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, model selection and variable scale

In looking at the formula for the AIC=-2*(LL)-2k and the formula for log likelihood, LL=-n/2*log(2*pi) - n/2*log(sse/n) - n/2, I notice that the term with sse is sensitive to the scale of the ...
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AIC for multiple nonlinear regression models

How do we got about using AIC for multiple nonlinear regression models ? For example: If i have a dataset with N instances, and they can be explained by a collection of 3 models where each model has ...
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Can I compare different estimations approaches with AIC?

I'm running two different panel models. Model 1 is a Random Effects regression estimated using Maximum Likelihood and bootstrapped standard errors. Model 2 has the same main dependent variables and ...
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Is it appropriate to compare two different estimation approaches using AIC?

validated folks, I've got a panel data regression model I am estimating using both random effects and a spatial maximum likelihood approach. Same regressors and DV, same data -- but different ...
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12 views

Computing weighted AIC scores [duplicate]

I am trying to compute the weighted AIC using the example posted here as a basis: $$ w_i = \frac{e^{(-0.5\mathsf{\Delta}_i)}}{\sum_{r=1}^Re^{(-0.5\mathsf{\Delta}_i)}}. $$ where ${\Delta}_i$ is the ...
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can AIC be used to compare the fit of a single function and mixture model

I am trying to model a nonparametric probability density function with a continuous function or a mixture model, I am doing this with the R GAMLSS package. Given that a single function may have 4 ...
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30 views

Proper use of model inference (AIC) (Burnham and Anderson) - when to explore more models

I am starting an analysis, for which I have a binomial response variable (species relative abundance) and continuous predictors (habitat variables). I have done some data exploration, and there is ...
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2answers
17 views

Applying Akaike Information Criterion on collection of Gaussian fits

I am trying to apply Akaike Information Criterion on a collection of Gaussian mixtures fitted on some data points. My question is, can I use AIC even if the number of components of Gaussian mixtures ...
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72 views

How to fit piecewise constant (or step-function) model and compare to logistic model in R

I have x, y data where x is position (along a transect) and y is a continuous variable (e.g. temperature). ...
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1answer
83 views

Model selection and performance evaluation with different sample sizes

Suppose there are K experimental units. Each unit is associated with its own dataset consisting of 400 observations. For each unit, we set up a two-sample test, 200 vs 200. Because of a large sample ...
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28 views

Correct way to compare regression models where dependent variable is euclidean distance

I am working on a psycholinguistics problem. I am modelling the response of perceived "goodness" (as assessed by human listeners providing their judgements on a 1-5 scale) of different collections of ...
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1answer
26 views

Using LOOCV, AIC for Weighted Multiple Regression Model Selection?

I am currently attempting to determine the most predictive weighted multiple linear regression model to use and am trying to figure out the best combination of variables to use in the model. My first ...
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45 views

When to choose which model for time series?

What are the applications of AR and MA model? To put my question exactly, when to use AR model and when to use MA model(for example, like when it is seasonal or when there is a trend, etc). In other ...
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43 views

TIC criterion for normal regression model

I'm looking for the application of the TIC criterion in r. The TIC is an adaptation of the AIC criterion where the penalty term is replaced by the trace of the score and the Fisher information matrix ...
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1answer
43 views

Reasons for EGARCH(1,1) producing higher/worse AIC/BIC than GARCH(1,1)

I am using the log returns of 3 different stock indices. Two of them show improvements in AIC/BIC critereon when I fit EGARCH(1,1) in comparison to GARCH(1,1). One does not. Assuming that estimation ...
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1answer
34 views

Comparabilty of BIC, AIC and ICL from Mclust. HDclassif and fem objects

I have a question regarding the way BIC, AIC and ICL are computed in the packages mclust, HDclassif and fisherEM. Both of these packages use the negation of AIC, BIC, ICL (bigger is better). This is ...
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49 views

AIC/BIC score on summary object in R

I have a fixed effects model in R where I need to use Newey-West standard errors and use the AIC score to compare models. ...
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20 views

Data Assumptions for AIC model comparisons

I recently started digging into statistical information criteria, more specifically the Akaike Information Criterion. As the literature I have read so far does not cover this, I was wondering whether ...
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1answer
127 views

Lag selection for Augmented Dickey Fuller test

Apologies in advance, I am a beginner so these questions might be quite simple. I am testing log real exchange rates for unit root stationarity for EU15 countries. I was wondering what is the best way ...
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31 views

Modeling different lag structures

I know there are various information criteria that can be used to compare model specifications, including those with different lag structures. I can easily compare the Akaike Information Criterion ...
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1answer
19 views

Duplicate AICc values for multiple models with interactions

I am going through a model selection process with a mixed-model with 3 variables: A, B, and C. B and C are orthogonal factors. B or C may interact with A, so my full model would be: fixed: ...
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51 views

ARX model selection

I have an autoregressive model with exogenous variables: $S_{t} = \sum_{i=1}^{p} a_i S_{t-i} + \sum_q \sum_{i=1}^{r} b^q_i X^{q}_{t-i}$ where $S_t$ is the signal I want to predict and $X^q_t$ the ...
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74 views

Can you compare different functional models using Akaike criterion?

I have two regression models. One is a simple linear regression model ($y$ is regressed on $x_i$'s), while the other is a double log model (log of $y$ is regressed on log of the $x_i$'s). They have ...
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22 views

Using QIC in glm (geeglm) when there is a warning of glm.fit: fitted probabilities numerically 0 or 1 occurred

I am using geepack in R to look for the best model for my data. I run the gee function with family=binomial(link="logit"). From the results I use QIC to find the ...
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Should information crtieria be applied to training or validation data?

