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Questions tagged [aic]

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 for Causal Inference

I read a post explaining why the Akaike Criterion cannot be used for deciding if A cause B or B caused A. I'm curious about a more general case of using AIC for causal inference (with observational ...
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3D plot of Akaike Information Criterion (AIC) for suitable ranges of Lˆ and k

Giving that Akaike Information Criterion (AIC) is as follow: How can I Produce a 3D plot of AIC for suitable ranges of Lˆ and k. In other words what could be a suitable ranges of L to try? Moreover,...
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Is it possible that AIC = BIC?

Two well-known (and related) measures of model complexity from statistics are the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). When might AIC = BIC?
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inconsistency in AIC and AICc - null and an alternative model

I have a dataset containing one response variable, and 3 independent variables. There are 6 number of observations. I want to see, in AICc framework, which of these independent variables best explain ...
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Linear Regression, Formula to Calculate AIC based on Residual Sum of Squares + Number of Predictors

In linear regression, suppose I have Residual Sum of Squares, how to calculate AIC from it? ...
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Find (or calculate) log-likelihood value, AIC, and BIC for SUR model (for each equation) with systemfit

I have estimated SUR model with systemfit (R package). With the estimated results, I am trying to get logLik, AIC and BIC for ...
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Interpretation of singularities in AICc and adjusted r-square

Wikipedia states the small sample size AIC for an univariate, linear in paramters mode with normal residuals as: $$ AICc=AIC+2\tfrac{k^2+k}{n-k-1}, $$ where $n$ denotes sample size and $k$ the number ...
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What can I consider to choose between the same model but estimated with different estimators?

I estimated a standard regression equation with ML and GMM. The question is: how can I know which estimator provides the best estimate? (e.g., the GMM is more efficient if errors are not normally ...
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What is the prerequisites “the same dataset” for AIC/BIC?

Let make a example. Suppose I'm doing model selection and my observation data is $Y_{N\times 1}$ and $X_{N\times K}$.(More specify, K=6) Now I have two model, M1 and M2. M1 includes the first ...
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Comparing AIC, BIC and HQC for selection of nested model

I am working with spline regression and in this step what I want to do is to somehow reduce the number of knots by applying backward selection. Technically what I am doing is to delete sequentially ...
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AIC influences by the number of the model parameters

From the different published paper about mixture models, I found that AIC is affected by the number of model components. That is due to the plenty term in ...
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Can I ignore statistical distribution if errors are small

I'm struggling to find the right distribution for my data and only after I know which distribution suits best I wanted to select a certain statistical model. But now I can't find an appropriate ...
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How can I compare parametric and semiparametric survival models?

On a given dataset, I am running a semiprametric Cox proportional hazards model, together with a series of parametric models (Weibul, gamma, lognormal, exponential, etc.). How can I know which is ...
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How can I choose correct variant of ADF test?

Sorry for this question, but I am not sure in this problem. Can I make decision according to AIC, BIC and so on?
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Comparing non-nested GLMMs with AIC

Suppose I want to compare four non-nested models: m0 = lm(y ~ 1) m1 = lm(y ~ x) m2 = lmer(y ~ 1 +(1|A)) m3 = lmer(y ~ x + (1|A)) Can we use AIC to compare ...
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Why do we get the same AIC for different models in a GLMM?

Our problem here described is to interprete the AIC from a GLMM negbin. Our data compose by 2 Categorical variables (Yes/Not), 2 Numerical variables and our random factor, all without any NA. We ...
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Relation between the AIC and the Kullback-Leibler Divergence

I am searching a formal derivation of the Akaike Information Criterion from the Kullback-Leibler Divergence. Can you show me one, or point me toward a book/article in which this is done? Here I set ...
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Extremely large difference in AICs between two models

I am currently fitting a mixed model where I analye longitudinal trends in migration between country pairs (68335 observations nested in 6442 groups). One of the first questions I wanted to have ...
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Generalising AIC results over multiple samples

This is slightly related to my previous question (AIC Calculation using log likelihood) Though, I think now I am actually clear as to what I am asking. I am modelling activity of cells, I have data ...
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Selection optimum polynomial fit

I have fitted polynomial model of orders 1-4. I have three predictors with 7 levels and my response is 400 values from 0.6-0.9, which seems to be bad for information criterions. I am interested in ...
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Is the use of loglik or AIC to compare logit/probit/cloglog models valid?

I would like to know whether I can use AIC, or if the models have the same number of predictors, the log-likelihood, to compare logit vs probit vs cloglog models (fitted for instance with glmer or ...
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AIC Calculation using log likelihood

I have a dataset that has 40 experimental observations of cells' activity, $n=40$, I tested several models using each of these samples. The model can only explain one cell at a time due to variability ...
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Standardizing qualitative variables in R to perform glm's, glm.nb's and lm's [closed]

I want to standardize the variables of a biological dataset. I need to run glm's, glm.nb's and lm's using different response variables but the same explanatory variables. The dataset contains counts ...
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Calculating the relative likelihood with AIC values

I'm using AIC for model selection, and would like to use a relative likelihood measure to quantify how many times a model with minimum AIC (AICmin) fits better than the alternative (with AICi). For ...
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Understanding Intuition for ETS Damping Selection via AIC/BIC

I'm trying to understand how ETS selects whether to use a damped model via information criteria (I'm not sure which of AIC, AICc or BIC are used). I have a time series and I'm comparing two ETS ...
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AIC formula in R vs Python [closed]

I have been trying to calculate a GLM's AIC both in python (package Statsmodels) and R (native glm function). For exactly the same model I get two different AIC estimates. The formula for AIC is: -...
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When to disregard AIC as a criterion in model selection

I have the following problem: I'm working on a dataset and it looks completely quadratic. A quadratic regression fits the data really good. However, when using piecewise linear functions I get a lower ...
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Selecting between OLS regression and ARIMA for time series, why AIC or BIC for ARIMA is much larger in my data?

