| Title: | Measure of Agreement Between Two Raters |
| Version: | 0.2.0.3 |
| Author: | Antonio Rodriguez [aut, cre], Pedro Femia [cph, ctb], Antonio Martin [cph, ctb] |
| Maintainer: | Antonio Rodriguez <tonirodriguezcontesti@gmail.com> |
| Description: | Measure of agreement delta was originally by MartÃn & Femia (2004) <doi:10.1348/000711004849268>. Since then has been considered as agreement measure for different fields, since their behavior is usually better than the usual kappa index by Cohen (1960) <doi:10.1177/001316446002000104>. The main issue with delta is that can not be computed by hand contrary to kappa. The current algorithm is based on the Version 5 of the delta windows program that can be found on https://www.ugr.es/~bioest/software/delta/cmd.php?seccion=downloads. |
| Depends: | R (≥ 3.2.0) |
| Imports: | stats |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2019-12-09 06:20:46 UTC; FabiToni |
| Repository: | CRAN |
| Date/Publication: | 2019-12-09 07:30:02 UTC |
Main Check Input function
Description
This function perform multiple tasks. First of all, check the parameters specified by the user. Also asign default values to some parameters not defined by the user. Finally it generates error messages and halt the execution in case it is needed.
Usage
CheckInput(datatable, fixedrows = FALSE, gstandard = "No",
maxits = 1000, tol = 1e-12, dplaces = 4, showall = FALSE)
Arguments
datatable |
Matrix. Expected to be square matrix with at least 2 rows (columns), non negative values and at least an element different of zero. |
fixedrows |
Boolean. Indicate if sample rows are fixed beforehand. Default is TRUE. |
gstandard |
Text. Indicate if there are a Gold Standard by Rows or columns. Only first letter matter without Case sensitivity. Options are: "N" for None, "R" for in Rows and "C" for in Columns. Default is "N". |
maxits |
Whole number. Indicate the maximum number of iterations of the numeric method to calculate B. Expected to be 100 <= maxits <= 5000. Default is 1000. |
tol |
Double number. Indicate the precision of the numeric method to calculate B. Expected to be 1e-6 <= tol <= 1e-15.Default is 1e-12. |
dplaces |
Whole number. Decimal placed to be shown in the result. Expected to be 1 <= dplaces <0 6. Default 4. |
showall |
Boolean. Indicate if all output should be shown. If TRUE also shown hidden results. If FALSE shown only main output. By default is FALSE. |
Examples
CheckInput(matrix(c(1,2,3,4),2,2),fixedrows=FALSE,gstandard="No",maxits=100,tol=1e-12,dplaces=4)
Check Input Matrix function
Description
This function checks that matrix introduced is as expected. Should be a matrix, squared, with a dimension greater or equal to two, without negative entries and at least an entry different of 0.
Usage
CheckInputData(datatable)
Arguments
datatable |
Matrix. Expected to be square matrix with at least 2 rows (columns), non negative values and at least an element different of zero. |
Examples
CheckInputData(matrix(c(1,2,3,4),2,2))
Check Sampling type function
Description
This function checks that fixedrows and gstandard parameters are correct. Also return a value indicating if it is or not valid and what kind of output should be shown at the end of the execution.
Usage
CheckSampling(fixedrows, gstandard)
Arguments
fixedrows |
Boolean. Indicate if sample rows are fixed beforehand. Default is TRUE. |
gstandard |
Text. Indicate if there are a Gold Standard by Rows or columns. Only first letter matter without Case sensitivity. Options are: "N" for None, "R" for in Rows and "C" for in Columns. Default is "N". |
Examples
CheckSampling(TRUE,"rows")
CheckSampling(TRUE,"Columns")
Delta coefficient function
Description
This function provides an analysis of the matrix provided, returning all all the parameters estimations and SE calculations that have sense with the fixedrows and gstandard provided.
Usage
Delta(datatable, fixedrows = FALSE, gstandard = "No", maxits = 1000,
tol = 1e-12, dplaces = 4, showall = FALSE)
## S3 method for class 'Delta'
print(x, ...)
