Akaike information criterion

Akaike information criterion for model selection.

Usage

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

Arguments

model

An object of class lm.

method

A character vector; specify the method to compute AIC. Valid options include R, STATA and SAS.

corrected

Logical; if TRUE, returns corrected akaike information criterion for SAS method.

Value

Akaike information criterion of the model.

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.

See also

Other model selection criteria: ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc(), ols_sbic()

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