# auc: Area Under ROC Curve In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

 auc R Documentation

## Area Under ROC Curve

### Description

Compute the AUC (area under the Receiver Operating Characteristic curve) for an observed point pattern.

### Usage

``````auc(X, ...)

## S3 method for class 'ppp'
auc(X, covariate, ..., high = TRUE)

``````

### Arguments

 `X` Point pattern (object of class `"ppp"` or `"lpp"`) or fitted point process model (object of class `"ppm"`, `"kppm"`, `"slrm"` or `"lppm"`). `covariate` Spatial covariate. Either a `function(x,y)`, a pixel image (object of class `"im"`), or one of the strings `"x"` or `"y"` indicating the Cartesian coordinates. `high` Logical value indicating whether the threshold operation should favour high or low values of the covariate. `...` 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 point pattern `X` and a covariate `Z`, the AUC is a numerical index that measures the ability of the covariate to separate the spatial domain into areas of high and low density of points. Let `x_i` be a randomly-chosen data point from `X` and `U` a randomly-selected location in the study region. The AUC is the probability that `Z(x_i) > Z(U)` assuming `high=TRUE`. That is, AUC is the probability that a randomly-selected data point has a higher value of the covariate `Z` than does a randomly-selected spatial location. The AUC is a number between 0 and 1. A value of 0.5 indicates a complete lack of discriminatory power.

### Value

Numeric. For `auc.ppp` and `auc.lpp`, the result is a single number giving the AUC value.

\spatstatAuthors

.

### 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.

`roc`
``````  auc(swedishpines, "x")