## S3 method for class 'Delta'
summary(object, ...)
Arguments
datatable |
Matrix. Expected to be square matrix with at least 2 rows (columns), non negative values and at least an element different of zero. |
fixedrows |
Boolean. Indicate if sample rows are fixed beforehand. Default is TRUE. |
gstandard |
Text. Indicate if there are a Gold Standard by Rows or columns. Only first letter matter without Case sensitivity. Options are: "N" for None, "R" for in Rows and "C" for in Columns. Default is "N". |
maxits |
Whole number. Indicate the maximum number of iterations of the numeric method to calculate B. Expected to be 100 <= maxits <= 5000. Default is 1000. |
tol |
Double number. Indicate the precision of the numeric method to calculate B. Expected to be 1e-6 <= tol <= 1e-15.Default is 1e-12. |
dplaces |
Whole number. Decimal placed to be shown in the result. Expected to be 1 <= dplaces <0 6. Default 4. |
showall |
Boolean. Indicate if all output should be shown. If TRUE also shown hidden results. If FALSE shown only main output. By default is FALSE. |
x |
List produced by Delta |
... |
Other print options |
object |
List produced by Delta |
Details
This function study the matrix provided by the user. This function modify the matrix deleting missing rows and columns and if it is needed for the estimation, adding 0.5 to each cell.
Also calculate Cohen's Kappa coefficient and the goodness of fit for the Delta model.
Value
NULL
NULL
Examples
Delta(matrix(c(1,2,3,4),2,2))
Delta(matrix(c(65,5,10,20),2,2),fixedrows=TRUE,gstandard="Row")
Calculate Asintotic Delta related parameters function
Description
This function perform all needed calculations to get all Delta related parameters, for a 2x2 matrix. All calculations are asintotics.
Usage
GetAsinDeltaParams(mx, fixedrows = TRUE)
## S3 method for class 'GetAsinDeltaParams'
print(x, ...)
Arguments
mx |
Matrix. Agreement contingency table to perform calculations |
fixedrows |
Boolean. Indicate if sample rows are fixed beforehand. |
x |
List produced by GetAsinDeltaParams |
... |
Other print options |
Value
NULL
Examples
GetAsinDeltaParams(matrix(c(60,10,10,20),2,2),TRUE)
Calculate B function
Description
This function solve numericaly the non lineal inequation of the Delta system. Also return the s(i) values of the equation.
Usage
GetB(mx, tol = 1e-12, maxits = 1000)
Arguments
mx |
Matrix. Modified matrix to have a solution. Usually GetMx$M1 for k>2 and GetMx$M2 in case of k = 2. |
tol |
Double number. Indicate the precision of the numeric method to calculate B. Expected to be 1e-6 <= tol <= 1e-15.Default is 1e-12. |
maxits |
Whole number. Indicate the maximum number of iterations of the numeric method to calculate B. Expected to be 100 <= maxits <= 5000. Default is 1000. |
Examples
GetB(mx = matrix(c(1,0,0,0,2,0,0,0,3),3,3),tol = 1e-12, maxits = 1000)
GetB(mx = matrix(c(1,2,0,3,4,0,0,0,1),3,3),tol = 1e-12, maxits = 1000)
Calculate Covariance function
Description
This function calculate covariance for combinations Cov(Delta,Delta), Cov(Delta,Pi) and Cov(Pi,Pi).
Usage
GetCovariance(mx, Delta, Pi, B)
Arguments
mx |
Matrix. Modified matrix to have a solution. Usually GetMx$M1 for k>2 and GetMx$M2 in case of k = 2. |
Delta |
Vector. Each element indicate the probability of recognize an element i. |
Pi |
Vector. Each element indicate the probability of classify at random an element in category i. |
B |
Double. Numerical solution to the equation given by the model. |
Examples
GetCovariance(mx = matrix(c(1.5,0.5,0.5,0.5,2.5,0.5,0.5,0.5,3.5),3,3),
Delta = c(0.4,0.5714286,0.666667),
Pi = c(0.3333,0.333333,0.33333),B = 4.5)
GetCovariance(mx = matrix(c(60,0,3,2,50,1,3,2,79),3,3),
Delta = c( 0.8945724, 0.9522836, 0.8962094),
Pi = c( 0.2703707, 0.1939561, 0.5356732), B = 17.94867)
Calculate Delta related parameters function
Description
This function perform all needed calculations to get all Delta related parameters. For do the exact calculations some variables previously calculated are needed.
