Compute AICc of fitted model objects

Source: R/AICc.R

Compute AICc for one or several fitted model objects for which a log-likelihood value can be obtained.

AICc(object, ..., k = 2)

Arguments

object

A fitted model object from splm(), spautor(), spglm(), or spgautor() where estmethod is "ml" or "reml".

...

Optionally more fitted model objects.

k

The penalty parameter, taken to be 2. Currently not allowed to differ from 2 (needed for generic consistency).

Value

If just one object is provided, a numeric value with the corresponding AICc.

If multiple objects are provided, a data.frame with rows corresponding to the objects and columns representing the number of parameters estimated (df) and the AICc.

Details

When comparing models fit by maximum or restricted maximum likelihood, the smaller the AICc, the better the fit. The AICc contains a correction to AIC for small sample sizes. The theory of AICc requires that the log-likelihood has been maximized, and hence, no AICc methods exist for models where estmethod is not "ml" or "reml". Additionally, AICc comparisons between "ml" and "reml" models are meaningless -- comparisons should only be made within a set of models estimated using "ml" or a set of models estimated using "reml". AICc comparisons for "reml" must use the same fixed effects. To vary the covariance parameters and fixed effects simultaneously, use "ml".

Hoeting et al. (2006) study AIC and AICc in a spatial context, using the AIC definition \(-2loglik + 2(estparams)\) and the AICc definition as \(-2loglik + 2n(estparams) / (n - estparams - 1)\), where \(n\) is the sample size and \(estparams\) is the number of estimated parameters. For "ml", \(estparams\) is the number of estimated covariance parameters plus the number of estimated fixed effects. For "reml", \(estparams\) is the number of estimated covariance parameters.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
AICc(spmod)
#> [1] 1.073229
AIC(spmod)
#> [1] 0.1501516
BIC(spmod)
#> [1] 4.353744