R: The corrected AIC

AICc {sme} | R Documentation

## The corrected AIC

### Description

Calculates the corrected AIC (AICc) of Hurvich and Tsai (1989). The AICc modifies the standard AIC with a correction for small sample sizes.

### Usage

    AICc(object)

### Arguments

`object` | a fitted model object for which there exists a `logLik` method to extract the corresponding log-likelihood or an object inheriting from class `logLik`

### Details

AIC is an asymptotic result and may be inappropriate when the sample size is small, the number of estimated model parameters is large, or both. For the specific case of a linear model with homogeneous errors then Hurvich and Tsai (1989) derived a corrected AIC (AICc) which includes a correction for small sample sizes as AICc = AIC + (2*k*(k+1))/(n-k-1) where AIC is the standard AIC, k is the number of parameters in the model and n is the number of observations.

While this is an exact result, it only applies in the very specific circumstances in which it was derived. However, as Burnham and Anderson (2002) point out, whenever the sample size is small some form of correction to the standard AIC is necessary, to the extent that they argue the AICc of Hurvich and Tsai (1989) should be used regardless of context unless a specific correction can be derived. In fact Burnham and Anderson (2004) go so far as to argue that it should be used irrespective of sample size as it tends to the standard AIC when n is large.

### Value

A numeric value with the AICc of the model

### Author(s)

Maurice Berk maurice.berk01@imperial.ac.uk

### References

Berk, M. (2012). Smoothing-splines Mixed-effects Models in R. Preprint

Hurvich, C. M. & Tsai, C.-L. (1989). Regression and Time Series Model Selection in Small Samples. Biometrika, 76, 297-307

Burnham, K. P. & Anderson, D. R. (2002). Model Selection and Multimodel Inference: a Practical Information-theoretic Approach. Springer

Burnham, K. P. & Anderson, D. R. (2004). Multimodel Inference: Understanding AIC and BIC in Model Selection. Sociological Methods Research, 33, 261-304

### Examples

      data(MTB)
      fit <- sme(MTB[MTB$variable==6031,c("y","tme","ind")])
      AICc(fit)

[Package sme version 0.8 Index]