Usage
GetDeltaParams(mx, Delta, Pi, k)
Arguments
mx |
Matrix. Agreement contingency table to perform calculations |
Delta |
Vector. Each element indicate the probability of recognize an element i. |
Pi |
Vector. Each element indicate the probability of classify at random an element in category i. |
k |
Integer. Dimension of the problem. |
Examples
GetDeltaParams(mx = matrix(c(60,0,3,2,50,1,3,2,79),3,3),
Delta = c( 0.8945724, 0.9522836, 0.8962094),
Pi = c( 0.2703707, 0.1939561, 0.5356732), k = 3)
Calculate Delta related parameters variance function
Description
This function perform all needed calculations to get all Delta related parameters variance. For do the exact calculations some variables previously calculated are needed.
Usage
GetDeltaParamsVar(mx, fixedrows = FALSE, Delta, Pi, k, Cov, E)
Arguments
mx |
Matrix. Agreement contingency table to perform calculations |
fixedrows |
Boolean. Indicate if sample rows are fixed beforehand. |
Delta |
Vector. Each element indicate the probability of recognize an element i. |
Pi |
Vector. Each element indicate the probability of classify at random an element in category i. |
k |
Integer. Dimension of the problem. |
Cov |
Matrix. Covariance matrix of Delta. |
E |
Double. Value calculated for Cov matrix derivation. |
Examples
GetDeltaParamsVar(mx = matrix(c(60,0,3,2,50,1,3,2,79),3,3),
fixedrows = FALSE,Delta = c( 0.8945724, 0.9522836, 0.8962094),
Pi = c( 0.2703707, 0.1939561, 0.5356732), k = 3,
Cov = matrix(c(0.002736490, 0.000004188, -0.001074704,
0.000004188, 0.001141059, -0.000181746,
-0.001074704, -0.000181746, 0.004912131),3,3),
E = c(0.03159824, 0.01304313, -0.88650011))
Calculate Delta and Pi parameters function
Description
This function provide an estimation of Pi and Delta for each category. To do so, it is needed to solve the non-linear equation of B, given by the function GetB.
Usage
GetDeltaPi(mx, dtp, tol = 1e-12, maxits = 1000, original.mx = TRUE)
Arguments
mx |
Matrix. Modified matrix to have a solution. Usually GetMx$M1 for k>2 and GetMx$M2 in case of k = 2. |
dtp |
String. Type of delta problem. |
tol |
Double number. Indicate the precision of the numeric method to calculate B. Expected to be 1e-6 <= tol <= 1e-15.Default is 1e-12. |
maxits |
Whole number. Indicate the maximum number of iterations of the numeric method to calculate B. Expected to be 100 <= maxits <= 5000. Default is 1000. |
original.mx |
Boolean. Indicate if the dtp parameter correspond to the current mx parameter. By default TRUE. |
Details
In some type of problems, the solution is on the borderline, and in those situation we may have not solutions at all, only one or infinity of them.
Examples
GetDeltaPi(mx = matrix(c(1,0,0,0,2,0,0,0,3),3,3), dtp = "DN0", tol = 1e-12, maxits = 1000)
GetDeltaPi(mx = matrix(c(1.5,2.5,0.5,3.5,4.5,0.5,0.5,0.5,1.5),3,3), dtp = "DN2",
tol = 1e-12, maxits = 1000, original.mx = FALSE)
Get Delta problem type function
Description
This function apply Test to identify where are the solution located. We have mainly 3 situations for k > 2 and 2 for k = 2. For k > 2 we have: DN2 = No estimators in the boundary. DN1 = Some estimator in the boundary and global agreement imaginary. DN0 = Any other case For k = 2 we have: DA0 = Some estimator in the boundary. DA1 = Any other case
Usage
GetDeltaProblemType(Mx)
Arguments
Mx |
Matrix. Matrix reduced. |
Examples
GetDeltaProblemType(matrix(c(1,2,0,3,4,0,0,0,1),3,3))
GetDeltaProblemType(matrix(c(1,0,0,0,2,0,0,0,3),3,3))
Calculate Goodness of fit function
Description
This function provide an Chi-square test for the given matrix, Delta and Pi provided.
