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 model averaging when models are correlated

AIC model-averaging: In "standard" AIC model averaging we average models with weights proportional to $$w_i \propto \exp( -0.5 \times \Delta \text{AIC}_i ),$$ where $\Delta \text{AIC}_i$ is ...
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Lower IC vs less lags (Stepwise)

So I used auto.arima for my regression and compared it to the result with stepwise=False. And I got different results. If stepwise is enabled I get an ARIMA(1,1,3) model with an AIC of 3765.347. If I ...
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How to pick a “best” AIC for ARMA

I'm just tackling time data for the first time. I'm looking at a data set of motor vehicle accidents in New York City between 2012-2020, and I want to run an ARMA on it. I read that a good way to ...
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Can I use `Y ~ X + X:Z` when `Z` does not follow a linear relationship with `Y`?

General case I want to model the relationship between Y and X, but I am also interested in knowing if this relationship changes ...
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52 views

Akaike Information Criterion I cannot interpret the result

Maybe is a silly question, or maybe I'm doing something wrong. I've tried to implement AIC criterion to estimate the optimum number of parameters using Auto Regressive (AR) linear models using white ...
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Is AIC appropriate for comparing non linear models?

In R, when trying to compare non linear models with AIC, you can use the function AIC on an nls object, which is the least ...
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To use AIC and BIC to select models the data used must be normally distributed?

I'm studying AR(p) and ARMA models and when I was studying about information criterion I couldn't understand if my data needs to be normally distributed or not? Is it a pre-requisite, to have normally ...
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Model Selestion - Compare AIC of data and its subset

I am trying to use AIC to assess the difference between replicates. In my experiment, each treatment has three replicates. The data from each replicates was fitted exponential model. And then combine ...
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1answer
26 views

Test to select best models in production

I've got four models in production and using the average of them as the served prediction. We get ground truth data immediately. I've optimized them and found the best models during my training/...
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AIC/BIC vs the rule of “must include lower order interaction”

I am running a series of mixed effect models, which include both linear and quadratic term of a variable T (continuous) and the main IV I (categorical), and facing a dilemma. Model 2 include ...
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AIC/BIC formula wrong in James/Witten?

Reading "An Introduction to Statistical Learning" (by James, Witten, Hastie and Tibshirani), on p.211 I came across the following formula for BIC in case of linear regression: $ BIC = \frac{...
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Kolmogorov-Smirnov and AIC giving opposite goodness-of-fit results. Is this possible/surprising/normal?

I have some data on the duration of several activities (rounded to the nearest half hour). I'm trying to add up these random variables (one per activity) so that I can calculate the total duration of ...
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AIC to determine optimal degrees of freedom for natural spline in GLMM?

Is it appropriate to use AIC to determine the optimal degrees of freedom for a natural spline? I have measured 200 animals at six points in time. My data look like below. ...
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Does the size of the training dataset affect the AIC?

I'm conducting an experiment in which I want to compare the performances of 2 models. Both trained using the same algorithm (Logistic regression). I split the data ($n=10000$) I have into 3 parts, <...
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The similarity between Mallows Cp and AIC?

It is possible to compute the log-likelihood used for AIC as $n /log(RSS/n) + const$ or even as $RSS/\sigma^2 + n\log(\sigma) + const$ considering the least-square or MLE scenario for linear and non-...
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AIC vs. Likelihood ratio test [duplicate]

Please, can someone explain the main differences of AIC and LRT? I understand, that both methods test, whether a new variable should be included in the model. Both methods integrated the Likelihood. ...
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Using AIC weights to determine prediction intervals for a single model structure

I am working with fitting regression models to data, and producing prediction intervals would be useful. Unfortunately, the data often has few data points, and is reported as mean rather than ...
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45 views

Critique of AIC usage

This note https://www.significancemagazine.com/science/580-graphical-interpretations-of-data-walking-the-line provides an interesting interpretation of something that first looks likes a trend but ...
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Akaike Information Criteria applied on Random Forest

I am implementing a Random Forest model for predicting a variable "A" which is function of other 4 variables: $$A = f(B,C,D,E)$$ I developed a good RF model (i.e. high accuracy, good ...
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Using AIC to Measure Clustering Quality, how many k to account for Variance Parameter(s)?

I have written a custom clustering function which takes a vector of initial position estimates of k cluster centres (a 1 dimensional vector). Internally the function then "calibrates" the ...
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AIC model-comparison from one level to the next

Validated community, I have an fMRI dataset that consists of 35 subjects in which I measure a signal at 450 time points at around 3000 locations (voxels) in two hemispheres. I have two competing ...
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Calculate AIC value from a given BIC value?

Is it valid, given a certain BIC value (an output from an R package) with known n and k, to transform the BIC value via mathematical manipulation of the formulae for BIC and AIC to get the "...
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getting same AIC (or any other comparison criterion values) even after using different var-cov structures when comparing GLMM models

We are comparing models that are GLMM , in which for each one of them the fixed effects are exactly the same, but in the random effects portion, we used different variance-covariance structures (i.e ...
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Differences between formulas for AIC and BIC

I have a question regarding the information criteria AIC and BIC: I found different formulas for the AIC/BIC, the common ones including the likelihood $\mathcal{L}$ are $$AIC = 2K - 2 ln(\mathcal{L})\...
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91 views

Log-Likelihood Computation for AIC & BIC

Considering $n$ observations that an be modelled by a Gaussian error model and two nested motion models with $p = 4$ and $p = 7$ parameters, I want to compute the log likelihoods $L$ given the Maximum ...
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How can I compare overall explanatory power across a group of models using different sets of features?

