# CAvariants: Six variants of correspondence analysis In CAvariants: Correspondence Analysis Variants

## Description

It performs
1) simple correspondence analysis
2) doubly ordered correspondence analysis
3) singly ordered correspondence analysis
4) non symmetrical correspondence analysis
5) doubly ordered non symmetrical correspondence analysis
6) singly ordered non symmetrical correspondence analysis

## Usage

 ```1 2 3``` ```CAvariants( Xtable, mj = NULL, mi = NULL, firstaxis = 1, lastaxis = 2, catype = "CA", ellcomp = TRUE, Mell = min(nrow(Xtable), ncol(Xtable)) - 1, alpha = 0.05) ```

## Arguments

 `Xtable` The two-way contingency table. `mi` The assigned ordered scores for the row categories. By default, `mi = NULL`, which gives consecutive integer valued (natural) scores. `mj` The assigned ordered scores for the column categories, By default, `mj = NULL`, which gives consecutive integer valued (natural) scores.
 `firstaxis` The horizontal polynomial or principal axis. By default `firstaxis = 1`. `lastaxis` The vertical polynomial or principal axis. By default `lastaxis = 2`. `catype` The input parameter for specifying what variant of correspondence analysis is considered. By default, `catype = "CA"`. Other possible values are: `catype = "SOCA"`, `catype = "DOCA"`, `catype = "NSCA"`, `catype = "SONSCA"`, `catype = "DONSCA"`. `ellcomp` This input parameter ensures that the characteristics of the algebraic confidence ellipses are computed and stored. When `ellcomp = TRUE` (which is by default), the output includes the characteristics of the ellipses. The eccentricity of the confidence ellipses is summarised by the quantity `eccentricity`, this is the distance between the center and either of its two foci, which can be thought of as a measure of how much the conic section deviates from being circular (when it is equal to zero then the region becomes circular). The semi-major axis length of the ellipse for each row and column point is given by `HL Axis 1` while `HL Axis 2` gives the semi-minor axis length of the points along the second axis. The area of the ellipse for each row and column category is given by `Area` while the p-value of each category is defined by `P-value`. `Mell` The number of axes `Mell` considered in determining the structure of the elliptical confidence regions. By default, `Mell = min(nrow(Xtable), ncol(Xtable)) - 1`, i.e. the rank of the data matrix. `alpha` The confidence level of the elliptical regions. By default, `alpha = 0.05`.

## Details

This function belongs to the object class called `cacorporateplus`

## Value

Description of the output returned

 `Xtable ` The two-way contingency table. `rows` The row number of the two-way contingency table. `cols` The column number of the two-way contingency table. `r` The rank of the two-way contingency table. `rowlabels` The label of the row variable. `collabels` The label of the column variable. `Rprinccoord` The row principal coordinates. When the input parameter `catype` is `"DOCA"`, `"SOCA"`, `"SONSCA"` or `"DONSCA"`, they are row principal polynomial coordinates. `Cprinccoord` The column principal coordinates. When the input parameter `catype` is `"DOCA"` or `"DONSCA"`, they are column principal polynomial coordinates. `Rstdcoord ` The row standard coordinates. When the input parameter `catype` is `"DOCA"` or `"DONSCA"`, they are row standard polynomial coordinates. `Cstdcoord ` The column standard coordinates. When the input parameter `catype` is `"DOCA"`, `"SOCA"`, `"SONSCA"` or `"DONSCA"`, they are column standard polynomial coordinates. `tauden` The tau denominator is given when the input parameter `catype` is `"NSCA"`, `"SONSCA"`, or `"DONSCA"`, otherwise it is a null value. `tau` The tau index is given when the input parameter `catype` is `"NSCA"`, `"SONSCA"`, or `"DONSCA"`, otherwise it is a null value. `inertiasum` The total inertia of the classical correspondence analysis when catype is `"CA"`, `"DOCA"` or `"SOCA"` (the Pearson's index), or the inertia of non symmetrical correspondence analysis when `catype` is `"NSCA"`, `"DONSCA"` or `"SONSCA"` (numerator of the Goodman-Kruskal tau index). `inertias` The associated inertia in absolute value and percentage, in the row space for each principal or polynomial axis. `inertias2` The associated inertia in absolute value and percentage, in the column space for each principal or polynomial axis. When `catype` is `"CA"` or `"NSCA"` the associated inertia in the row and column spaces are the same for each principal axis. `comps` The polynomial components of inertia when the variables are ordered. The inertia of row and/or column space is partitioned in terms of polynomial components in ordered CA variants. `catype` The kind of correspondence analysis chosen. `mj` The ordered scores of a column variable. When `mj = NULL`, the natural ordered numbers are shown. `mi` The ordered scores of a row variable. When `mi = NULL`, the natural ordered numbers are shown. `pcc` The weighted centered column profile matrix. `Jmass` The weight matrix of the column variable. `Imass` The weight matrix of the row variable. `Trend` The inner product, `Inner product`, of the biplot coordinates (concerning the first two axes when `firstaxis=1` and `lastaxis=2`) `Z` The generalized correlation matrix when catype is `"SOCA"`, `"DOCA"` , `"SONSCA"`, `"DONSCA"`, but when catype is `"CA"`, `"NSCA"`, it gives again the inner product matrix of biplot coordinates. `ellcomp` The flag parameter, `ellcomp`, specifies that the characteristics of the confidence ellipses (eccentricity, semi-axis, area, p-values) are computed. By default, `ellcomp = TRUE`. `risell` When the input parameter, `ellcomp`, is set to `ellcomp = TRUE`, the output includes the characteristics `risell` of the confidence ellipses, the eccentricity of the confidence ellipses, `risell\$eccentricity`, for each row and column point, the summary results, `risell\$row.summ` and `risell\$col.summ`, contain the semi-major axis length of the ellipse, `HL Axis 1`, the semi-minor axis length for the ellipse, `HL Axis 2`, the area of the ellipse, `Area` and the p-value, `P-value`. `Mell` The number of axes `Mell` considered in determining the structure of the elliptical confidence regions. By default, `Mell = min(nrow(Xtable), ncol(Xtable)) - 1`, i.e. the rank of the data matrix.