Usage
GetGoodness(mx, Pi, Delta)
## S3 method for class 'GetGoodness'
print(x, ...)
Arguments
mx |
Matrix. Modified matrix to have a solution. Usually GetMx$M1 for k>2 and GetMx$M2 in case of k = 2. |
Pi |
Vector. Each element indicate the probability of classify at random an element in category i. |
Delta |
Vector. Each element indicate the probability of recognize an element i. |
x |
List produced by GetGoodness |
... |
Other print options |
Value
NULL
Examples
GetGoodness(mx = matrix(c(1,0,0,0,2,0,0,0,3),3,3), Delta = c(1,1,1), Pi = NULL)
GetGoodness(mx = matrix(c(1.5,2.5,0.5,3.5,4.5,0.5,0.5,0.5,1.5),3,3),
Delta = c(-0.2662395, 0.2047577, 0.5664672),
Pi = c(0.42564365, 0.49700867, 0.07734769))
GetGoodness(mx = matrix(c(60,0,3,2,50,1,3,2,79),3,3),
Delta = c( 0.8945724, 0.9522836, 0.8962094),
Pi = c( 0.2703707, 0.1939561, 0.5356732))
Calculate Cohen's Kappa coefficient function
Description
This function perform Cohen's Kappa coefficient calculations. The function provide the Kappa coefficient and SE.
Usage
GetKappa(mx)
## S3 method for class 'GetKappa'
print(x, ...)
Arguments
mx |
Matrix. Agreement contingency table to perform calculations |
x |
List produced by GetKappa |
... |
Other print options |
Value
NULL
Examples
GetKappa(matrix(c(50,10,10,20),2,2))
Get Kappa problem type function
Description
This function apply Test to identify where kappa solutions are placed K0 = Full agreement (diagonal matrix) K1 = Any other case
Usage
GetKappaProblemType(Mx)
Arguments
Mx |
Matrix. Matrix reduced. |
Examples
GetKappaProblemType(matrix(c(1,2,0,3,4,0,0,0,1),3,3))
GetKappaProblemType(matrix(c(1,0,0,0,2,0,0,0,3),3,3))
Get reduced matrix (M1) function
Description
This function reduce matrix provided by the user deleting missing categories, those j where sum(datatable[j,]) = sum(datatable[,j]) = 0. Also provide a list of the categories deleted and provides the new size of the problem
Usage
GetM1(datatable)
## S3 method for class 'GetM1'
print(x, ...)
Arguments
datatable |
Matrix. Expected to be square matrix with at least 2 rows (columns), non negative values and at least an element different of zero. |
x |
List produced by GetM1 |
... |
Other print options |
Value
NULL
Examples
GetM1(matrix(c(1,2,0,3,4,0,0,0,0),3,3))
Get matrix of the problem (Mx) function
Description
This function produce 3 new auxiliar matrix. Those matrix are always defined, but depending of the problem they will be used or not. All the auxiliar matrices are created to be able to solve the problem and avoid issues with solutions in the boundary or not completly defined.
Usage
GetMx(M1)
Arguments
M1 |
Matrix. Initial matrix without missing categories. |
Details
The matrix are defined as follows - M2: Extended M1 with $c_33$ of 1 and increased by 0.5 - M3: M1 increased by 0.5 - M4: M1 increased by 1
In case of M1 is not 2x2, M2 and M3 are the same matrix.
Examples
GetMx(matrix(c(1,2,0,3,4,0,0,0,1),3,3))