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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range of possible values and model complexity

I have a prediction model where the likelihood is a function of two components $(A,B)$ $L \sim \bf{A}^\alpha + \bf{B}^\beta$ , where both $\bf{A}$ and $\bf{B}$ are $n\times n$ matrices ($n$ is the ...
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Model Averaging: Standard Error vs Adjusted Standard Error

I'm having trouble understanding when to use Std. Error or Adjusted SE in model averaging (model.avg). What/Why/When to use Adjusted SE? This is my code: ...
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28 views

AIC and nested models

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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Different AIC values for the same SARIMA model in different R packages

I've been trying to run a simple time series model for a data set. My biggest question is when I run the auto.arima model (from package "forecast) for this data set ...
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39 views

logistic regression - class created with non significant coefficients?

I've created an example table (just in order to create a function) with: ...
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AIC on Savitzky-Golay width

I want to use a Savitzky-Golay filter to smooth some data. There is a right width to use based on the data that it is smoothing. A number of papers basically use "eyeball norm" on the parameters but ...
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Likelihood ratio test seems to show little difference between models with AICc difference of 3

I'm running a multinomial logistic regression analysis of the behavioural responses of deer to camera traps using no reaction, reaction and strong reaction as dependent variables and season, camera ...
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Variable selection vs Model selection

So I understand that variable selection is a part of model selection. But what exactly does model selection consist of? Is it more than the following: 1) choose a distribution for your model 2) ...
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Scenario of how to compare models

I have a binary classification problem where the distribution of classes is skewed. I've already trained some scoring models with logistic regression. Now I would like to compare them. How to do this ...
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Is it meaningful to compare a logit and probit model with the same no. of observations and independent variables using AIC and BIC?

For my dissertation i want to show that the logit and probit model produce the same results. So far i've compared the marginal effects, percent correctly predicted and done a scatter plot of the ...
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Does BIC try to find a true model?

This question is a follow-up or attempt to clear up possible confusion regarding a topic I and many others find a bit difficult, regarding the difference between AIC and BIC. In a very nice answer by ...
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Comparing categorical variable importance across groups; zero and one beta regression

I am attempting to compare behavioral responses across two species (one native and one invasive). Predictors run the range of types including continuous (size), discrete (day of trial) and ...
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How can a result from reduced mixed model be insignificant (with smaller BIC and AIC) when the whole model gave significant results

Hi I have made a linear mixed model with a number of covariants that could be relevant to control for. This entire model gave me a significant result. However when I reduce the model, removing the ...
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53 views

Log-likelihood ratio test vs. information criteria for model selection

I am trying to select the model with the best fit among GARCH(1,1), ARMA(2,2) and GJR-GARCH(1,1) models for a time series of log returns. The results from IC (Akaike, Bayesian) and likelihood-ratio ...
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24 views

Justification for AIC/BIC vs F-statistic when using stepwise backward elimination

I note that some stepwise backwards elimination methods use AIC to make the decision about which variables to eliminate, and others use the F-statistic. Why would I use one over the other, and is ...
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1answer
25 views

Using AICc distributions to assess goodness-of-fit and model selection

I have a couple of ordinary differential equation models that I'm trying to fit to time-dependent biological data ($y_n$). One model is more complex than then other as it has more free parameters. I ...
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37 views

Is it inherently invalid to use BIC for model averaging?

If I understand AIC/AICc vs. BIC correctly, AIC presumes that there is no "true" model and that any given model is simply a "best worst approximation". However, BIC presumes that there IS a "true" ...
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17 views

Model comparison: better AIC, but worse Mean Actual/Predicted Response

I have made two regression models using gamma regression, and fitted them to 80% of my data, with the intention of doing out-of-sample analysis on the 20%. Model 2 is just Model 1, with one extra ...
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Usage of AIC for comparing models [duplicate]

Can AIC be used to compare a model with exponential smoothing with linear regressions?
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When should I use AIC instead of cross-validation?

Both can be used to select a best model and both penalize overfitting. However, CV is easier to understand and to apply in practice. Thus, when should I use AIC instead?
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How to decide between quasi-poisson and negative binomial?

I tried quasi-poisson and negative binomial glms on my counted data in R. The estimates are pretty much the same but p-value are different. Quasi-poisson gives insignificant result. NB give ...
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1answer
60 views

Time series model selection: AIC vs. out-of-sample SSE and their equivalence

AIC is frequently recommended as criterion to compare models for time series forecasting. See for example this in the context of dynamic regression models: The AIC can be calculated for the final ...
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23 views

Threshold for AIC for fitting probability distributions to data

I'm fitting probability distributions to my dataset (using Matlab). It is continuous data (later I will probably also face discrete data). I'm ranking the distributions with the corrected AIC score. ...
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73 views

Understanding specifics of glm() model in R

I have been provided a sample logistic regression as follows: ...
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101 views

AIC versus Likelihood Ratio Test in Model Variable Selection

The software that I am currently using to build a model compares a "current run" model to a "reference model" and reports (where applicable) both a chi-squared p-value based on likelihood ratio tests ...
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Why is the AIC different between these two models?

First, let us generate some data: ...
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Higher SIC and lower S.E. of residuals

I used the Schwarz Information Criterion (a.k.a., BIC) and the Akaike Information Criterion (AIC) to select the models for a time series Analysis. AIC got me an ARMA (5,4) and SIC got me ARMA (2,1). ...
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Will AIC become smaller when we add more regressors?