I have several datasets of measured outcomes from different subjects, all measured in the same experimental setup. There are many possible explanatory features that may predict the outcome, but the ...
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How to compare count data to determine

I am performing an experiment to check which information criterion performs best, better and least among Akaike Information Criterion (aic), Bayesian Information Criterion (bic) and aicc. I am ...
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Is there a way to calculate the maximum likelihood from a tree regression model?

When fitting a tree regressor model, I would like to calculate the AIC and BIC metrics. However I need the maximum of the likelihood function to do this. Is there a closed form solution or some other ...
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Can this closed form solution of AIC for OLS be applied to tree regressors?

Gordon (2015, p. 201) has a simple clossed form solution for AIC in the framework of OLS $$\text{AIC} = n\log\left(\frac{SSE}{n}\right) + 2k$$ where SSE is the standard $SSE = \sum_i(y_i - \hat{y_i})^...
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How do you count the number of parameters for AIC?

Suppose I have an $n$ by $10$ data matrix $X$ and a continuous target $y$. I want to compare 2 models: $m_0$, which is an OLS regression model, and $m_1$, which is a deep neural network with $10^6$ ...
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70 views

Why AIC for log-linear model in glm returns Inf?

I am trying to calculate the AIC for log-linear model in R, but i get Inf as a result. The model aim is to predict sales in euros based on some variables. As far as ...
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SECR AIC compatibility

I'm a student in ecology and I'm currently doing an internship to validate the first year of my master degree in France. I have to calculate roe deer density for the Mavrovo National Park in Macedonia ...
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How do I interpret model fit for ordinal regression when AICc and likelihood ratio test conflict?

I'm working with 4 nested models using ordinal regression (same sample, n=344, and dependent variable across models). The -2LL for each successive model increases and becomes statistically significant....
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AIC and transformation of the independent variable [duplicate]

I set up different models: always same dependent variable and dataset, only the independent variable changes. All model assumptions are fullfilled. Now i do a model selection with the AIC. I look at ...
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19 views

Using stepAIC to help select final model [duplicate]

So I have a full model such as; ...
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1answer
32 views

Question about significance in glm and plotting effects model

Okays I have a quick question that I'm a little confused about. During my glm model selection, the AIC from my most complicated model (model with say 7 predictors) and then the dredge function ...
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42 views

Using RMSE and AIC to compare three separate “final” models (one with double observations)?

I'm looking at three models (linear mixed effect) looking at crime. The first looks at total crime so there are ~96000 observations. In the second model, I look at crime as a function of crime type (...
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1answer
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Adjusting the number of parameters for AIC / BIC calculation in case of correlated predictors

My current understanding: Both AIC and BIC take the number of parameters as input when comparing nested models with a different number of parameters / predictors. My question: Is it necessary / a good ...
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39 views

Selecting the correct Gaussian process prior for a regression function

Let $$ y_i = f(x_i) + \varepsilon_i \quad i=1,\ldots,n $$ where the $\varepsilon_i$ are iid $N(0,\sigma^2)$. Consider the Gaussian process priors $\pi_1$ and $\pi_2$: $$ \pi_1: f \sim GP(0,\lambda A) $...
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Selection of covariance structures in SAS PROC GLIMMIX

Stroup and Claassen (2020) recently published an article titled Pseudo-Likelihood or Quadrature? What We Thought We Knew, What We Think We Know, and What We Are Still Trying to Figure Out in the ...
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NB multivariate GLM (mvabund): significant interaction, but AIC indicates to drop it

I am modelling multivariate species abundance data with two categorical factors as predictors using a negative binomial family in the manyglm function from mvabund in R. The full model includes both ...
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Hannan–Quinn information criterion and Kashyap information criterion (KIC)

As we may know, the capacity of a model to overfit could easily increase by an increase in the complexity of that model (take complexity roughly as a number of parameters). To handle this problem, ...
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Comparing functional hypotheses accounting for uncertain interpretation of their predictions

I am interested in using an information-theoretic approach (likely AIC) to compare the explanatory power of several functional hypotheses. As an example, hypothesis H1 predicts significant association ...
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19 views

Comparing models when their performance may depend on a continuous variable

I am interested in using an information-theoretic approach (likely AIC) to compare the fit of several models to a dependent variable X. M1 may take the form ...
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16 views

Choosing the best fitting model with AIC and p-value

I have a financial time series, exchange rates. Between ARCH(10) and GARCH(1,1) I would like to see which model fits best my TS. For ARCH I have a p-value smaller than 0.05 and for GARCH p-value is ...
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1answer
72 views

Compare models with AIC when log transforming predictors but keeping the response variable exactly the same

Can I compare say two models where one have predictor P and the other have log(P) all else being equal? I have found posts on the topic but I can only decipher from those that you cannot transform the ...
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1answer
23 views

How to use LR test (likelihood ratio test)?

I have used LR test for testing my models. My model 1 is a logit model with control variables and Model 2 is a model with both predictors and controls. But the LR test is coming to be non-significant ...
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Comparing different specifications of GARCH models with different distributional assumptions [closed]

For purely educational reasons I'm currently trying to fit different types of GARCH models, varying on the order parameters as well as flavor (standard, eGARCH, iGARCH, GJR-GARCH) and different ...
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When AIC and pseudo-R2 give opposite conclusions in beta regression models

I conducted an experiment to quantify the effect of two factors on a response variable: the response variable (Y) is a proportion (percentage cover) factor A is represented by the continuous ...

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