kstat: Similarity of categorical maps
In environmentalinformatics-marburg/Rsenal: Magic R Functions for Things Various

kstat

R Documentation

Similarity of categorical maps

Description

Calculation of Kappa indices as well as quantity and location (dis)agreements to assess similarity of two categorical maps. Might be used mainly to compare a raster of ground truth sites with a classified map or to compare a model output with a reference map.

Usage

kstat(a, b, mask = "", perCategory = TRUE)

Arguments

`a`	A vector or an object of type "raster" containing categorical data
`b`	A vector or an object of type "raster" containing categorical data. Must be of the same dimensions as a.
`mask`	if a,b is a RasterLayer: A string vector of category numbers which are are to be ignored in the calculations. The numbers must be identical to the values of the input rasters. (optional)
`perCategory`	If TRUE indices are calculated per category in addition to overall indices.

Details

Calculation of kappa index, kappa of quantity, Kappa of location (see Cohen 1960, Pontius 2000, Hagen 2002) for the overall map and for each category (Monserud and Leemans 1992) as well as quantity and location (dis)agreements according to Pontius (2011). The first step to calculate the indices is to calculate a contingency table:


		M	A	P		A

		1	2	..	c	Total
M	1	p11	p12	..	p1c	p1T
A	2	p21	p22	..	p2c	p2T
P	..	..	..	..	..	..
	c	pc1	pc2	..	pcc	pcT
B	Total	pT1	pT2	..	pTc	1

From the contingency table the following statistics are calculated:

Fraction of Agreement: P(A)=\sum_{i=1}^{c}p_{ii}
Fraction of Agreement subject to the observed distribution: P(E)=\sum_{i=1}^{c}p_{iT}*p_{Ti}
Maximum Fraction of Agreement subject to the observed distribution: P(max) = \sum_{i=1}^{c}min(p_{iT}, p_{Ti})

From theses statistics, the kappa indices are calculated as:

Kappa index: K=\frac{P(A)-P(E)}{1-P(E)}
Kappa of location: K_{loc}=\frac{P(A)-P(E)}{P(max)-P(E)}
Kappa of histogram: K_{histo}=\frac{P(max)-P(E)}{1-P(E)}

Disagreements are calculated as:

Chance agreement: CA=100*min((1/cmax),P(A),P(E))
Quantity agreement: QA=ifelse(min((1/cmax),P(E),P(A)==(1/cmax),100*min((P(E)-1/cmax),P(A)-1/cmax),0)
Allocation disagreement: AD=100*(P(Max)-P(A))
Quantity disagreement: QD=100*(1-P(Max))

with cmax is the number of categories. The calculations of Kappa per category require a reclassification for each category:


			A

		i	other	Total
	i	pii	pi.-pii	pi.
B	other	p.i-pii	d	1-pi.
	Total	p.i	1-p.i	1

The Kappa per category i is calculate in the same way as the normal Kappa but from the reclassified contingency table. Thus, the formula for the Kappa per category is

K_i=\frac{Pii-Pi.P.i}{\frac{pi.+p.i}{2}-pi.p.i}

as introduced by Fleiss (1981) and applied in e. g. Monserud 1992 and Hagen (2002). The Disagreements per category are as well calculated as explained above but from the reclassified contingency table for each category.

Value

A data frame containing the values for overall kappa (K), Kappa of location (Kloc), Kappa of histogram (Khisto), chance agreement (CA), quantity agreement (QA), allocation agreement (AA), allocation disagreement (AD), quantity disagreement (QD).

Note

The calculation of kappa per category bases on the approach of Fleiss (1981). Dont get confused with the Kappa per category calculated in e.g. Idrisi which follows the approach of Light (1971) and is an asymmetric Kappa index depending on which map is treated as reference map.

Author(s)

Hanna Meyer

References

Cohen, J., (1960): A coefficient of agreement for nominal scales, Educational and Psychological Measurements, 20: 37-46. Fleiss, J.L., (1981): Statistical Methods for Rates and Proportions (2nd edition). John Wiley and Sons, New York, NY, 321 pp. Hagen, A. (2002): Multi-method assessement of map similarity. Proceeding of 5 th AGILE Conference on Geographic Information Science, April. 25-27 Spain, 171-182. Light RJ (1971) Measure of response agreement for qualitative data: some generalizations and alternatives. Psychol Bull 76:365-377. Monserud, R. A., and Leemans, R.(1992): Comparing global vegetation maps with the kappa statistic. Ecological Modeling, 62: 275-293. Pontius, R.G. (2000): Quantifcation Error Versus Allocation Error in Comparison of Categorical Maps. Photogrammatric Engineering and Remote Sensing, 66: 1011-1016. Pontius, R.G., Jr., and Millones, M. (2011): Death to Kappa: Birth of Quantity Disagreement and Allocation Disagreement for Accuracy Assessment. International Journal of Remote Sensing, 32: 4407-4429.

Examples

#### Example 1: Calculate the indices to compare two Land cover maps
#load data
library(raster)
LUC1990 <- raster(system.file("LUC1990.rst", package="Rsenal"))
LUC2006 <- raster(system.file("LUC2006.rst", package="Rsenal"))

#plot to get an impression:
par(mfrow=c(1,2))
plot(LUC1990,main="LUC Marburg 1990")
plot(LUC2006,main="LUC Marburg 2006")

#calculate indices:
kstat(LUC1990,LUC2006)


#### Example 2: Calculate the indices to compare a land cover map with a map of ground truth sites
#load data:
LUC1990 <- raster(system.file("LUC1990.rst", package="Rsenal"))
trainingSites <- raster(system.file("training.rst", package="Rsenal"))

#plot to get an impression:
par(mfrow=c(1,2))
plot(LUC1990,main="LUC Marburg 1990")
plot(trainingSites,main="Training sites (Ground truth)")

#calculate indices
#(consider to mask the background since ground truth sites don't cover the whole area)
kstat(LUC1990,trainingSites,mask="0")

#For an example of an other field of application of these indices see 
#http://giswerk.org/doku.php?id=people:c:creudenbach:alpenwerk:achtunglawine

environmentalinformatics-marburg/Rsenal documentation built on July 28, 2023, 6:09 a.m.