poor fit is a good fit

I'm trying to find the best polynomial fit for a set of data. It calculates the AIC for each polynomial fit of a certain degree, and then chooses the one with the lowest AIC. To my knowledge (which I ...
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### On George Box, Galit Shmueli and the scientific method?

(This question might seem like it is better suited for the Philosophy SE. I am hoping that statisticians can clarify my misconceptions about Box's and Shmueli's statements, hence I am posting it here)....
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### Do I choose the logistic regression model with the better F1 statistic on the validation set or the lower AIC?

I am deciding whether to keep an interaction term in my logistic regression model. If I keep it in, the AIC of the model improves. If I leave it out, I get a better F1 score with my validation set. ...