auc.ppm {spatstat.model}

Area Under ROC Curve

Description

Compute the AUC (area under the Receiver Operating Characteristic curve) for a fitted point process model.

Usage

## S3 method for class 'ppm'
auc(X, ...)

## S3 method for class 'kppm'
auc(X, ...)

## S3 method for class 'slrm'
auc(X, ...)

Arguments

X

Point pattern (object of class "ppp" or "lpp") or fitted point process model (object of class "ppm", "kppm", "slrm" or "lppm").

...

Arguments passed to as.mask controlling the pixel resolution for calculations.

Details

This command computes the AUC, the area under the Receiver Operating Characteristic curve. The ROC itself is computed by roc.

For a fitted point process model X, the AUC measures the ability of the fitted model intensity to separate the spatial domain into areas of high and low density of points. Suppose \lambda(u) is the intensity function of the model. The AUC is the probability that \lambda(x_i) > \lambda(U). That is, AUC is the probability that a randomly-selected data point has higher predicted intensity than does a randomly-selected spatial location. The AUC is not a measure of the goodness-of-fit of the model (Lobo et al, 2007).

(For spatial logistic regression models (class "slrm") replace “intensity” by “probability of presence” in the text above.)

Value

Numeric. For auc.ppm, auc.kppm and auc.lppm, the result is a numeric vector of length 2 giving the AUC value and the theoretically expected AUC value for this model.

Author(s)

Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].

References

Lobo, J.M., Jimenez-Valverde, A. and Real, R. (2007) AUC: a misleading measure of the performance of predictive distribution models. Global Ecology and Biogeography 17(2) 145–151.

Nam, B.-H. and D'Agostino, R. (2002) Discrimination index, the area under the ROC curve. Pages 267–279 in Huber-Carol, C., Balakrishnan, N., Nikulin, M.S. and Mesbah, M., Goodness-of-fit tests and model validity, Birkhauser, Basel.

See Also

roc

Examples

  fit <- ppm(swedishpines ~ x+y)
  auc(fit)