## Note

This function recalls internally many other functions, depending on the setting of the input parameter `catype`, it recalls one of the six functions which does a variant of correspondence analysis. After performing a variant of correspondence analysis, it gives the output object necessary for printing and plotting the results. These two important functions are `print.CAvariants` and `plot.CAvariants`. This function belongs to the class `cacorporateplus`.

## Author(s)

Rosaria Lombardo and Eric J Beh

## References

Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons. Lombardo R Beh EJ Variants of Simple Correspondence Analysis. The R Journal (accepted).

## Examples

 ```1 2 3 4 5 6 7 8``` ```data(asbestos) CAvariants(asbestos, catype = "CA", firstaxis = 1, lastaxis = 2) CAvariants(asbestos, catype = "DOCA", firstaxis = 1,lastaxis = 2) CAvariants(asbestos, catype = "DONSCA",firstaxis=1, lastaxis = 2, ellcomp = FALSE) data(shopdataM) CAvariants(shopdataM, catype = "NSCA", firstaxis = 1, lastaxis = 2) CAvariants(shopdataM, catype = "SONSCA", firstaxis = 1, lastaxis = 2) CAvariants(shopdataM, catype = "SOCA", firstaxis = 1, lastaxis = 2) ```

### Example output

```Loading required package: tools

RESULTS for CA Correspondence Analysis

Data Matrix:
0-9 10-19 20-29 30-39 40+
none   310   212    21    25   7
grade1  36   158    35   102  35
grade2   0     9    17    49  51
grade3   0     0     4    18  28

Row weights: Imass
none   0.515  0.000  0.000  0.000
grade1 0.000  0.328  0.000  0.000
grade2 0.000  0.000  0.113  0.000
grade3 0.000  0.000  0.000  0.045

Column Weights: Jmass
0-9 10-19 20-29 30-39   40+
0-9   0.31 0.000 0.000 0.000 0.000
10-19 0.00 0.339 0.000 0.000 0.000
20-29 0.00 0.000 0.069 0.000 0.000
30-39 0.00 0.000 0.000 0.174 0.000
40+   0.00 0.000 0.000 0.000 0.108

Total inertia  0.581

The inertia values, their percentage contribution to the total inertia and
the cumulative percent inertias
inertia inertiapc cuminertiapc
value1   0.489    84.215       84.215
value2   0.089    15.352       99.567
value3   0.003     0.433      100.000

Column standard coordinates = column principal axes
Axis 1  Axis 2
0-9    -1.023   0.949
10-19  -0.368  -0.917
20-29   0.668  -0.582
30-39   1.093  -0.739
40+     1.901   1.714

Row standard coordinates = row principal axes
Axis 1  Axis 2
none    -0.847   0.472

Column principal  coordinates
Axis 1  Axis 2
0-9    -0.715   0.283
10-19  -0.258  -0.274
20-29   0.468  -0.174
30-39   0.764  -0.221
40+     1.330   0.512

Row principal coordinates
Axis 1  Axis 2
none    -0.592   0.141

Column distances from the origin of the plot
Axis 1  Axis 2
0-9     0.512   0.080
10-19   0.066   0.075
20-29   0.219   0.030
30-39   0.584   0.049
40+     1.768   0.262

Row distances from the origin of the plot
Axis 1  Axis 2
none     0.351   0.020

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
0-9  10-19  20-29  30-39    40+
none    0.739  0.089 -0.478 -0.751 -0.885
grade1 -0.677  0.260  0.427  0.613 -0.133
grade2 -1.038 -0.704  0.689  1.182  2.842
grade3 -0.932 -1.150  0.634  1.174  3.983

Eccentricity of ellipses
[1] 0.904

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2  Area P-value
none       0.175     0.075 0.041       0
grade1     0.217     0.093 0.063       0
grade2     0.282     0.120 0.107       0
grade3     0.405     0.173 0.220       0

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
0-9       0.221     0.094 0.065       0
10-19     0.187     0.080 0.047       0
20-29     0.334     0.143 0.150       0
30-39     0.293     0.125 0.115       0
40+       0.358     0.153 0.172       0

RESULTS for DOCA Correspondence Analysis

Data Matrix:
0-9 10-19 20-29 30-39 40+
none   310   212    21    25   7
grade1  36   158    35   102  35
grade2   0     9    17    49  51
grade3   0     0     4    18  28

Row weights: Imass
none   0.515  0.000  0.000  0.000
grade1 0.000  0.328  0.000  0.000
grade2 0.000  0.000  0.113  0.000
grade3 0.000  0.000  0.000  0.045

Column Weights: Jmass
0-9 10-19 20-29 30-39   40+
0-9   0.31 0.000 0.000 0.000 0.000
10-19 0.00 0.339 0.000 0.000 0.000
20-29 0.00 0.000 0.069 0.000 0.000
30-39 0.00 0.000 0.000 0.174 0.000
40+   0.00 0.000 0.000 0.000 0.108

Total inertia  0.581

Inertias, percent inertias and cumulative percent inertias of the row space

