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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Can AIC be used to compare an ARMA model to an ARMA-GARCH model?

Suppose I have one time series and two competing models that describe it. Model 1 is ARMA$(p_1,q_1)$, model 2 is ARMA$(p_2,q_2)$-GARCH$(r,s)$. I obtain AIC values of model 1 and model 2. I would ...
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Normalized likelihoods

AIC (BIC) model selection methods are widely used. These methods can select non-nested models unlike likelihood ratio type selection that requires model to be nested. The AIC has definition ...
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45 views

Prediction vs. Explanation and its Effect on Statistical Methods [duplicate]

In layman's terms, what is the difference between predicting and explaining in statistics? I was looking for the differences between AIC and BIC and found this post with an answer stating: My ...
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Number of parameters for AIC for a particular model

I know there have been a few well answered questions on this topic, but i have found myself in a bit of a special case this time. I am using AIC for model selection, and i am having trouble counting ...
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Correlation between predictor variables in an AIC model

I'm using multinomial logistic regression analysis to analyse deer behavioural responses to camera traps based on 7 predictor variables. I have 2 models which are very close together in AIC value ...
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What is the upside of treating a factor as random in a mixed model?

I have a problem embracing the benefits of labeling a model factor as random for a few reasons. To me it appears like in almost all cases the optimal solution is to treat all of the factors as fixed. ...
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Choosing models with similar AIC values [duplicate]

I'm using a multinomial logistic regression analysis to examine deer behavioural responses to camera traps in terms of 7 predictors (both singly and their interactions). I have found that the model ...
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31 views

Understanding output stepAIC

I am using the stepAIC function in R to do a bi-directional (forward and backward) stepwise regression. I do not understand what each return value from the function ...
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27 views

How can I use Akaike's Information Criterion to compare two models of multi-peaked emission spectra?

I have several photoluminescence emission spectra that I am trying to fit curves to. The spectra each have a slight baseline and four peaks. The independent variable $x_i$ is wavelength (converted to ...
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46 views

Is cross validation for validating a model or for selecting best model in different kinds of models?

I am confused about the concept of cross validation and its usage. As I read about cross validation before, it is a way of validating a model. I did cross validation in my project (developing ...
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21 views

Akaike test and random effect model

I am analyzing a panel data (25 years x 30 countries) through OLS, FE, RE and mixed model (xtmixed). The results I get from the LM test and the Hausman show that I have to focus on the RE model. For ...
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14 views

IT-AIC approach for mixed effects model

I was reading around the Information Theoretic-AIC approach of model selection where AIC values are used to select the candidate set of models. I am quite clear on this. My question is this: for ...
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37 views

Model diagnostics for a glmmPQL in R mixed-effects model

Several texts (both online and published books) have been reviewed prior to asking this. What diagnostics are accepted as best practise for a generalised linear mixed-effects model fitted in R using ...
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142 views

AIC, BIC and GCV: what is best for making decision in penalized regression methods?

My general understanding is AIC deals with the trade-off between the goodness of fit of the model and the complexity of the model. $AIC =2k -2ln(L)$ $k$ = number of parameters in the model $L$ = ...
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31 views

Model without endogeneity correction has lower AIC than one with correction

I have two models, one with endogeneity correction (includes correction terms obtained using Heckman) and one without. The correction terms are significant in the second stage model, yet the AIC/BIC ...
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93 views

Unimodal or bimodal data (MATLAB)?

I am trying to figure out what I did wrong or what I could do to get accurate results. I have n vectors of data, and I am trying to decide whether each dataset is unimodal or bimodal. I assumed that ...
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63 views

The 'best' model selected with AICc have lower $R^2$ -square than the full/global model

I have used the R lme function (nlme package) to construct linear mixed models, with a single random effect (as a random intercept) and a varIdent variance structure on a fixed effect (that is a ...
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32 views

Cross-Validation vs. AICc for LASSO

I was working on a research project in which I try to estimate the the individual contribution of a group of regional political leaders to local economic growth. The major challenge is that there is ...
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If summarizing stats from multiple models is it meaningful to report a mean AIC?

I am currently summarizing results from several groups of models. Is it meaningful to report a mean AIC for each group of models? If not then how best to give a summary measure for each model ...
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after using AIC, how to determine the contribution or effect size of a individual covariate?

I am confused and looking for advise. I have found myself in this same situation repeatedly in the last few months. I want to know if covariate X is influential or important. However, I also ...
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55 views

How to refer to AIC model-averaged parameters and confidence intervals

I am writing up results from regression analysis where I used AICc model averaging to arrive at my final parameter estimates. I am wondering how best to refer to these parameters and their 95% ...
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28 views

Choose random structure in LME. Should I rely on AIC?

I want to choose the best random structure for my mixed-effects model. I have compared four models: without a random part, random intercept, random intercept and slope, and random effects: ...
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Does Box-Cox parameter estimation count towards parameters for AIC?

Suppose I have a regression model with e.g. 2 parameters $y = ax + b$ But the data are non-normal so before regressing I transform both sides with Box-Cox estimation. Thus I get two Box-Cox ...
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Meaning of 'number of parameters' in AIC

When computing AIC, $AIC = 2k - 2 ln L$ k means 'number of parameters'. But what counts as a parameter? So for example in the model $y = ax + b$ Are a and b always counted as parameters? What ...
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Possible to calculate AIC from $r^2$, $\sigma$ and/or p-value for $r^2$

As per the heading, is it possible to add AIC to some previously computed models based on the stats I have (which include $r^2$, its p-value, $\sigma$ for each variable individually)? They are all ...
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Model averaging effect sizes of Gamma family GLMs

I'm trying to get some model averaged effect sizes from a set of candidate models, all of them assuming a Gamma error distribution, according to the theory given by the book from Burnham and Anderson ...
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Can you calculate a AIC value using the non-linear maximization (nlm) minimum value in R?

