# calculates difference metrics at the category level from a square contingency table

### Description

calculates quantity, exchange and shift components of difference, as well as the overall difference, at the category level from a contingency table derived from the crosstabulation between a comparison variable (or variable at time *t*), and a reference variable (or variable at time *t*+1).

Quantity difference is defined as the amount of difference between the reference variable and a comparison variable that is due to the less than maximum match in the proportions of the categories. Exchange consists of a transition from category *i* to category *j* in some observations and a transition from category *j* to category *i* in an identical number of other observations. Shift refers to the difference remaining after subtracting quantity difference and exchange from the overall difference.

### Usage

1 | ```
diffTablej(ctmatrix)
``` |

### Arguments

`ctmatrix` |
matrix representing a square contingency table between a comparison variable (rows) and a reference variable (columns) |

### Value

data.frame containing difference metrics at the category level between a comparison variable (rows) and a reference variable (columns). Output values are given in the same units as `ctmatrix`

### References

Pontius Jr., R.G., Millones, M. 2011. *Death to Kappa: birth of quantity disagreement and allocation disagreement for accuracy assessment*. International Journal of Remote Sensing 32 (15), 4407-4429.

Pontius Jr., R.G., Santacruz, A. 2014. *Quantity, exchange and shift components of difference in a square contingency table*. International Journal of Remote Sensing 35 (21), 7543-7554.

### See Also

`overallQtyD`

### Examples

1 2 3 4 5 6 7 8 9 | ```
comp <- raster(system.file("external/comparison.rst", package="diffeR"))
ref <- raster(system.file("external/reference.rst", package="diffeR"))
ctmatCompRef <- crosstabm(comp, ref)
diffTablej(ctmatCompRef)
# Adjustment to population assumming a stratified random sampling
(population <- matrix(c(1,2,3,2000,4000,6000), ncol=2))
ctmatCompRef <- crosstabm(comp, ref, percent=TRUE, population = population)
diffTablej(ctmatCompRef)
``` |