inertia inertiapc cuminertiapc
value1   0.478    82.355       82.355
value2   0.079    13.589       95.945
value3   0.024     4.055      100.000
Inertias, percent inertias and  cumulative percent inertias of the column space

inertia2 inertiapc2 cuminertiapc2
value1    0.486     84.937        84.937
value2    0.085     14.795        99.733
value3    0.002      0.267       100.000

Polynomial Components of Inertia

** Row Components **
Component Value P-value
Location                            534.331       0
Dispersion                           88.170       0
Error                                26.310       0
** Chi-squared Statistic **         648.812       0

** Column Components **
Component Value P-value
Location                            543.141   0.000
Dispersion                           94.609   0.000
Cubic                                 1.709   0.635
Error                                 9.352   0.025
** Chi-squared Statistic **         648.812   0.000

Generalized correlation matrix of Bivariate Moment Decomposition
v1     v2     v3     v4
u1  0.689  0.024 -0.003  0.052
u2 -0.085  0.264  0.023  0.040
u3 -0.064 -0.120  0.031 -0.063

Column standard polynomial coordinates = column polynomial axes
Axis 1  Axis 2
0-9    -1.049   0.931
10-19  -0.316  -0.868
20-29   0.417  -1.341
30-39   1.149  -0.487
40+     1.882   1.693

Row standard polynomial coordinates = row polynomial axes
Axis 1  Axis 2
none    -0.817   0.497

Column principal polynomial coordinates
Axis 1  Axis 2
0-9    -0.693   0.328
10-19  -0.265  -0.199
20-29   0.433  -0.267
30-39   0.738  -0.298
40+     1.353   0.332

Row principal polynomial coordinates
Axis 1  Axis 2
none    -0.594   0.132

Column distances from the origin of the plot
Axis 1  Axis 2
0-9     0.480   0.107
10-19   0.070   0.039
20-29   0.187   0.071
30-39   0.545   0.089
40+     1.829   0.110

Row distances from the origin of the plot
Axis 1  Axis 2
none     0.353   0.017

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
0-9  10-19  20-29  30-39    40+
none    1.341  0.125 -1.618 -1.793 -2.717
grade1 -1.211  0.412  2.446  1.280 -0.265
grade2 -1.919 -1.051  0.681  3.131  8.405
grade3 -1.717 -1.807 -1.016  3.362 12.006

Eccentricity of ellipses
[1] 0.909

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2  Area P-value
none       0.175     0.073 0.040       0
grade1     0.196     0.082 0.051       0
grade2     0.236     0.099 0.073       0
grade3     0.545     0.227 0.389       0

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
0-9       0.218     0.091 0.063       0
10-19     0.181     0.076 0.043       0
20-29     0.477     0.199 0.298       0
30-39     0.231     0.097 0.070       0
40+       0.347     0.145 0.158       0

RESULTS for DONSCA Correspondence Analysis

Data Matrix:
0-9 10-19 20-29 30-39 40+
none   310   212    21    25   7
grade1  36   158    35   102  35
grade2   0     9    17    49  51
grade3   0     0     4    18  28

Row weights: Imass
none      1      0      0      0
grade1    0      1      0      0
grade2    0      0      1      0
grade3    0      0      0      1

Column Weights: Jmass
0-9 10-19 20-29 30-39   40+
0-9   0.31 0.000 0.000 0.000 0.000
10-19 0.00 0.339 0.000 0.000 0.000
20-29 0.00 0.000 0.069 0.000 0.000
30-39 0.00 0.000 0.000 0.174 0.000
40+   0.00 0.000 0.000 0.000 0.108

Total inertia  0.141

Inertias, percent inertias and cumulative percent inertias of the row  space

inertia inertiapc cuminertiapc
value1   0.099    70.464       70.464
value2   0.035    24.858       95.321
value3   0.007     4.679      100.000
Inertias, percent inertias and  cumulative percent inertias of the column space

inertia2 inertiapc2 cuminertiapc2
value1    0.117     83.953        83.953
value2    0.022     15.947        99.901
value3    0.000      0.099       100.000

Predictability Index for Variants of Non symmetrical Correspondence Analysis:

Numerator of Tau Index predicting the row categories from the column categories

[1] 0.141

Tau Index predicting the row categories from the column categories

[1] 0.229

C-statistic 768.0696 and p-value 0

Polynomial Components of Inertia

** Row Components **
Component Value P-value
Location                            541.209       0
Dispersion                          190.925       0
