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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Can I use the AIC to compare ordered logistic regression models based on different datasets?

I performed ordered logistic regression using the polr() command in R. I did this with the same independent and dependent variable (the X and Y are the same for every model), but the exact data in ...
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MLE with higher order markov chain model

I am trying to estimate my Markov chain model. I understand that in a standard model, a higher order will lead to overfitting and higher likelihood. Hence, one can use AIC/BIC to find the order of the ...
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Model selection: Two-Part Mixed Effects Model for Semi-Continuous Data

I have now been studying mixed models for about a month, I am still a pure beginner. I have zero inflated semi continuous dependent variable (yield of trees between two periods). Exploring ...
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Averaging GLM's based on delta AIC < 2 and using the resulting coefficient estimates with their associated raster to build a predictive raster

I'm trying to construct a predictive spatial raster based on averaged GLM's Not the exact code but an example: mod1 <- glm(c~ x1 + x2 + x3, data=data) mod2 <- glm(c~ x1 + x2, data=data) mod3 &...
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Code incorrectly determines that a poor fit is a good fit

I'm trying to find the best polynomial fit for a set of data. It calculates the AIC for each polynomial fit of a certain degree, and then chooses the one with the lowest AIC. To my knowledge (which I ...
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On George Box, Galit Shmueli and the scientific method?

(This question might seem like it is better suited for the Philosophy SE. I am hoping that statisticians can clarify my misconceptions about Box's and Shmueli's statements, hence I am posting it here)....
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Do I choose the logistic regression model with the better F1 statistic on the validation set or the lower AIC?

I am deciding whether to keep an interaction term in my logistic regression model. If I keep it in, the AIC of the model improves. If I leave it out, I get a better F1 score with my validation set. ...
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Model selection with AIC/BIC, which variables to remove?

I am running a Generalized Linear Mixed Model analysis in SPSS 25, and have gotten to the point where I would like to justify the selection of my final model based on information criteria. However, ...
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Weighting of multiple linear regressions in an ensemble

If I have a continuous dependent variable and N continuous predictors, and I fit all possible regressions with zero up to N variables, how should I weight those regressions for prediction? One ...
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Applying AIC to determine appropriate ARIMA model

If I somehow know that a variable $Y$ is explained by an ARIMA process, and I know the number of times that the observations must be "differenced" to obtain a stationary series, I have read that it is ...
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Manually computed AIC differs from statsmodels AIC

I tried to manually code a formula for the AIC. I want to use it in connection with scikit learn. For testing if i coded correctly, I compared the AIC values from statsmodels given the same datasets. ...
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AICc for small sample size

I would like to test the effects of salinity and temperature on parasite infection. Temperature and salinity are the fixed factors, the first one has two levels, the second one three levels. ...
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Why does AIC model rank order change in lme models with standardization of predictor variables?

I can't figure this out. The AIC/AICc rank of my mixed effect models are different whether or not I standardize my predictor values using rescale. Note, I'm not concerned that AICc is changing, as ...
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Can you run an AIC twice in a row?

I came across this paper that seems to make a bunch of models, run an AIC, select the best models from that, then run the AIC again. Am I interpreting this correctly? And is that okay to do? Couldn't ...
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Is my model selection procedure problematic for inference?

I'm not sure if this is "step-wise" model selection, but here is what I'm doing Decide a handful of models through exploratory data analysis. Fit the models to the data, and calculate their AIC. Pick ...
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Example and counterexample for Stone's (1977) assumption

Stone (1977) considers the problem of the choice of predicting density for $y$ given $x$ from a prescribed class of formal predicting densities $\{f(y|x,\alpha,S), \alpha \in \mathscr{A}\}$ whose ...
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Is this a typo in Stone's (1977) paper on asymptotic equivalence between AIC and LOOCV?

I am unsure about an expression in Stone's (1997) paper on asymptotic equivalence between AIC and LOOCV. Section 4., third line from the bottom of page 45 starts with $L(\theta)-1(y_i|x_i,\theta)$. ...
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Equivalence of AIC and LOOCV under mismatched loss functions

Under certain conditions, AIC and LOOCV (leave-one-out cross validation) are asymptotically equivalent (Stone, 1977). Stone's paper is less than 4 pages long, but quite mathy, so I turn here for some ...
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AIC criteria for a matrix decomposition problem

I am trying to decompose a matrix such that $$A \approx UV_1 \approx UV_2V_1 \approx UV_3V_2V_1V_2$$ where $A \in R^{n \times l}$, $U \in R^{n \times k_1}$, $V_1 \in R^{k_1 \times l}$, $V_2 \in R^{k_2 ...
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Does a high Chi square p-value for a whole model mean it is insignificant if likelihood ratio tests indicated variables should be added?

I've been estimating lots of versions of the same model by incrementally adding variables. With some variables, if I add them to the model, the likelihood ratio test indicates that they are ...
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AICc value How to derive?

initially let me introduce a concept widely used in ARIMA in the following. $AICc = AIC + \frac {2k^2+2k} {n-k-1}$ where n denotes the sample size and k denotes the number of parameters. Thus, AICc is ...
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AIC for increasing sample size

I am using AIC as a model selection criteria in one of my projects. However, since AIC isn't dependent on the number of points sampled, for large n the log likelihood term rapidly outscales the ...
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AIC for latent variable models

I'm trying to use BIC/AIC for model comparison and want to know what the number of parameters is. The models I'm unsure about are linear Gaussian state space models with nonlinear observations. ...
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45 views

Can I compare AIC values for similar models fitted for two samples from the same population?

If I have two samples (n=300) from the same population and I'm fitting a GLMM (Generalised Linear Mixed-effects Model) with a similar response and explanatory variables but with a completely different ...
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AIC, BIC values keep changing with lag.max in VAR model

I'm using a VARselect function from vars package in R to select order for my model. My data set has 2 time series with 21 data points. When I give ...
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P-values shows something different than AIC or delta AIC. What to do?

I applied an glmer model on data derived from several raster (image) files. Together, my dataset had several hundred thousand rows. My model was something like this: ...
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Is there a measure of “complexity” for linear/nonlinear model terms?

My apologies if this is grossly misunderstood or mis-worded, but I've been mildly bugged by a question to which I've not found a satisfactory answer. I can't say that I have seen a discussion about ...
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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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238 views

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 ...