# Tagged Questions

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 2-dimensional data

Let's consider a univariate (experimental) distribution, and two 1-dimensional models to describe it (e.g., a Gaussian distribution and a mixture of two Gaussians). One then computes for each model ...
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### Link functions for Binomial Regression

So I have a dataset of presence (1) and absence (0) data, but it mainly consists of 0's (~80% of the 5200 observations). Now while constructing my binomial logistic model I am reading (Zuurt et al. ...
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### Calculate AIC for random model (0 parameters)

I want to compare some action-selection models (e.g. soft-max and epsilon-greedy) to the simplest model I can think of. A random model, one that picks an action randomly among the available ones. To ...
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### AIC only applicable to maximum likelihood fit (not least squares)?

When I read about AIC I see that it is calculated for maximum likelihood model estimation. For example, R function arima0 estimated by ...
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### GLMM- relationship between AICc weight and random effects?

I am developing GLMM's in order to assess habitat selection (using GLMMs' coeficients to construct Resource selection functions). I have (telemetry) data from 5 study areas, and each area has a ...
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### Logistic regression variable selection methods

I'm having trouble to understand Backward elimination in Logistic Regression model. I was looking at this example of Agresti, Categorical Data Analysis, to see how Backward elimination works. What ...
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### How to read this table? Mixed effect models [closed]

Hello community! I have been lost trying to interpret this table! Could someone please help me out?
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### Inexplicable AIC/BIC growth from base model in SPSS 23 in a mixed model

I am running a mixed model with a binary dependent variable and a logit link using SPSS 23´s Generalized linear mixed model procedure. The data is multilevel (1 Subject, 5 questions/data points per ...
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### GLMM: relationship between AIC, R squared and overdispersion?

First of all, I am a beginner in statistics, and I have been reading some questions and comments here regarding this matter but I am still a bit lost. My problem: I am constructing GLMM's in order to ...
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### AIC for Geographically Weighted Logistic Regression

We know that AIC (Akaike Information Criterion) for Logistic Regression can be obtained by this formula : $AIC = 2k - 2ln(L)$ where k is number of estimated parameter and L is likelihood. Now, I'm ...
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### Combining AIC and BIC [closed]

For my dataset of ~19K data points to cluster, I want to use a criterion to choose the number of clusters. BIC (Bayesian Information Criterion) gives too few clusters (~180) while AIC (Akaike ...
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### AIC (QIC) - comparision of models?

I am comparing models created by geeglm function in R software. Does QIC of a model need to be lower than QIC of a null model? (in geeglm, geepack, R)
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### Difference between non significant coefficient p-values and variable exclusion using AIC

I am trying to fit a linear regression model with two continuous explanatory variables and one factor with two levels. Rather than predictability, I am especially interested in the interpretability of ...
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### Different AIC values in trace and final output in auto.arima

I am trying to fit a time series with function auto.arima in the "forecast" package in R that is choosing the best model automatically. Since I am using it for my ...
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### Is it valid to reduce the AICc penalty for multiple variables, when some variables should be grouped?

I have a data set of mean trait values for each of 18 populations, and want to test whether several ecological variables are related to variation in traits. I'm using the corrected Akaike information ...
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### Determine best ARIMA model with AICc and RMSE

I have done a training set to fit different ARIMA models and then a test set to assess their performance (with R). From what I understood, I can use the AICc to determine the best model by choosing ...
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### AICc and value for k

Looking for some confirmation. We have a set of 12 soil water sensors and originally were planning on using RMSE to determine our best model of six for each sensor, but have since decided to include ...
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### Averaging linear regression model using AIC's relative likelihood

I've learned here that when two models have a big relative likelihood, one could compute a weighted average of those models in order to estimate the "unconditional" variable effect. However, some ...
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### Use of post hoc tests following model selection based on AIC

I am working on a dataset of vegetation characteristics recorded over three seasons in two different areas used by buffalo. I have run generalised linear mixed models to determine whether vegetation ...
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### Simple linear regression, p-values and the AIC

I realise this topic has come up a number of times before e.g. here, but I'm still unsure how best to interpret my regression output. I have a very simple dataset, consisting of a column of x values ...
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### Model comparison via AIC or BIC for different likelihood maximization procedures

Maximum likelihood estimation of different models (which all model the same variable and assume the same likelihood function) is done by a different method for each model. Simple numerical ...
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### Assess the model of Multinomial Logistic Regression

Some people told me that AIC and residual deviance are good statistics to assess multinomial logistic regression model. But I don't know how to use it in multinomial logistic regression. Anyone here ...
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### How are “MuMIn::mod.sel()” and “car::Anova()”/"lmerTest::anova() different for selecting the most optimal model? Is it only the AIC and AICc?

I want to compare several models built using the codes I have written in R for a mixed-effects model. I already knew that anova() function in car package provides <...
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### Are models within 2 deltaDIC of each other considered equivalent?

I think its a rule when using AIC that should the best model be within 2 unit AIC of the second best model, both are considered with equal weight. Does the same rule-of-thumb apply to Deviance ...
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### Comparing count data models?