Error                                35.935       0
** Chi-squared Statistic **         768.070       0

** Column Components **
Component Value P-value
Location                            639.152    0.00
Dispersion                          121.410    0.00
Cubic                                 0.756    0.86
Error                                 6.752    0.08
** Chi-squared Statistic **         768.070    0.00

Generalized correlation matrix of Bivariate Moment Decomposition
v1     v2     v3     v4
u1  0.312 -0.034 -0.004  0.015
u2 -0.139  0.124  0.007  0.016
u3  0.001 -0.076  0.009 -0.027

Column standard polynomial coordinates = column polynomial axes
Axis 1  Axis 2
0-9    -1.049   0.931
10-19  -0.316  -0.868
20-29   0.417  -1.341
30-39   1.149  -0.487
40+     1.882   1.693

Row standard polynomial coordinates = row polynomial axes
Axis 1  Axis 2
none    -0.586   0.357

Column principal polynomial coordinates
Axis 1  Axis 2
0-9     0.356  -0.260
10-19   0.080   0.065
20-29  -0.229   0.172
30-39  -0.369   0.245
40+    -0.530   0.038

Row principal polynomial coordinates
Axis 1  Axis 2
none    -0.306   0.068

Column distances from the origin of the plot
Axis 1  Axis 2
0-9     0.127   0.067
10-19   0.006   0.004
20-29   0.053   0.030
30-39   0.136   0.060
40+     0.280   0.001

Row distances from the origin of the plot
Axis 1  Axis 2
none     0.094   0.005

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
0-9  10-19  20-29  30-39    40+
none    0.384  0.038 -0.219 -0.385 -0.460
grade1 -0.221  0.079  0.210  0.175 -0.029
grade2 -0.120 -0.069  0.020  0.147  0.312
grade3 -0.043 -0.047 -0.012  0.063  0.177

Eccentricity of ellipses
[1] 0.9

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2  Area P-value
none       0.056     0.025 0.004       0
grade1     0.051     0.022 0.004       0
grade2     0.036     0.016 0.002       0
grade3     0.052     0.023 0.004       0

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
0-9       0.098     0.043 0.013       0
10-19     0.082     0.036 0.009       0
20-29     0.214     0.093 0.063       0
30-39     0.104     0.045 0.015       0
40+       0.156     0.068 0.033       0

RESULTS for NSCA Correspondence Analysis

Data Matrix:
M12<  M13 M16 M19 M25 M35 M45 M57 M65+
clothing      81  138 304 384 942 359 178 137   45
accessories   66  204 193 149 297 109  53  68   28
tobacco      150  340 229 151 313 136 121 171  145
stationary   667 1409 527  84  92  36  36  37   17
books         67  259 258 146 251  96  48  56   41
records       24  272 368 141 167  67  29  27    7
household     47  117  98  61 193  75  50  55   29
candy        430  637 246  40  30  11   5  17   28
toys         743  684 116  13  16  16   6   3    8
jewelry      132  408 298  71 130  31  14  11   10
perfumes      32   57  61  52 111  54  41  50   28
hobby        197  547 402 138 280 200 152 211  111
other        209  550 454 252 624 195  88  90   34

Row weights: Imass
clothing accessories tobacco stationary books records household
clothing           1           0       0          0     0       0         0
accessories        0           1       0          0     0       0         0
tobacco            0           0       1          0     0       0         0
stationary         0           0       0          1     0       0         0
books              0           0       0          0     1       0         0
records            0           0       0          0     0       1         0
household          0           0       0          0     0       0         1
candy              0           0       0          0     0       0         0
toys               0           0       0          0     0       0         0
jewelry            0           0       0          0     0       0         0
perfumes           0           0       0          0     0       0         0
hobby              0           0       0          0     0       0         0
other              0           0       0          0     0       0         0
candy toys jewelry perfumes hobby other
clothing        0    0       0        0     0     0
accessories     0    0       0        0     0     0
tobacco         0    0       0        0     0     0
stationary      0    0       0        0     0     0
books           0    0       0        0     0     0
