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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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. ...
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48 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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9 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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31 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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24 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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149 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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125 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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137 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 ...
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50 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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2answers
177 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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55 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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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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24 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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56 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. ...
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52 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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41 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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15 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
82 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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74 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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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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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 ...
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What do I do when values of AIC are low and approximately equal?

Chris Chatfield, whose many quality books and papers I enjoyed reading, in (1) gives the following advice: For example, the choice between ARIMA time-series models with low and approximately ...
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Include specific interaction terms

I have a question regarding interactions in GLM. I run a Poisson regression with the purpose of predicting claims in insurance. I have the following problem : ...
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292 views

AIC guidelines in model selection

I typically use BIC as my understanding is that it values parsimony more strongly than does AIC. However, I have decided to use a more comprehensive approach now and would like to use AIC as well. I ...
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49 views

Bayesian justification for AIC/BIC

Can someone point me to a straightforward and comprehensible Bayesian discussion justifying AIC and/or BIC? Or even better, can someone give a self-contained such discussion in this forum?
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46 views

Computing a multi-sample (i.e., pooled) Akaike Information Criterion

I have a set of multivariate time series observations that I am trying to model using VAR processes, using AIC to choose the best model. However, instead of determining the best model order for each ...
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353 views

Correct number of parameters of AR models for AIC / BIC ?

I have a time series and want to use AIC / BIC to decide which of the following model is most appropriate: A) AR(1), no constant with Gaussian innovation term B) AR(2), no constant with Gaussian ...
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56 views

AIC and BIC for Support Vector Machine inside e1071

After training a support using the e1071 package of R, how can I calculate an information criterion such as AIC or BIC?
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180 views

When is it appropriate to select models by minimising the AIC?

It is well established, at least among statisticians of some higher calibre, that models with the values of the AIC statistic within a certain threshold of the minimum value should be considered as ...
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77 views

Using AIC to test the direction of causality

I would like to ask the opinion of this community in regard to the following discussion between me and my colleague. The case is this: we have two variables, let's call them Y and X. The AIC of a ...
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56 views

Select a formula-based model by AIC

Let's say I want to investigate if there is any correlation between the response (continuous) variable individual_fish_size and the three explanatory (continuous) ...
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38 views

Information theoretic alternative to hypergeometric test

Is there any information-theoretic alternative to the hypergeometric test (or Fisher's exact test)? In other word, is it possible to calculate AIC values for data which one would classically analyse ...
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44 views

The number 2 in Deviance

What is the additional coefficient 2 in AIC, or other deviance criteria? In the books or on the internet I keep reading "historical reasons". What the heck are those historical reasons? Is there a ...
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2answers
121 views

Correct use of AIC

It is well known that the AIC can be used to compare nested models. Additionally, I believe I am correct in saying that you can also use the AIC to compare non-nested models on the same dataset ...
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119 views

Is AIC appropriate for model selection when the parameters are fitted by least-squares rather than MLE

I want to compare the fit of a linear model (M1) and nonlinear model (M2): M1: $y = b_0 + b_1x_1 + b_2x_2 + b_3x_1x_2 + \epsilon, \epsilon \sim N(0, \sigma^2)$ M2: $y = b_0 + b_1x_1 + b_2x_2 + b_1 ...
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228 views

Generalized linear mixed models: model selection

This question/topic came up in a discussion with a colleague and I was looking for some opinions on this: I am modeling some data using a random effects logistic regression, more precisely a random ...
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149 views

Can I compare AIC values of a linear function with a non-linear function?

Can I compare AIC values of a linear function with a non-linear function? Because I get totally different results. One is 4000 other the 6000000. Estimation is done on the same data setvariables.
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456 views

Are models identified by auto.arima() parsimonious?

I have been trying to learn and apply ARIMA models. I have been reading an excellent text on ARIMA by Pankratz - Forecasting with Univariate Box - Jenkins Models: Concepts and Cases. In the text the ...
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177 views

Correct definition of number of parameters $K$ in Akaike Information Criterion

What is the term $K$ in Akaike information criterion? The AIC is defined as $2K-2log(L)$, where $L$ is the maximized value of the likelihood function for the estimated model. On the internet, I found ...
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76 views

Herbivore density and group density modelling: Poisson GLM that overfits the data, or higher ranked negative binomial model that underfits the data?

I am an ecologist that has counted 11 different species of herbivores in about 110 blocks of two habitat types over 18 months, and I am interested in predicting the density across the study area from ...
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45 views

Rescaling AIC values to select the model

I have a set of 492 observations that I fit between a exponential or a logarithimic curve. Both curves share the same amount of explanatory variables. My question lies on, to use the rule of thumb ...
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1answer
175 views

Huge ΔAIC between GAM and GAMM models

I'm working with spatial fisheries catch data and environmental variables, and I'm correlating the abundance in the catch to some oceanographic parameters. I'm using a Generalised Additive Model (GAM) ...
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147 views

How to choose between two competing linear models?

I have the following data: ...
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33 views

Model selection with different outcome spaces

My question is about model selection/comparison in the case of discrete outcome spaces and when the number of distinct outcomes depends on the dimension. (For the curious minded, this arises ...
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218 views

Using AIC to select between models that use nested and non-nested variables

I'm using SPSS to try and find a mixed model that adequate explains the data that I have. Two of the explanatory variables are closely related ('Sample group' and 'individual'), as an individual is ...
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156 views

Two different formulas for AICc

Wikipedia's page on AIC gives a formula for the AICc, a "corrected" version of the AIC that helps to avoid overfitting when the sample size is small relative to the number of parameters in the models ...