I am trying to fit Negative binomial, Zero Inflated Negative Binomial, Negative Binomial Hurdle, and Random effects negative binomial. Here is the value of AIC for different model: Negative Binomial: ...
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### What to conclude about these models? Random intercept + Fixed Slope vs. Random intercept and Slope

In the 'nlme' R package, for instance, I ran the following models: ...
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### What does the Akaike Information Criterion (AIC) score of a model mean?

I have seen some questions here about what it means in layman terms, but these are too layman for for my purpose here. I am trying to mathematically understand what does the AIC score mean. But at ...
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### What is the point of dividing data into training and test parts to assess prediction properties when we have AIC?

Asymptotically, minimizing the AIC is equivalent to minimizing the leave-one-out cross-validation MSE for cross-sectional data [1]. So when we have AIC, why does one at all use the method of dividing ...
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### AICc is picking overly complex models - something stricter?

I'd like to know if there are stricter alternatives to automated model selection than AICc / AIC / BIC. We have approximately ten thousand curves, and for each we'd like to find the most parsimonious ...
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### Multiple testing & model selection using AICc

I have a situation very similar to this post. I am finding the best-fit mixed effects model among a set of 5 candidate models for 7 different dependent variables (y1 to y7) using the same dataset of ...
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### AIC of a two-part/hurdle model?

I have continuous data with a point mass at zero, so my plan is to use a two-part model where I first model whether an observation is zero or non-zero in a logistic regression and then model the ...
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### Using the drop1 command in R and AIC

While using the drop1 command in R for model building, it is said the variable with the lowest AIC value must be dropped. What could be the reason for the same? I know AIC talks about information loss ...
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### How freqently are the information conditons for proper Akaike information criterion application actually met?

Akaike information criterion (AIC) is limited to goodness-of-fit for assumed distributions. That is, for an assumed distribution (especially homoscedastic) one can assume a maximum likelihood function....
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### ARMA model selection: in-sample vs. out-sample accuracy measures

I have a time series for 1000 days for many firms. I am interested to know, in general, on what basis I should select an ARMA model (the nature of my problem restricts integration order to 0). Should ...
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### Why are the both of two models' AIC the same?

I would like to ask a question of AIC when we use Generalized Linear Model with R. I show you 4 my models. "x" is continuous variable. "f" is categorical variable and has two levels, C and T. "x*f" ...
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### VAR model: include all lags up to AIC-suggested order or just the significant ones?

I'm building a regression model in which I have a dependent variable OSE, and two independent variables, MSCI and Brent. In this model I wish to include lagged variables. I performed an AIC for my ...
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### AIC, model selection and overfitting

I am looking for references that specifically show that Akaike's Information Criterion (AIC), or its corrected form (AICc), can in some practical applications -- that is, not in the asymptotic regime -...
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### Obtaining AICc weights after glm.nb

I am performing negative binomial regression using glm.nb() function from MASS package and calculating AICc using package "AICcmodavg". I need also to obtain the (AICc) weights using aictab() function ...
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### Is AIC a valid criterion for the selection of variance structures in GLS?

In generalized least squares, I’ve specified a weights function that accounts for heterogeneity in residual variance that exist along the range of a covariate. The validation graphs (residuals ...
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### range of possible values and model complexity

I have a prediction model where the likelihood is a function of two components $(A,B)$ $L \sim \bf{A}^\alpha + \bf{B}^\beta$ , where both $\bf{A}$ and $\bf{B}$ are $n\times n$ matrices ($n$ is the ...
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### Model Averaging: Standard Error vs Adjusted Standard Error

I'm having trouble understanding when to use Std. Error or Adjusted SE in model averaging (model.avg). What/Why/When to use Adjusted SE? This is my code: ...
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### AIC and nested models

There is a related question here but two highly upvoted answers there don't seem to agree with each other, and in any case I wanted to take a different tack. Is AIC useful for comparing: non-nested ...
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### Different AIC values for the same SARIMA model in different R packages

I've been trying to run a simple time series model for a data set. My biggest question is when I run the auto.arima model (from package "forecast) for this data set ...
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### logistic regression - class created with non significant coefficients?

I've created an example table (just in order to create a function) with: ...
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### AIC on Savitzky-Golay width

I want to use a Savitzky-Golay filter to smooth some data. There is a right width to use based on the data that it is smoothing. A number of papers basically use "eyeball norm" on the parameters but ...
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### Likelihood ratio test seems to show little difference between models with AICc difference of 3

I'm running a multinomial logistic regression analysis of the behavioural responses of deer to camera traps using no reaction, reaction and strong reaction as dependent variables and season, camera ...
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### Variable selection vs Model selection

So I understand that variable selection is a part of model selection. But what exactly does model selection consist of? Is it more than the following: 1) choose a distribution for your model 2) ...
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### Scenario of how to compare models

I have a binary classification problem where the distribution of classes is skewed. I've already trained some scoring models with logistic regression. Now I would like to compare them. How to do this ...