records         0    0       0        0     0     0
household       0    0       0        0     0     0
candy           1    0       0        0     0     0
toys            0    1       0        0     0     0
jewelry         0    0       1        0     0     0
perfumes        0    0       0        1     0     0
hobby           0    0       0        0     1     0
other           0    0       0        0     0     1

Column Weights: Jmass
M12<  M13   M16   M19   M25   M35   M45   M57  M65+
M12< 0.137 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M13  0.000 0.27 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M16  0.000 0.00 0.171 0.000 0.000 0.000 0.000 0.000 0.000
M19  0.000 0.00 0.000 0.081 0.000 0.000 0.000 0.000 0.000
M25  0.000 0.00 0.000 0.000 0.166 0.000 0.000 0.000 0.000
M35  0.000 0.00 0.000 0.000 0.000 0.067 0.000 0.000 0.000
M45  0.000 0.00 0.000 0.000 0.000 0.000 0.039 0.000 0.000
M57  0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.045 0.000
M65+ 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.026

Total inertia  0.038

The inertia values, their percentage contribution to the total inertia and
the cumulative percent inertias
inertia inertiapc cuminertiapc
value1   0.030    79.884       79.884
value2   0.004     9.857       89.741
value3   0.003     8.440       98.181
value4   0.000     0.921       99.103
value5   0.000     0.670       99.772
value6   0.000     0.168       99.940
value7   0.000     0.047       99.987
value8   0.000     0.013      100.000

Predictability Index for Variants of Non symmetrical Correspondence Analysis:

Numerator of Tau Index predicting the row categories from the column categories

[1] 0.038

Tau Index predicting the row categories from the column categories

[1] 0.041

C-statistic 10331.51 and p-value 0

Column standard coordinates = column principal axes
Axis 1  Axis 2
M12<   1.377   0.801
M13    0.949  -0.191
M16    0.041  -0.349
M19   -0.956   0.674
M25   -1.233   1.101
M35   -1.172   0.159
M45   -1.011  -1.151
M57   -0.834  -2.437
M65+  -0.584  -3.564

Row standard coordinates = row principal axes
Axis 1  Axis 2
clothing     -0.559   0.463
accessories  -0.131   0.051
tobacco      -0.139  -0.497
stationary    0.545   0.041
books        -0.092  -0.027
records      -0.047   0.003
household    -0.088  -0.038
candy         0.300   0.041
toys          0.447   0.324
jewelry       0.080   0.032
perfumes     -0.069  -0.086
hobby        -0.083  -0.583
other        -0.165   0.276

Column principal  coordinates
Axis 1  Axis 2
M12<   0.238   0.049
M13    0.164  -0.012
M16    0.007  -0.021
M19   -0.166   0.041
M25   -0.214   0.067
M35   -0.203   0.010
M45   -0.175  -0.070
M57   -0.144  -0.148
M65+  -0.101  -0.217

Row principal coordinates
Axis 1  Axis 2
clothing     -0.097   0.028
accessories  -0.023   0.003
tobacco      -0.024  -0.030
stationary    0.094   0.003
books        -0.016  -0.002
records      -0.008   0.000
household    -0.015  -0.002
candy         0.052   0.002
toys          0.077   0.020
jewelry       0.014   0.002
perfumes     -0.012  -0.005
hobby        -0.014  -0.035
other        -0.029   0.017

Column distances from the origin of the plot
Axis 1  Axis 2
M12<   0.057   0.002
M13    0.027   0.000
M16    0.000   0.000
M19    0.027   0.002
M25    0.046   0.004
M35    0.041   0.000
M45    0.031   0.005
M57    0.021   0.022
M65+   0.010   0.047

Row distances from the origin of the plot
Axis 1  Axis 2
clothing      0.009   0.001
accessories   0.001   0.000
tobacco       0.001   0.001
stationary    0.009   0.000
books         0.000   0.000
records       0.000   0.000
household     0.000   0.000
candy         0.003   0.000
toys          0.006   0.000
jewelry       0.000   0.000
perfumes      0.000   0.000
hobby         0.000   0.001
other         0.001   0.000

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
M12<    M13    M16    M19    M25    M35    M45    M57   M65+
clothing    -0.300 -0.187 -0.033  0.393  0.370  0.457  0.329  0.057 -0.275
accessories -0.077 -0.042 -0.005  0.083  0.077  0.105  0.097  0.053  0.013
tobacco     -0.155 -0.033  0.023  0.009 -0.009  0.091  0.298  0.443  0.763
stationary   0.357  0.171  0.007 -0.312 -0.279 -0.427 -0.495 -0.401 -0.401
books       -0.063 -0.029  0.000  0.050  0.044  0.072  0.091  0.082  0.094
