GKappa: Inference of the statistic Kappa

In ujaen-statistics/ThemAAs:

Description

General function that groups the inference of the statistic Kappa. This function is made up of: the statistic Kappa is a coefficient of agreement for nominal scales which measures the relationship of beyond chance agreement to expected disagreement, the standard deviation is the square root of the Kappa variance that it is computed using the Delta method, the confidence interval for Kappa statistic to confidence level 95 % by default.

Usage

GKappa(object,alpha)

Arguments

object	a coMa object (confusion matrix object)
alpha	Significance level

Details

Assuming a multinomial sampling model Cohen's Kappa is the maximum likelihood estimate of Kappa. The standard deviation is calculated using the variance of Kappa according to Congalton.

The variance of Kappa is

\frac{1}{n}≤ft( \frac{θ_1(1-θ_1)}{(1-θ_2)^2} + \frac{2(1-θ_1)(2θ_1θ_2-θ_3)}{(1-θ_2)^3} + \frac{(1-θ_1)^2(θ_4-4θ_2^2)}{(1-θ_2)^4} \right)

where n is the sample size,

θ_1 = \frac{1}{n}∑_{i = 1}^k n_{ii},

θ_2 = \frac{1}{n^2}∑_{i = 1}^k n_{i+}n_{+i},

θ_3 = \frac{1}{n^2}∑_{i = 1}^k n_{ii}(n_{i+} + n_{+i}),

and

θ_4 = \frac{1}{n^3}∑_{i = 1}^k ∑_{j = 1}^k n_{ij}(n_{j+} + n_{+i})^2.

Confidence intervals can be computed using the approximate large sample variance and the fact tha de statistic is asymptotically normally distributed.

Value

GKappa returns a list with the following elements:

References

Cohen, J. (1960). A coefficient of agreement of nominal scales. Educational and Psychological Measurement, 20, 37-46.

Rosenfield, G. H., & Fitzpatrick-Lins, K. (1986). A coefficient of agreement as a measure of thematic classification accuracy. Photogrammetric Engineering and Remote Sensing, 52, 223-227.

Congalton, R.G., Green, K. (2009) Assessing the accuracy of Remote Sensed Data. Principles and Practices. CRC Press. Taylor & Francis Group.

Examples

#Let evaluate the inference of statistic Kappa.
## Confusion matrix included in Congalton and Green (2009), pg. 108.
x <- coMa(cbind(c(65,6,0,4),c(4,81,11,7),c(22,5,85,3),c(24,8,19,90)))
## Inference of statistic Kappa
InfKappa <- GKappa(x,0.02) # By default alpha = 0.05

ujaen-statistics/ThemAAs documentation built on Nov. 5, 2019, 11:03 a.m.