Information criteria for selecting models seem to be applied to training data in general. Could they also be applied to validation data to decide the most predictive and simple model, or is this ...
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23 views

negative AIC or positive AIC? [duplicate]

I have calculated AIC by using R-studio to compare models. However, I got the following both negative and positive AIC AIC 8.52 0.41 -7.70 -5.84 -3.84 -2.10 Should I select the negative AIC or ...
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R: Why does step function of a Linear Modegives different AIC/BIC than AIC function?

I don't understand what I make or think wrong, but if one tries to evaluate the linear model of the data (which you can find in R in the Package AIC(stats)), then ...
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21 views

BIC for Bayesian ANOVA

I am doing a Bayesian ANOVA as follows: BIC0 = -2 * logLik0 + k0 * log(N) # null hypothesis BIC BIC1 = -2 * logLik1 + k1 * log(N) # alternate hypothesis BIC ...
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244 views

Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. ...
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43 views

Information criteria for ARIMA model: missing log-likelihood for null model

I am trying to fit an ARIMA model on the time series of exchange rate. I have tried several kinds of ARIMA specifications (MA(1), MA(1,2), ...) and I am evaluating the particular setting according to ...
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39 views

Does AIC require the residuals of the model to be normally distributed?

Does AIC require the residuals of the models to be compared to be normally distributed?
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87 views

GLM model selection using AICc with Tweedie distribution

I have two questions regarding use of Tweedie GLM in R. I am new in using this distribution and despite a thorough search on different forums, I could not find my answers. I am now running several ...
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45 views

Comparing logistic model predictive ability with same sample but different IV

I would like to compare two logit models. Both models use the exact same sample (1 - pass a test and 0 - fail a test). The first model will use one IV (IV1) and the second model will use a different ...
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Sampling from a set of non-nested models

Consider a collection $\mathcal{M}$ of $m$ different model classes $\mathcal{M} = \{M_1,\dots,M_m\}$, where each model class has a parameter set $\Theta_i$, $i=1,\dots,m$. The model classes are not ...
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76 views

When AIC and Adjusted $R^2$ lead to different conclusions

I hope it's okay to ask theoretically driven R questions here. R has given me the following results from my 'tournament of models'. All models are entirely distinct except from 3 basic control ...
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55 views

Multiple linear regression: does BIC drop (vaguely) collinear variables?

Say I have the following multiple linear regression: Y ~ X1 + X2 + X3 + X4 All X variables are independent, but X1 and X2 look kind of linearly related when ...
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30 views

How do I interpret which model is the best fit for my distribution (AIC)?

I'm new here so looking for some guidance; How do I interpret the following variables to understanding which model is considered the best fit to my distribution. ...
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34 views

Akaike information criterion for categorical and numerical data

How should I compute AIC for categorical and for numeric variables in classification problems? I see in Chapter 6 of Zumel and Mount that they use AIC before they train classification algorithms ...
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35 views

Alternative to AIC for feature selection in classification

I want to know what are the most common methods for feature selection in classification problems (binary and mutli-class). I see in Chapter 6 of Zumel and Mount that they use AIC before they train ...
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How to apply AIC to a situation where the mean of a multivariate normal is a 0-1 d-dimensional vector with exactly k 1's

I am trying to apply AIC to estimate mean in the following case: Let us consider that I have $n$ random variables $X_1, \ldots, X_n$, drawn i.i.d. from a normal distribution of mean $\mu\in\{0,1\}^d$ ...
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101 views

Model selection: can I compare the AIC from models of count data between linear and poisson models?

I am modeling count data (with offset / exposure parameter). My modeling strategy is use of a Poisson model and a negative binomial regression model. I compare model AICs, which are about -760 for my ...
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136 views

AIC versus cross validation in time series

I am interested in model selection in a time series setting. For concreteness, suppose I want to select an ARMA model from a pool of ARMA models with different lag orders. The ultimate intent is ...
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172 views

Selecting the number of mixtures / hidden states / latent variables

My question is regarding Gaussian Mixture models, Hidden Markov models (HMM) or any type of clustering or latent variable model, for which we can devise a likelihood function. Specifically, I train a ...
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1answer
330 views

Interpretation of (scale of) AIC, AICc and BIC when comparing different models

I'm trying to fit a model to a time series, but I am pretty confused as to which is the best. I'm looking at an arima model, and ets model and an stlf model, which each performed best within their ...
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70 views

Why would the residuals from these two models result in the wrong AIC being calculated?

We run two linear regressions, Model 1 and Model 2. The residuals from these two models are plotted against the predicted values. If I understand correctly, the AIC from these two models would be ...
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AIC/BIC values keeps falling as I add more and more lags. How do I select the appropriate lag length?

I am trying to minimize the values of the Akaike and Bayesian Information Criteria to figure out the optimal lag structure for my ARDL error correction model. I am using Stata to run my analysis and ...
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41 views

Parameter Estimation vs Inference Error

I am having trouble reconciling (or maybe even understanding properly) the following issues: We have a dataset. We hypothesize a functional form for probability density. Then we estimate the ...
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GLMM with 2 insignificant variables has lower AIC or BIC compared to same model without those variables…?

Background This post has been heavily edited from its previous version (three months ago). I am investigating habitat selection of 35 territorial wolves over several years of denning seasons (41 ...
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comparing $R^2$ across two data sets

I have a set of covariates that characterize the type of experience a worker has (industry experience, general management experience, etc), and I am regressing compensation on these measures of ...
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250 views

Fixed term is “(Intercept)” --Dredge function

I'm currently building a glmer model for a resource selection analysis. See code below: ...