records     -0.030 -0.015 -0.001  0.028  0.025  0.037  0.040  0.030  0.025
household   -0.062 -0.027  0.000  0.046  0.040  0.068  0.091  0.087  0.108
candy        0.199  0.094  0.003 -0.169 -0.151 -0.235 -0.279 -0.233 -0.245
toys         0.331  0.134 -0.009 -0.214 -0.182 -0.340 -0.509 -0.532 -0.723
jewelry      0.056  0.025  0.000 -0.042 -0.037 -0.062 -0.082 -0.077 -0.094
perfumes    -0.056 -0.020  0.003  0.028  0.022  0.051  0.091  0.108  0.161
hobby       -0.130 -0.013  0.029 -0.036 -0.053  0.043  0.279  0.465  0.844
other       -0.070 -0.058 -0.017  0.136  0.132  0.140  0.048 -0.081 -0.271

Eccentricity of ellipses
[1] 0.936

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2 Area P-value
clothing        0.015     0.005    0   0.000
accessories     0.012     0.004    0   0.000
tobacco         0.013     0.004    0   0.000
stationary      0.012     0.004    0   0.000
books           0.014     0.005    0   0.000
records         0.009     0.003    0   0.629
household       0.017     0.006    0   0.072
candy           0.015     0.005    0   0.000
toys            0.013     0.005    0   0.000
jewelry         0.014     0.005    0   0.019
perfumes        0.017     0.006    0   0.000
hobby           0.013     0.004    0   0.000
other           0.012     0.004    0   0.000

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
M12<     0.035     0.012 0.001       0
M13      0.026     0.009 0.001       0
M16      0.020     0.007 0.000       0
M19      0.029     0.010 0.001       0
M25      0.036     0.013 0.001       0
M35      0.029     0.010 0.001       0
M45      0.034     0.012 0.001       0
M57      0.052     0.018 0.003       0
M65+     0.070     0.025 0.005       0

RESULTS for SONSCA Correspondence Analysis

Data Matrix:
M12<  M13 M16 M19 M25 M35 M45 M57 M65+
clothing      81  138 304 384 942 359 178 137   45
accessories   66  204 193 149 297 109  53  68   28
tobacco      150  340 229 151 313 136 121 171  145
stationary   667 1409 527  84  92  36  36  37   17
books         67  259 258 146 251  96  48  56   41
records       24  272 368 141 167  67  29  27    7
household     47  117  98  61 193  75  50  55   29
candy        430  637 246  40  30  11   5  17   28
toys         743  684 116  13  16  16   6   3    8
jewelry      132  408 298  71 130  31  14  11   10
perfumes      32   57  61  52 111  54  41  50   28
hobby        197  547 402 138 280 200 152 211  111
other        209  550 454 252 624 195  88  90   34

Row weights: Imass
clothing accessories tobacco stationary books records household
clothing           1           0       0          0     0       0         0
accessories        0           1       0          0     0       0         0
tobacco            0           0       1          0     0       0         0
stationary         0           0       0          1     0       0         0
books              0           0       0          0     1       0         0
records            0           0       0          0     0       1         0
household          0           0       0          0     0       0         1
candy              0           0       0          0     0       0         0
toys               0           0       0          0     0       0         0
jewelry            0           0       0          0     0       0         0
perfumes           0           0       0          0     0       0         0
hobby              0           0       0          0     0       0         0
other              0           0       0          0     0       0         0
candy toys jewelry perfumes hobby other
clothing        0    0       0        0     0     0
accessories     0    0       0        0     0     0
tobacco         0    0       0        0     0     0
stationary      0    0       0        0     0     0
books           0    0       0        0     0     0
records         0    0       0        0     0     0
household       0    0       0        0     0     0
candy           1    0       0        0     0     0
toys            0    1       0        0     0     0
jewelry         0    0       1        0     0     0
perfumes        0    0       0        1     0     0
hobby           0    0       0        0     1     0
other           0    0       0        0     0     1

Column Weights: Jmass
M12<  M13   M16   M19   M25   M35   M45   M57  M65+