My data set is quarterly time seires data (around 140 data points). Method 1: simple OLS regression with 5-6 exogenous variables, which are drivers of the dependent variable. None of the explanatory ...
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Better AIC but worse cross validation error rate

I learn that AIC is usually used for assessing goodness of fit of a model and the criterion takes into account both goodness of fit and number of parameters used so that it could regulates the issue ...
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How many candidate models to include in AIC model selection?

Is there a rule of thumb, perhaps related to sample size, for how many models to include in AIC model selection? Too many may seem like fishing while too few would be insufficient. I'm familiar with ...
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Fitting an ARMA-GARCH using AIC

I am trying to fit an ARFIMA(p,d,q)-GARCH(1,1) model to an asset returns time series. I start with an ARFIMA(0,0,0)-GARCH(1,1). The diagnostics tests like persistence requirement, Ljung Box test for ...
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Stepwise AIC - Does there exist controversy surrounding this topic?

I've read countless posts on this site that are incredibly against the use of stepwise selection of variables using any sort of criterion whether it be p-values based, AIC, BIC, etc. I understand why ...
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AIC calculated in lm(y~1) and stepwise selection in R

http://www.stat.wisc.edu/courses/st333-larget/aic.pdf The AIC calculated with the model lm(SAT~1) was 560.4736, but the AIC calculated with stepwise selection starting with lm(SAT~1) was 419.42. May ...
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Shrinkage methods - are they any good for statistical inference or should they be used for prediction goals only?

I am working on my master thesis with a goal to find regressors which influence companies' decisions on how to pay for a target in acquisitions (cash, stock or a mix of both). I have 13 regressors to ...
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AIC based model selection, hyperparameter optimization and in-sample prediction

I'm using AIC to perform model selection along with hyperparameters optimization. The exact setup is the following: I have two input variables (A and B), and a single target variable. All variables ...
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Information criterion when model could be mis-specified and data is dependent

Common information criteria (AIC, BIC, etc) require the user to specify the likelihood function, while in practice rarely the user has the luxury to know the correct likelihood function. In the case ...
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How is the Akaike information criterion (AIC) affected by sample size?

I am evaluating several logistic regression models predicting college student retention. I am using some basic and well-established predictors, such as high school GPA and SAT scores. I understand ...
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Aikaike Information Criterion: derivation in original paper

I have been reading AIC paper 'Information theory and an extension of the maximum likelihood principle' by Akaike (1974). I have been able to understand up to the third section of the paper, but I am ...
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Convince me that AIC can't be used to compare models with different sample sizes

Conventional statistical wisdom says we cannot compare AIC (or other information criteria predictive sample statistics) when the sample sizes for the compared models are different (See here for ...
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DIC/MDIC is negative. Is this a red-flag or normal?

I have fit a few mixture models of multivariate normals. When calculating the MDIC (modified DIC) to compare the models, they come up as negative. In contrast, all examples in my lecture notes are ...
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How can we calculate AIC from a negative binomial GLMM?

Our problem here described is to calculate AIC from a GLMM negbin. Our data compose by 2 Categorical variables (Yes/Not), 3 Numerical variables and our random factor, all without any NA. We want to ...
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Linear regression AIC and Randomisation Test

The problem is that I used AIC as the criterion for model selection and that gives me a model with 3 parameters (the model has the lowest AIC). $$y = \beta_0 + \beta_1X_1+\beta_2X_2+\beta_3X_3$$ ...
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Effect sizes for model averaging

The goal is to find if one factor is stronger than the other in the models I have considered. I am using the information-theoretic approach. Since $n/K>40$, I am using AIC. Firstly the model is ...
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Why do we use a criterion like AIC for Copula model selection?

If we look at the AIC formula: AIC = -2*log(ML) + 2k where k is the number of parameters in the model and is considered as the 'penalizing term' for complexity or over-fitting. Does this ...
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Can you use AIC to compare OLS and SMA regressions?

I've come across SMA (Standard Major Axis) regression recently and was wondering if it would be appropriate to compare SMA and OLS models with AIC? When I use the aicc function from the package bbmle, ...
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EM algorithm and AIC criteria

I am using EM algorithm to estimate the model parameters. EM-algorithm iterates until the loglikelihood is converged. After that, I need to compute AIC criteria. As known, AIC is a loglikelihood ...
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AIC and BIC and number of quantization level

I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data ...
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Proof of AIC criterion

I was recently read the book "Elements Of Statistical Learning" by Hastie et.al. In chapter $7$, AIC criterion is definite as follows: $$-2.E[log Pr_\hat\theta(Y)]\approx -\frac{2}{N}.E[loglik]+2\...
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Time series analysis VAR model: AIC and BIC test criteria

Consider two variables. Imagine you want to analyse the effects of the lags of variable A on variable B. The possiblity you see an effect of variable A on B is reasonable, but there is absolutely no ...
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What is the actual significance of a difference in AIC or BIC values?

Usually, when a difference of a statistic is discussed, that discussion is presented in the context of a significance of that difference. When self-entropy, i.e., information content, is examined, ...