afc: Simple Correspondence Analysis
In NominalLogisticBiplot: Biplot representations of categorical data
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
This function calculates simple correspondence analysis for a data matrix.
Usage
1
Arguments
x
A frequency matrix or a binary matrix obtained from the original data set of nominal variables.
dim
Number of dimensions for the solution
alpha
Biplot weight for rows and columns. 1 means rows in principal coordinates and columns in standard coordinates, 0 means rows in standard coordinates and columns in principal coordinates.
Value
An object of class "afc.sol".This has some components:
Title
Title of the statistical technique
Non_Scaled_Data
Original data
Minima
vector with the minimum values for each column of the initial data matrix
Maxima
vector with the maximum values for each column of the initial data matrix
Initial_Transformation
Name of the transformation for the data
Scaled_Data
Scaled data according to the transformation
nrows
Number of rows of the data set
ncols
Number of columns of the data set
dim
Number of dimensions for the solution
CumInertia
Acumulated Inertia
Scale_Factor
Scale factor for the transformation
RowCoordinates
Coordinates for the individuals in the reduced dimension space
ColCoordinates
Coordinates for the variables in the reduced dimension space
RowContributions
Contributions of the dimensions to explain the inertia of each row
ColContributions
Contributions of the dimensions to explain the inertia of each column
Inertia
Inertia for each dimension
Eigenvalues
Eigenvalues
Author(s)
Jose Luis Vicente-Villardon,Julio Cesar Hernandez Sanchez
Maintainer: Jose Luis Vicente-Villardon <villardon@usal.es>
References
BENZECRI, J.P. (1973) L'analyse des Donnees. Vol. 2. L'analyse des correspondences. Dunod. Paris.
See Also
Examples
1
2
3
4
5
6
data(HairColor)
G = NominalMatrix2Binary(data.matrix(HairColor))
mca=afc(G,dim=2)
mca
Example output
Loading required package: mirt
Loading required package: stats4
Loading required package: lattice
Loading required package: gmodels
Loading required package: MASS
$Title
[1] "Correspondence Analysis"
$Non_Scaled_Data
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
I1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0
I2 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0
I3 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0
I4 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0
I5 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0
I6 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0
I7 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1
$Minima
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
$Maxima
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
$Initial_Transformation
[1] "Correspondence Analysis"
$Scaled_Data
V1 V2 V3 V4 V5 V6
I1 0.01224490 -0.01224490 0.01632653 -0.004081633 -0.004081633 -0.008163265
I2 0.01224490 -0.01224490 -0.01224490 0.024489796 -0.004081633 -0.008163265
I3 -0.01632653 0.01632653 0.01632653 -0.004081633 -0.004081633 -0.008163265
I4 0.01224490 -0.01224490 -0.01224490 -0.004081633 -0.004081633 0.020408163
I5 -0.01632653 0.01632653 -0.01224490 -0.004081633 0.024489796 -0.008163265
I6 -0.01632653 0.01632653 0.01632653 -0.004081633 -0.004081633 -0.008163265
I7 0.01224490 -0.01224490 -0.01224490 -0.004081633 -0.004081633 0.020408163
V7 V8 V9 V10 V11 V12
I1 0.01632653 -0.008163265 -0.008163265 0.020408163 -0.008163265 -0.01224490
I2 -0.01224490 0.020408163 -0.008163265 -0.008163265 0.020408163 -0.01224490