M12< 0.137 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M13  0.000 0.27 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M16  0.000 0.00 0.171 0.000 0.000 0.000 0.000 0.000 0.000
M19  0.000 0.00 0.000 0.081 0.000 0.000 0.000 0.000 0.000
M25  0.000 0.00 0.000 0.000 0.166 0.000 0.000 0.000 0.000
M35  0.000 0.00 0.000 0.000 0.000 0.067 0.000 0.000 0.000
M45  0.000 0.00 0.000 0.000 0.000 0.000 0.039 0.000 0.000
M57  0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.045 0.000
M65+ 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.026

Total inertia  0.038

Inertias, percent inertias and cumulative percent inertias of the row  space

inertia inertiapc cuminertiapc
value1   0.030    79.884       79.884
value2   0.004     9.857       89.741
value3   0.003     8.440       98.181
value4   0.000     0.921       99.103
value5   0.000     0.670       99.772
value6   0.000     0.168       99.940
value7   0.000     0.047       99.987
value8   0.000     0.013      100.000
Inertias, percent inertias and  cumulative percent inertias of the column space

inertia2 inertiapc2 cuminertiapc2
value1    0.022     59.832        59.832
value2    0.010     25.576        85.408
value3    0.003      7.329        92.737
value4    0.002      5.183        97.920
value5    0.000      0.820        98.739
value6    0.000      0.739        99.478
value7    0.000      0.349        99.828
value8    0.000      0.172       100.000

Predictability Index for Variants of Non symmetrical Correspondence Analysis:

Numerator of Tau Index predicting the row categories from the column categories

[1] 0.038

Tau Index predicting the row categories from the column categories

[1] 0.041

C-statistic 10331.51 and p-value 0

Polynomial Components of Inertia

** Column Components **
Component Value P-value
Location                           6181.536       0
Dispersion                         2642.363       0
Cubic                               757.192       0
Error                               750.418       0
** Chi-squared Statistic **       10331.509       0

Generalized correlation matrix of Hybrid Decomposition
v1     v2     v3     v4     v5     v6     v7     v8
m1 -0.147  0.084  0.018 -0.030  0.011  0.005 -0.005  0.003
m2 -0.028 -0.034 -0.032  0.024  0.005 -0.010  0.003  0.001
m3 -0.013 -0.037  0.036 -0.016 -0.004  0.006 -0.006  0.002
m4 -0.001  0.002  0.006  0.014 -0.010  0.005 -0.001 -0.001
m5 -0.001 -0.001 -0.007 -0.006 -0.007  0.009 -0.004 -0.004
m6  0.000  0.000 -0.001  0.000  0.000 -0.001 -0.006  0.005
m7  0.000  0.000  0.000 -0.001 -0.002 -0.003 -0.001 -0.002
m8  0.000  0.000  0.000  0.000 -0.001  0.000  0.001  0.001
m9  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000

Column standard polynomial coordinates = column polynomial axes
Axis 1  Axis 2
M12<  -1.232   1.352
M13   -0.759   0.142
M16   -0.285  -0.652
M19    0.188  -1.029
M25    0.661  -0.991
M35    1.135  -0.536
M45    1.608   0.336
M57    2.081   1.624
M65+   2.554   3.328

Row principal polynomial coordinates
Axis 1  Axis 2
clothing      0.072  -0.056
accessories   0.017  -0.014
tobacco       0.039   0.017
stationary   -0.084   0.033
books         0.012  -0.012
records       0.000  -0.021
household     0.015  -0.004
candy        -0.045   0.027
toys         -0.067   0.049
jewelry      -0.017  -0.006
perfumes      0.014   0.000
hobby         0.030   0.015
other         0.014  -0.030

Column distances from the origin of the plot
Axis 1  Axis 2
M12<   0.057   0.002
M13    0.027   0.000
M16    0.000   0.000
M19    0.027   0.002
M25    0.046   0.004
M35    0.041   0.000
M45    0.031   0.005
M57    0.021   0.022
M65+   0.010   0.047

Row distances from the origin of the plot
Axis 1  Axis 2
clothing      0.005   0.003
accessories   0.000   0.000
tobacco       0.001   0.000
stationary    0.007   0.001
books         0.000   0.000
records       0.000   0.000
household     0.000   0.000
candy         0.002   0.001
toys          0.005   0.002
jewelry       0.000   0.000
perfumes      0.000   0.000
hobby         0.001   0.000
other         0.000   0.001

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
M12<    M13    M16    M19    M25    M35    M45    M57   M65+
clothing     0.111  0.097  0.014 -0.112 -0.150 -0.118 -0.065 -0.012  0.044
accessories  0.029  0.022  0.002 -0.024 -0.031 -0.027 -0.019 -0.011 -0.002
