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, 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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22 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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63 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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35 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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23 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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1answer
105 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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12 views

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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36 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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25 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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92 views

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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358 views

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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1answer
87 views

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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23 views

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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27 views

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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1answer
60 views

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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38 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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39 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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22 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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1answer
32 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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1answer
17 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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1answer
129 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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1answer
73 views

AICc results in R

I used the model: ...
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47 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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1answer
59 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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12 views

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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1answer
64 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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59 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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1answer
90 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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19 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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133 views

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
59 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
306 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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1answer
166 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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2answers
159 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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153 views

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 ...
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1answer
94 views

Why does the log-likelihood change when a variable is linearly transformed in a hierarchical model?

I ran into (what I think is) an inconsistency when running a random-intercept model (using the lmer function in the lme4 package in R). Here is what I do: I first run a model with a set of ...
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333 views

Calculating AIC “by hand” in R

I have tried calculating the AIC of a linear regression in R but without using the AIC function, like this: ...
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1answer
98 views

AIC values and their use in stepwise model selection for a simple linear regression

The Wikipedia article for AIC says the following (emphasis added): As an example, suppose that there were three models in the candidate set, with AIC values 100, 102, and 110. Then the second ...
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536 views

AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC — Can I use them interchangeably?

On p. 34 of his PRNN Brian Ripley comments that "The AIC was named by Akaike (1974) as 'An Information Criterion' although it seems commonly believed that the A stands for Akaike". Indeed, when ...
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1answer
26 views

SUM of AICc vs SUM of LL and then AICc

I have a technical question concerning calculating AICc for two possible models. For the data set I am working with there are 12 subjects and 10 phases of the experiment. Two different models, a ...
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93 views

Can the Burnham-Anderson book on multimodel inference be recommended?

As motivated by the recent change of the default model selection statistic in the R's forecast package from AIC to AICc, I am curious whether the latter is indeed applicable wherever the former is. ...
2
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1answer
88 views

Corrected AIC (AICC) for k-means

I want to calculate the $AIC_c$ (corrected $AIC$) for k-means to decide on the number of clusters, but there is an overfitting problem that I don't know how to solve. Let's say that I have $n$ data ...
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68 views

Using QAICc with Poisson, or AIC with Poisson lognormal, in information theoretic approach?

I am trying to use an IT approach to analyse some ecological data. I have a mixed model with nested random effects (I'm using glmer in package lme4 in R). I initially fit the model with a Poisson ...
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21 views

Stochastic minimization of AIC criteria

I am trying to choose the relevants parameters for a logistic regression with a huge number of parameters. I don't know the business signification of most of them, but I still have to optimize my ...
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1answer
280 views

Negative values for AIC in General Mixed Model

I'm trying to select the best model by the AIC in the General Mixed Model test. The best model is the model with the lowest AIC, but all my AIC's are negative! So is the biggest negative AIC the ...
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1answer
94 views

When does AIC lose its power to discriminate models?

There are two simple questions at the end, but I think it is also useful to share the background that motivated them. It comes from this question on an unexpected forecast from the fully automatic ...
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38 views

AIC doesn't agree with model checking [duplicate]

I have two glm, one with a gaussian distribution and identity link and one with gamma family and log link. The predictors are the same, the only thing that change is the response that in the gaussian ...
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88 views

comparing AIC and adjusted $R^2$

So, I have a homework assignment in which I'm being asked to compare the fit of two similar models by comparing their $R^2$ and AIC. Both models were run in R, one using the ...