I3 -0.01224490 0.020408163 -0.008163265 -0.008163265 -0.008163265 0.01632653
I4 -0.01224490 -0.008163265 0.020408163 -0.008163265 -0.008163265 0.01632653
I5 -0.01224490 -0.008163265 0.020408163 -0.008163265 0.020408163 -0.01224490
I6 0.01632653 -0.008163265 -0.008163265 0.020408163 -0.008163265 -0.01224490
I7 0.01632653 -0.008163265 -0.008163265 -0.008163265 -0.008163265 0.01632653
V13 V14 V15
I1 0.01632653 -0.01224490 -0.004081633
I2 -0.01224490 0.01632653 -0.004081633
I3 -0.01224490 0.01632653 -0.004081633
I4 -0.01224490 0.01632653 -0.004081633
I5 0.01632653 -0.01224490 -0.004081633
I6 0.01632653 -0.01224490 -0.004081633
I7 -0.01224490 -0.01224490 0.024489796
$Expected
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.28888060 0.38517414 0.9983912 -2.0357908 -0.1932878 -0.38304753
[2,] 0.09864940 -0.13153253 -1.1453578 2.7434482 1.0056851 -0.15652990
[3,] 0.03027146 -0.04036195 -0.2898051 0.6848545 0.2365775 -0.02600842
[4,] 0.62884650 -0.83846201 -0.7287854 0.7534033 -1.2666924 1.34982261
[5,] -0.84277717 1.12370289 0.1851999 1.0056851 2.6222212 -2.09175299
[6,] -0.57290942 0.76387922 1.2132966 -2.0851372 0.5123100 -1.03353126
[7,] 0.94679983 -1.26239977 -0.2329394 -1.0664631 -2.9168136 2.34104750
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 1.2261643 -1.2737713 -0.565475129 1.7534627 -1.1145393 -0.42594896
[2,] -1.7291304 1.7141513 0.879544184 -2.0604640 1.8745666 0.12393156
[3,] -0.4301570 0.4279548 0.217280688 -0.5202351 0.4607160 0.03967941
[4,] -0.3159676 0.4756936 -0.001742137 -1.1921700 -0.2566445 0.96587635
[5,] -0.8659305 0.6211313 0.677764394 0.1595111 1.8139531 -1.31564282
[6,] 1.1827410 -1.3069278 -0.467183752 2.0843041 -0.7864136 -0.86526032
[7,] 0.9322801 -0.6582319 -0.740188248 -0.2244088 -1.9916384 1.47736477
[,13] [,14] [,15]
[1,] 1.1045459 -1.161735039 0.1715674
[2,] -1.0384143 1.393901994 -1.0664631
[3,] -0.2679642 0.351297803 -0.2500007
[4,] -1.2170108 0.738198412 1.4364371
[5,] 0.9804145 -0.008143256 -2.9168136
[6,] 1.5603060 -1.353511030 -0.6203850
[7,] -1.1218771 0.039991115 3.2456579
$nrows
[1] 7
$ncols
[1] 15
$dim
[1] 2
$EigenValues
[1] 5.904560e-01 5.453697e-01 4.142086e-01 2.638530e-01 1.592406e-01
[6] 2.687199e-02 1.692938e-32
$Inertia
[1] 2.952280e+01 2.726849e+01 2.071043e+01 1.319265e+01 7.962030e+00
[6] 1.343600e+00 8.464688e-31
$CumInertia
[1] 29.52280 56.79129 77.50172 90.69437 98.65640 100.00000 100.00000
$RowCoordinates
Dim 1 Dim 2
I1 -0.8927650 0.4021286
I2 0.9488720 -0.8152211
I3 0.2418074 -0.1981973
I4 0.7869238 0.3419815
I5 -0.4209591 -1.1253464
I6 -1.1567155 0.1513759
I7 0.4928364 1.2432788
$ColCoordinates
Dim 1 Dim 2
V1 0.5656083 0.5373272
V2 -0.7541443 -0.7164362
V3 -1.0204954 0.2171660
V4 1.6070155 -1.4948045
V5 -0.7129390 -2.0634561
V6 1.0837049 1.4533813
V7 -0.8787807 1.0982051
V8 1.0082710 -0.9291114
V9 0.3099000 -0.7181963
V10 -1.7355064 0.5074581
V11 0.4470382 -1.7791303
V12 0.8589788 0.8477815
V13 -1.3946506 -0.3495133
V14 1.1164270 -0.4103864
V15 0.8346708 2.2796991
$RowContributions
Dim 1 Dim 2
I1 54.97 11.15
I2 34.41 25.40
I3 3.73 2.51
I4 36.79 6.95
I5 6.48 46.33
I6 85.40 1.46
I7 10.19 64.86
$ColContributions
Dim 1 Dim 2
V1 25.19 20.99
V2 25.19 20.99
V3 46.12 1.93
V4 25.41 20.31
V5 5.00 38.70
V6 27.74 46.08
V7 34.20 49.33
V8 24.01 18.83
V9 2.27 11.25
V10 71.14 5.62
V11 4.72 69.05
V12 32.67 29.40
V13 86.14 5.00
V14 55.20 6.89
V15 6.86 47.24
$Scale_Factor
[1] 1
attr(,"class")
[1] "afc.sol"
NominalLogisticBiplot documentation built on May 2, 2019, 6:03 a.m.
