# TIC: Takeuchi's information criterion In SpatialExtremes: Modelling Spatial Extremes

## Description

Computes a the Takeuchi's information criterion which is equivalent to the AIC when the model is miss-specified.

## Usage

 `1` ```TIC(object, ..., k = 2) ```

## Arguments

 `object` An object of class `maxstab` or `spatgev`. Often, it will be the output of the `fitmaxstab` or `fitspatgev` function. `...` Additional objects of class `maxstab` or `spatgev` for which TIC should be computed. `k` Numeric. The penalty per parameter to be used. The case k = 2 (default) correspond to the classical TIC and k= log n, n number of observations, is the robust version of the BIC.

## Details

TIC is like AIC so that when comparing models one wants to get the lowest TIC score.

Numeric.

Mathieu Ribatet

## References

Gao, X. and Song, P. X.-K. (2009) Composite likelihood Bayesian information criteria for model selection in high dimensional data. Preprint.

Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986) Akaike Information Criterion Statistics. D. Reidel Publishing Company.

Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika 92(3):519–528.

`fitmaxstab`, `AIC`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```##Define the coordinate of each location n.site <- 50 locations <- matrix(runif(2*n.site, 0, 100), ncol = 2) colnames(locations) <- c("lon", "lat") ##Simulate a max-stable process - with unit Frechet margins data <- rmaxstab(40, locations, cov.mod = "whitmat", nugget = 0.2, range = 30, smooth = 0.5) M0 <- fitmaxstab(data, locations, "powexp", fit.marge = FALSE) M1 <- fitmaxstab(data, locations, "cauchy", fit.marge = FALSE) TIC(M0, M1) TIC(M0, M1, k = log(nrow(data))) ```

### Example output

```      M1       M0
415270.9 415278.9
M1       M0
415534.0 415543.9
```

SpatialExtremes documentation built on Jan. 5, 2018, 3 p.m.