tauW {aqp}

Compute weighted naive and tau statistics for a cross-classification matrix

Description

tauW: Computes: (1) unweighted naive, (2) weighted naive, (3) unweighted tau, (4) weighted tau accuracy statistics

Usage

tauW(
  CM,
  W = diag(sqrt(length(as.matrix(CM)))),
  P = rep(1/nrow(as.matrix(CM)), nrow(as.matrix(CM)))
)

summaryTauW(result.tau)

Arguments

CM

a square confusion (cross-classification) matrix (rows: allocation, columns: reference)

W

weights: 1 on diagonals, [-1..1] off giving partial credit to this error

P

prior probability vector, length = number of rows/columns in CM and W

result.tau

tauW() result

Details

summaryTauW: prints a summary of the results from tauW

xtableTauW: formats a LaTeX table with results from tauW and saves it as a .tex file for import into a LaTeX document.

Input matrices CM and W may be in data.frame format and will be converted

Weights matrix W: 0 = no credit; 1 = full credit; -1 = maximum penalty

If absent, default is no partial credit, i.e., unweighted.

Prior probabilities vector P: If absent, P are equal priors for each class. Special value P = 0 is interpreted as P = column marginals.

Error checks: CM must be square; P must have correct number of classes and sum to 1 +/- 0.0001; W & CM must be conformable

Value

Results are returned in a list with obvious R names

Author(s)

D.G. Rossiter

References

• Rossiter, D. G., Zeng, R., & Zhang, G.-L. (2017). Accounting for taxonomic distance in accuracy assessment of soil class predictions. Geoderma, 292, 118–127. doi:10.1016/j.geoderma.2017.01.012

• Ma, Z. K., & Redmond, R. L. (1995). Tau-coefficients for accuracy assessment of classification of remote-sensing data. Photogrammetric Engineering and Remote Sensing, 61(4), 435–439.

• Naesset, E. (1996). Conditional tau coefficient for assessment of producer’s accuracy of classified remotely sensed data. ISPRS Journal of Photogrammetry and Remote Sensing, 51(2), 91–98. doi:10.1016/0924-2716(69)00007-4

Examples

# example confusion matrix
# rows: allocation (user's counts)
# columns: reference (producer's counts)
crossclass <- matrix(data=c(2,1,0,5,0,0,
                            1,74,2,1,3,6,
                            0,5,8,6,1,3,
                            6,1,3,91,0,0,
                            0,4,0,0,0,4,
                            0,6,2,2,4,38),
                     nrow=6, byrow=TRUE)
row.names(crossclass) <- c("OP", "SA", "UA", "UC", "AV", "AC")
colnames(crossclass) <- row.names(crossclass)

# build the weights matrix
# how much credit for a mis-allocation
weights <- matrix(data=c(1.00,0.05,0.05,0.15,0.05,0.15,
                         0.05,1.00,0.05,0.05,0.05,0.35,
                         0.05,0.05,1.00,0.20,0.15,0.15,
                         0.15,0.05,0.25,1.00,0.10,0.25,
                         0.05,0.10,0.15,0.10,1.00,0.15,
                         0.20,0.30,0.10,0.25,0.20,1.00),
                  nrow=6, byrow=TRUE)

# unweighted accuracy
summaryTauW(nnaive <- tauW(crossclass))

# unweighted tau with equal priors, equivalent to Foody (1992) modified Kappa
tauW(crossclass)$tau

# unweighted tau with user's = producer's marginals, equivalent to original kappa
(priors <-  apply(crossclass, 2, sum)/sum(crossclass))
tauW(crossclass, P=priors)$tau

# weighted accuracy; tau with equal priors
summaryTauW(weighted <- tauW(crossclass, W=weights))

# weighted accuracy; tau with user's = producer's marginals
summaryTauW(tauW(crossclass, W=weights, P=priors))

# change in accuracy statistics weighted vs. non-weighted
(weighted$overall.weighted - weighted$overall.naive)
(weighted$user.weighted - weighted$user.naive)
(weighted$prod.weighted - weighted$prod.naive)