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Description Usage Arguments Value Author(s) References See Also Examples
Description
This function calculates simple correspondence analysis for a data matrix.
Usage
1 |
Arguments
x |
A frequency matrix or a binary matrix obtained from the original data set of nominal variables. |
dim |
Number of dimensions for the solution |
alpha |
Biplot weight for rows and columns. 1 means rows in principal coordinates and columns in standard coordinates, 0 means rows in standard coordinates and columns in principal coordinates. |
Value
An object of class "afc.sol".This has some components:
Title |
Title of the statistical technique |
Non_Scaled_Data |
Original data |
Minima |
vector with the minimum values for each column of the initial data matrix |
Maxima |
vector with the maximum values for each column of the initial data matrix |
Initial_Transformation |
Name of the transformation for the data |
Scaled_Data |
Scaled data according to the transformation |
nrows |
Number of rows of the data set |
ncols |
Number of columns of the data set |
dim |
Number of dimensions for the solution |
CumInertia |
Acumulated Inertia |
Scale_Factor |
Scale factor for the transformation |
RowCoordinates |
Coordinates for the individuals in the reduced dimension space |
ColCoordinates |
Coordinates for the variables in the reduced dimension space |
RowContributions |
Contributions of the dimensions to explain the inertia of each row |
ColContributions |
Contributions of the dimensions to explain the inertia of each column |
Inertia |
Inertia for each dimension |
Eigenvalues |
Eigenvalues |
Author(s)
Jose Luis Vicente-Villardon,Julio Cesar Hernandez Sanchez
Maintainer: Jose Luis Vicente-Villardon <villardon@usal.es>
References
BENZECRI, J.P. (1973) L'analyse des Donnees. Vol. 2. L'analyse des correspondences. Dunod. Paris.
See Also
Examples
1 2 3 4 5 6 |
data(HairColor)
G = NominalMatrix2Binary(data.matrix(HairColor))
mca=afc(G,dim=2)
mca
|
Example output
Loading required package: mirt
Loading required package: stats4
Loading required package: lattice
Loading required package: gmodels
Loading required package: MASS
$Title
[1] "Correspondence Analysis"
$Non_Scaled_Data
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
I1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0
I2 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0
I3 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0
I4 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0
I5 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0
I6 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0
I7 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1
$Minima
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
$Maxima
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
$Initial_Transformation
[1] "Correspondence Analysis"
$Scaled_Data
V1 V2 V3 V4 V5 V6
I1 0.01224490 -0.01224490 0.01632653 -0.004081633 -0.004081633 -0.008163265
I2 0.01224490 -0.01224490 -0.01224490 0.024489796 -0.004081633 -0.008163265
I3 -0.01632653 0.01632653 0.01632653 -0.004081633 -0.004081633 -0.008163265
I4 0.01224490 -0.01224490 -0.01224490 -0.004081633 -0.004081633 0.020408163
I5 -0.01632653 0.01632653 -0.01224490 -0.004081633 0.024489796 -0.008163265
I6 -0.01632653 0.01632653 0.01632653 -0.004081633 -0.004081633 -0.008163265
I7 0.01224490 -0.01224490 -0.01224490 -0.004081633 -0.004081633 0.020408163
V7 V8 V9 V10 V11 V12
I1 0.01632653 -0.008163265 -0.008163265 0.020408163 -0.008163265 -0.01224490
