Akaike information criterion for model selection.

## Usage

`ols_aic(model, method = c("R", "STATA", "SAS"), corrected = FALSE)`

## Details

AIC provides a means for model selection. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. R and STATA use loglikelihood to compute AIC. SAS uses residual sum of squares. Below is the formula in each case:

*R & STATA*
$$AIC = -2(loglikelihood) + 2p$$

*SAS*
$$AIC = n * ln(SSE / n) + 2p$$

*corrected*
$$AIC = n * ln(SSE / n) + ((n * (n + p)) / (n - p - 2))$$

where *n* is the sample size and *p* is the number of model parameters including intercept.

## References

Akaike, H. (1969). “Fitting Autoregressive Models for Prediction.” Annals of the Institute of Statistical Mathematics 21:243–247.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

## Examples

```
# using R computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model)
#> [1] 159.0696
# using STATA computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'STATA')
#> [1] 157.0696
# using SAS computation method
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'SAS')
#> [1] 66.25754
# corrected akaike information criterion
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_aic(model, method = 'SAS', corrected = TRUE)
#> [1] 103.6175
```