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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Calculation AIC without loglikelihood-function

I want to calculate the AIC without calculating the loglikelihood-function (which seems complicated). If the residuals are normally distributed, this can be done, according to wikipedia, as follows: ...
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AIC criterion: definition

I have two questions regarding the AIC criterion : AIC=$2k-2ln(l)$ Where does the number 2 comes from? As we usually minimize it why don't we consider only : $k-ln(l)$. (Maybe I am missing ...
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Exhibit 15.11 Nominal AIC of the TAR Models Fitted to the Log(predator) Series for 1 ≤ d ≤ 4 [migrated]

Using an average temperature data (Y1), I was trying to replicate the R command below as used in Time Series Analysis With Applications in R by Jonathan D. Cryer & Kung-Sik Chan, but I keep ...
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model comparison when alternatives are not all nested within one another

I am running a glmm with three fixed effects: opponent 1 size ("1") opponent 2 size ("2") opponent 1 size - opponent 2 size ("diff") I am unable to run all three variables in the model at once ...
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how to extract AIC(Akaike's Information Criterion) in LAR(Least Angle Regression) in R Studio?

I'm already done in conducting the whole LAR Algorithm using lars() function in R Studio. But my problem is how to extract or use AIC in R Studio for choosing enough the number of variable that will ...
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34 views

Comparing two models

I am interested in comparing two logistic regression models. The two models are nested: model 1 contains all predictors, and model 2 contains all predictors except 1. My goal is to test if removing ...
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29 views

the role of AIC versus p-values in model selection

Let's say you are trying to choose between two models. One has two significant fixed effects. The other includes only one of the two fixed effects from the aforementioned model but has a lower AIC ...
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28 views

Model selection using mean AIC for very huge data sets

I want to select a model which best performs for a very huge data set. However, the data set is too large to calculate a model within reasonable time. If this is the case, is the following a ...
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37 views

Choosing between two parameters in a model

I have a few parameters that are related (let's call them X1 and X2), and I want to use whichever one will provide the strongest model. The model has many other parameters. Would I simply be able to ...
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30 views

AICc and K for categorical factors and interactions

I am new to multimodel inference. I am trying to create a model that has multiple categorical factors and possible interactions. For example say that my model is... Y ~ X1 + factor(X2) + ...
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28 views

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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38 views

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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49 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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25 views

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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33 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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33 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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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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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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59 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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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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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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132 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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83 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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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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122 views

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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72 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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31 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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42 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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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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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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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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33 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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435 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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86 views

AICc results in R

I used the model: ...
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60 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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62 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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96 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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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. ...