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I have three non-nested models with different predictors over the same outcome variable and I used AIC to compare their relative quality. However, I am very confused as to how to interpret the output values and how to gauge their relative quality. Can you help me interpret it? Thank you.

    <dbl>   <dbl>
model1  5   2162.528
model2  5   2081.474
model3  5   2148.410```
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  • $\begingroup$ What is dbl and how did you obtain these numbers (i.e. by a software)? $\endgroup$
    – gunes
    Dec 22, 2019 at 14:44
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    $\begingroup$ They are from R. I don't know what it is but what i want to know is how to interpret the big values from each model. The middle numbers are df. $\endgroup$
    – Uni 13
    Dec 22, 2019 at 15:35
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    $\begingroup$ AIC values themselves have little (interpretational) meaning, they are used for model comparison. Usually, the model with the lowest AIC is deemed "best" out of the candidate models. $\endgroup$ Dec 22, 2019 at 15:49
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    $\begingroup$ What would you use to compare two completely different regression models over the same variable? $\endgroup$
    – Uni 13
    Dec 22, 2019 at 16:15

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As mentioned in comments by @COOLSerdash, the raw value of the AIC doesn't mean anything. However, the lowest AIC is considered the best fitting model. However, it is best not to rely on only one model fit statistic.

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  • $\begingroup$ So what should i use instead to compare the models? $\endgroup$
    – Uni 13
    Dec 22, 2019 at 20:04
  • $\begingroup$ This depends on the modeling goal. If the goal is the lowest average magnitude of error, use RMSE. If the goal is to determine which model explains the most variance in the dependent data, use R-squared. As I understand AIC, it combines both the sum-of-squared errors and number of model parameters to find the simplest model that fits the data well. I personally have used both maximum absolute error and percent error in calibration of industrial radiation measuring equipment. $\endgroup$ Dec 22, 2019 at 21:46
  • $\begingroup$ The raw value of AIC does mean something: it is twice the negative expected log-likelihood of the model for a new data point. So it is an estimate of the log-likelihood multiplied by a constant. You may choose likelihood as a measure of predictive accuracy, and AIC gives an estimate of it (just multiplied by a constant). $\endgroup$ Dec 23, 2019 at 13:53

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