As far as I know, AIC's function is similar to $R^2$, which checks fitness of a model. Will AIC become larger as we simply add more regressors on right hand side of regression? For instance adding ...
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81 views

GLM - which probability distribution to use for abundance data?

I'm fitting a generalized linear model to try to understand how the abundance of a species of freshwater fish varies in response to some environmental variables. I'm using the AIC to choose between ...
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35 views

auto.arima always produces infinite AICs for all MA models, despite being invertible [closed]

I have been fitting ARIMA models to panel data. My goal is to develop a single ARIMA model that explains growth across a number of different regions. To do this, I followed Rob Hyndman's excellent ...
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72 views

Why information criterion (not adjusted $R^2$) are used to select appropriate lag order in time series model?

In time series models, like ARMA-GARCH, to select appropriate lag or order of the model different information criterion, like AIC, BIC, SIC etc, are used. My question is very simple, why donot we ...
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Evaluate information lost of two different estimators using AIC?

I thinking about following issue. I have two type of estimators. 1) The first one is classic glm so the final rate is predicted values from glm. The second estimator use following method. At ...
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46 views

Finite maximum log-likelihood but infinite AIC (bug in R?)

I have a panel data set with binary dependent variable of 20,000 observations and 11 independent variables. I ran a logistic regression with fixed effects and the model returns maximum log likelihood ...
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72 views

auto.arima not giving the best model according to information criteria

I'm using auto.arima to get the best model for the MASS dataset deaths. However, ...
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1answer
45 views

p-values of the coefficients or AIC for model selection in multiple regression

I´ve got two models from a multiple linear regression (A and B, see below) and don´t know which to select. I want to predict a value called AW as good as possible, so I´d like to have the highest r². ...
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Post Model Selection Inference problems - which remedies exist?

Recently, Hannes Leeb from Yale University and Benedikt Pötscher from the University of Vienna have published a series of papers dealing with what they call Post Model Selection Inference problems.* ...
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Different AIC definitions

From Wikipedia there is a definition of Akaike's Information Criterion (AIC) as $ AIC = 2k -2 \log L $, where $k$ is the number of parameters and $\log L$ is the log-likelihood of the model. However, ...
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Combining AIC Scores

I am trying to combine two AIC scores from different parts of a single data set. I have two sigmoidal models that each predict about half of the data (imagine two sigmoidal curves attached end to ...
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substituting zeros in a Gamma regression

I modeled some right skewed data with a Gamma GLM (log link). This is common practice in my field. However, some observations have a value of zero and the Gamma distribution is only defined on the ...
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2answers
73 views

AIC/BIC and data transformation

Can you use AIC/BIC to compare models on untransformed data with models on transformed data (such as log, inverse hyperbolic sine, etc.)? I.e. if a model using logged data gives an AIC = 53.62 and a ...
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How to calculate AIC for multiple participants

I have a number of competing models that I fit separately to each participant's data. What is the correct way to calculate AIC in this case? Can I just write $AIC = 2nk-2\sum_{i=1}^n{LL_i}$, where $n$ ...
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AIC model selection in R. Transform and back-transform parameter estimates (slopes)

I have run an AIC model selection in R, (following Grueber etal 2011 J.Evo.Bio), and standardised my global model to a mean of 0 and SD of 2, using the "arm" package. AICc selection identified 2 ...
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57 views

AIC / BIC alternative in random effect model

I am looking at at panel data set. Hausmann recommends using random effects modeling, I have 3 nested models and Wald believes each step to add information. However, since some of the parameters had ...
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77 views

Using AIC or cross-validated MSE for selecting neural network models for time series prediction

I trained two basic feed-forward neural networks on time series data. The first one uses the observation at time step $t$ to predict $t+1$. Hence, it only has one predictor variable. The second ...
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57 views

Linear Discriminant Analysis for dimensionality reduction - choosing the dimension

I'm using Linear Discriminant Analysis to do dimensionality reduction of a multi-class data. What is the best method to determine the "correct" number of dimensions? Can I use a method similar to PCA, ...
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49 views

Model selection for random effects: can unselected random effects be used as fixed effects?

I am working on a mixed effects model. What I would consider random effects are year, sampling transect, and sampling location. There are multiple collections taken along each transect, and multiple ...
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31 views

Selecting model in GLM logistic with AICc, p-values for best AICc are all insignificant?

I have one potentially causal predictor and a number of covariates that I tested via AICc model selection in logistic GLM. I found that alone, the causal predictor has a low AICc (~19) and a ...
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27 views

Selecting best model in GLM logistic with AICc, p-values for best are insignificant?

I have one potentially causal predictor and a number of covariates that I tested via AICc model selection in logistic GLM. I found that alone, the causal predictor has a low AICc (~19) and a ...
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AIC comparison for models without maximum likelihood

AIC is a popular model comparison measure (despite of its potential shortcomings). I am wondering whether it is legit to compare AIC (or Akaike weights) for models that were fitted without requiring ...
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Interpretation of AIC value

Typical values of AIC that I have seen for logistic models are in thousands, at least hundreds. e.g. On http://www.r-bloggers.com/how-to-perform-a-logistic-regression-in-r/ the AIC is 727.39 While ...