So the formula for AIC is: AIC = 2k - 2ln(L) L is the maximized value of the likelihood function. I'm modeling oxygen data in R using Non-Linear Minimization (nlm) of a maximum likelihood estimation ...
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Different AIC values for the same model using step()?

I'm working with a GLM to try and optimize the model, and there are 152 predictive variables. A LOT of these are not significant, so I'm trying to figure out which ones to remove through use of the ...
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40 views

Different estimated parameters in similar models in R

A particular series (std), seems to exhibit a trend-like behavior. According to the ADF test for this series: ...
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51 views

Comparing AIC among models with different amounts of data

I have a data set with many missing observations for certain parameters (NA values) in it. I have been performing model selection using AIC. Based on AIC scores I have reduce the model to the form ...
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24 views

Where can I find examples of Takeuchi Information Criterion (TIC) at work?

I have been looking for examples of the TIC and couldn't find any. In particular I would like to know how exactly do you estimate the penalty term in TIC. That term consists of, as I found it ...
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40 views

Cannot replicate the AIC in a GARCH model

First I am confused what the ugarchfit in the rugarch package means by likelihood versus loglikelihood. In the complete ...
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30 views

Prerequisites for AIC/BIC model comparison

I have a question about model selection when using AIC/BIC. So, if two model structures are totally different, can I still directly apply AIC and BIC? Also, for a hierarchical model, how to compute ...
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285 views

Step function in R for regression modeling

I have to implement a regression model and i have about 30 variables in the model. Some variables does not have much influence on the model, but i need to use a formulized method for eliminating ...
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82 views

AICc results in R

I used the model: ...
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58 views

StepAIC on glm with interaction terms

I am investigating through logistic regression models the effect of different kinds of genetic variation (in a set of 27 genes), and of the number of genes hit by such variation, on a disease. At ...
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61 views

About logistic regression in R

What I have is a medical data set with several variables, all 0-1 variables. I want to make inference about them with logistic regression. I have a few problems: I have location variables for the ...
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Criteria for model selection for nested models fitted on nested data?

I consider a first model where the 6 observables (concentrations of metabolites) are fitted on the data set (the experimental measure of these 6 concentrations). I also have a second model, that is a ...
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88 views

Model comparison with AIC based on different sample size

Let's assume I have two models M1 and M2: M1: y ~ x1 + x2 + x3 M2: y ~ x1 + x2 + x3 + x4 Since variable x4 has some missing values the sample size of M2 is ...
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68 views

How to obtain predicted values from a gamm() using averaged coefficients (MuMIn)?

I want to extract the predicted values from a gamm() whose coefficients have been averaged using the package MuMIn, but I'm getting an error. ...
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106 views

Difference in AIC and BIC values between sem and lavaan packages in R

I ran the same SEM model in sem and lavaan. I got the same parameters and - generally - very close test values, with the exception of AIC and BIC which were immensely different between the two ...
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34 views

Model selection and parameter estimation in forecasting with a Dynamic Linear Model

I am implementing a general purpose prediction tool for time series. I want to tolerate missing values, so I decided to settle for DLMs. To make it as relevant as possible on a large number of ...
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41 views

Leaps() or AIC for model selection

I am deciding how many predictors to include in my model - I currently have 4. When I use the leaps() function, the smallest value for the residual standard error ...
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17 views

Negative AIC linear regression model [duplicate]

I used the following formula to calculate the AIC: AIC$=n\cdot\log\bigl(\frac{SSE}n\bigr)+2(p+1)$ where SSE is the sum of squared errors, $n$ is the total number of observations and $p$ is the number ...
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How to do external validation of logistic regression models and perform model benchmarking

Quality assessment in trauma has for > 25 years been done with the US derived logistic regression model, the TRISS model. DV: survival/death and IVs: physiologic derangement (continuous), anatomic ...
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1answer
68 views

Model selection for nonlinear regression of a Gaussian CDF mixture distribution

I have a number of distributions which I want to fit to a CDF that is comprised of one or more Gaussian CDFs. I was able to use weighted least squares regression to find the best fit parameters for ...
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1answer
360 views

AIC BIC Mallows Cp Cross Validation Model Selection

If you have several linear models, say model1, model2 and model3, how would you cross-validate it to pick the best model? (In R) I'm wondering this because my AIC and BIC for each model are not ...
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181 views

Equivalence of AIC and p-values in model selection

In a comment to the answer of this question, it was stated that using AIC in model selection was equivalent to using a p-value of 0.154. I tried it in R, where I used a "backward" subset selection ...
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164 views

Sparse parameters when computing AIC, BIC, etc

I'm designing large-scale, regularized logistic regression models with lots of sparse, binarized features. e.g. isUS, isFR, etc. As a result, a lot of the weights in the model are zero. I'm wondering ...
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Model selection with Firth logistic regression

In a small data set ($n\sim100$ ) that I am working with, several variables give me perfect prediction/separation. I thus use Firth logistic regression to deal with the issue. If I select the best ...