I2 -0.01224490 0.020408163 -0.008163265 -0.008163265 0.020408163 -0.01224490
I3 -0.01224490 0.020408163 -0.008163265 -0.008163265 -0.008163265 0.01632653
I4 -0.01224490 -0.008163265 0.020408163 -0.008163265 -0.008163265 0.01632653
I5 -0.01224490 -0.008163265 0.020408163 -0.008163265 0.020408163 -0.01224490
I6 0.01632653 -0.008163265 -0.008163265 0.020408163 -0.008163265 -0.01224490
I7 0.01632653 -0.008163265 -0.008163265 -0.008163265 -0.008163265 0.01632653
V13 V14 V15
I1 0.01632653 -0.01224490 -0.004081633
I2 -0.01224490 0.01632653 -0.004081633
I3 -0.01224490 0.01632653 -0.004081633
I4 -0.01224490 0.01632653 -0.004081633
I5 0.01632653 -0.01224490 -0.004081633
I6 0.01632653 -0.01224490 -0.004081633
I7 -0.01224490 -0.01224490 0.024489796
$Expected
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.28888060 0.38517414 0.9983912 -2.0357908 -0.1932878 -0.38304753
[2,] 0.09864940 -0.13153253 -1.1453578 2.7434482 1.0056851 -0.15652990
[3,] 0.03027146 -0.04036195 -0.2898051 0.6848545 0.2365775 -0.02600842
[4,] 0.62884650 -0.83846201 -0.7287854 0.7534033 -1.2666924 1.34982261
[5,] -0.84277717 1.12370289 0.1851999 1.0056851 2.6222212 -2.09175299
[6,] -0.57290942 0.76387922 1.2132966 -2.0851372 0.5123100 -1.03353126
[7,] 0.94679983 -1.26239977 -0.2329394 -1.0664631 -2.9168136 2.34104750
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 1.2261643 -1.2737713 -0.565475129 1.7534627 -1.1145393 -0.42594896
[2,] -1.7291304 1.7141513 0.879544184 -2.0604640 1.8745666 0.12393156
[3,] -0.4301570 0.4279548 0.217280688 -0.5202351 0.4607160 0.03967941
[4,] -0.3159676 0.4756936 -0.001742137 -1.1921700 -0.2566445 0.96587635
[5,] -0.8659305 0.6211313 0.677764394 0.1595111 1.8139531 -1.31564282
[6,] 1.1827410 -1.3069278 -0.467183752 2.0843041 -0.7864136 -0.86526032
[7,] 0.9322801 -0.6582319 -0.740188248 -0.2244088 -1.9916384 1.47736477
[,13] [,14] [,15]
[1,] 1.1045459 -1.161735039 0.1715674
[2,] -1.0384143 1.393901994 -1.0664631
[3,] -0.2679642 0.351297803 -0.2500007
[4,] -1.2170108 0.738198412 1.4364371
[5,] 0.9804145 -0.008143256 -2.9168136
[6,] 1.5603060 -1.353511030 -0.6203850
[7,] -1.1218771 0.039991115 3.2456579
$nrows
[1] 7
$ncols
[1] 15
$dim
[1] 2
$EigenValues
[1] 5.904560e-01 5.453697e-01 4.142086e-01 2.638530e-01 1.592406e-01
[6] 2.687199e-02 1.692938e-32
$Inertia
[1] 2.952280e+01 2.726849e+01 2.071043e+01 1.319265e+01 7.962030e+00
[6] 1.343600e+00 8.464688e-31
$CumInertia
[1] 29.52280 56.79129 77.50172 90.69437 98.65640 100.00000 100.00000
$RowCoordinates
Dim 1 Dim 2
I1 -0.8927650 0.4021286
I2 0.9488720 -0.8152211
I3 0.2418074 -0.1981973
I4 0.7869238 0.3419815
I5 -0.4209591 -1.1253464
I6 -1.1567155 0.1513759
I7 0.4928364 1.2432788
$ColCoordinates
Dim 1 Dim 2
V1 0.5656083 0.5373272
V2 -0.7541443 -0.7164362
V3 -1.0204954 0.2171660
V4 1.6070155 -1.4948045
V5 -0.7129390 -2.0634561
V6 1.0837049 1.4533813
V7 -0.8787807 1.0982051
V8 1.0082710 -0.9291114
V9 0.3099000 -0.7181963
V10 -1.7355064 0.5074581
V11 0.4470382 -1.7791303
V12 0.8589788 0.8477815
V13 -1.3946506 -0.3495133
V14 1.1164270 -0.4103864
V15 0.8346708 2.2796991
$RowContributions
Dim 1 Dim 2
I1 54.97 11.15
I2 34.41 25.40
I3 3.73 2.51
I4 36.79 6.95
I5 6.48 46.33
I6 85.40 1.46
I7 10.19 64.86
$ColContributions
Dim 1 Dim 2
V1 25.19 20.99
V2 25.19 20.99
V3 46.12 1.93
V4 25.41 20.31
V5 5.00 38.70
V6 27.74 46.08
V7 34.20 49.33
V8 24.01 18.83
V9 2.27 11.25
V10 71.14 5.62
V11 4.72 69.05
V12 32.67 29.40
V13 86.14 5.00
V14 55.20 6.89
V15 6.86 47.24
$Scale_Factor
[1] 1
attr(,"class")
[1] "afc.sol"
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