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Compute AIC and AICc of fitted model objects

Source: R/AIC.R, R/AIC_glm.R
AIC.spmodel.Rd

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

Usage

# S3 method for splm
AIC(object, ..., k = 2)

# S3 method for spautor
AIC(object, ..., k = 2)

# S3 method for spglm
AIC(object, ..., k = 2)

# S3 method for spgautor
AIC(object, ..., k = 2)

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

# S3 method for splm
AICc(object, ..., k = 2)

# S3 method for spautor
AICc(object, ..., k = 2)

# S3 method for spglm
AICc(object, ..., k = 2)

# S3 method for spgautor
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 AIC or 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 AIC or AICc.

Details

When comparing models fit by maximum or restricted maximum likelihood, the smaller the AIC or AICc, the better the fit. The AICc contains a correction to AIC for small sample sizes. The theory of AIC and AICc requires that the log-likelihood has been maximized, and hence, no AIC or AICc methods exist for models where estmethod is not "ml" or "reml". Additionally, AIC and 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". AIC and 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) defines that spatial AIC as \(-2loglik + 2(estparams)\) and the spatial AICc 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
)
AIC(spmod)
#> [1] 0.1501516
AICc(spmod)
#> [1] 1.073229