tobacco      0.057  0.017 -0.010 -0.003  0.004 -0.023 -0.059 -0.094 -0.122
stationary  -0.132 -0.089 -0.003  0.089  0.114  0.110  0.098  0.085  0.064
books        0.023  0.015  0.000 -0.014 -0.018 -0.018 -0.018 -0.017 -0.015
records      0.011  0.008  0.000 -0.008 -0.010 -0.010 -0.008 -0.006 -0.004
household    0.023  0.014  0.000 -0.013 -0.016 -0.018 -0.018 -0.018 -0.017
candy       -0.074 -0.049 -0.001  0.048  0.061  0.061  0.055  0.049  0.039
toys        -0.122 -0.070  0.004  0.061  0.074  0.088  0.101  0.113  0.115
jewelry     -0.021 -0.013  0.000  0.012  0.015  0.016  0.016  0.016  0.015
perfumes     0.021  0.010 -0.001 -0.008 -0.009 -0.013 -0.018 -0.023 -0.026
hobby        0.048  0.007 -0.012  0.010  0.021 -0.011 -0.055 -0.098 -0.135
other        0.026  0.030  0.007 -0.039 -0.054 -0.036 -0.010  0.017  0.043

Eccentricity of ellipses
[1] 0.757

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2 Area P-value
clothing        0.013     0.009    0   0.000
accessories     0.010     0.007    0   0.000
tobacco         0.011     0.007    0   0.000
stationary      0.010     0.007    0   0.000
books           0.012     0.008    0   0.000
records         0.008     0.005    0   0.000
household       0.015     0.010    0   0.000
candy           0.013     0.008    0   0.000
toys            0.011     0.007    0   0.000
jewelry         0.013     0.008    0   0.000
perfumes        0.015     0.010    0   0.297
hobby           0.011     0.007    0   0.000
other           0.011     0.007    0   0.000

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
M12<     0.034     0.022 0.002       0
M13      0.020     0.013 0.001       0
M16      0.020     0.013 0.001       0
M19      0.023     0.015 0.001       0
M25      0.025     0.016 0.001       0
M35      0.026     0.017 0.001       0
M45      0.031     0.020 0.002       0
M57      0.046     0.030 0.004       0
M65+     0.070     0.046 0.010       0

RESULTS for SOCA Correspondence Analysis

Data Matrix:
M12<  M13 M16 M19 M25 M35 M45 M57 M65+
clothing      81  138 304 384 942 359 178 137   45
accessories   66  204 193 149 297 109  53  68   28
tobacco      150  340 229 151 313 136 121 171  145
stationary   667 1409 527  84  92  36  36  37   17
books         67  259 258 146 251  96  48  56   41
records       24  272 368 141 167  67  29  27    7
household     47  117  98  61 193  75  50  55   29
candy        430  637 246  40  30  11   5  17   28
toys         743  684 116  13  16  16   6   3    8
jewelry      132  408 298  71 130  31  14  11   10
perfumes      32   57  61  52 111  54  41  50   28
hobby        197  547 402 138 280 200 152 211  111
other        209  550 454 252 624 195  88  90   34

Row weights: Imass
clothing accessories tobacco stationary books records household
clothing       0.123       0.000   0.000       0.00 0.000   0.000     0.000
accessories    0.000       0.056   0.000       0.00 0.000   0.000     0.000
tobacco        0.000       0.000   0.084       0.00 0.000   0.000     0.000
stationary     0.000       0.000   0.000       0.14 0.000   0.000     0.000
books          0.000       0.000   0.000       0.00 0.059   0.000     0.000
records        0.000       0.000   0.000       0.00 0.000   0.053     0.000
household      0.000       0.000   0.000       0.00 0.000   0.000     0.035
candy          0.000       0.000   0.000       0.00 0.000   0.000     0.000
toys           0.000       0.000   0.000       0.00 0.000   0.000     0.000
jewelry        0.000       0.000   0.000       0.00 0.000   0.000     0.000
perfumes       0.000       0.000   0.000       0.00 0.000   0.000     0.000
hobby          0.000       0.000   0.000       0.00 0.000   0.000     0.000
other          0.000       0.000   0.000       0.00 0.000   0.000     0.000
candy  toys jewelry perfumes hobby other
clothing    0.000 0.000   0.000    0.000 0.000  0.00
accessories 0.000 0.000   0.000    0.000 0.000  0.00
tobacco     0.000 0.000   0.000    0.000 0.000  0.00
stationary  0.000 0.000   0.000    0.000 0.000  0.00
books       0.000 0.000   0.000    0.000 0.000  0.00
records     0.000 0.000   0.000    0.000 0.000  0.00
household   0.000 0.000   0.000    0.000 0.000  0.00
candy       0.069 0.000   0.000    0.000 0.000  0.00
toys        0.000 0.077   0.000    0.000 0.000  0.00
jewelry     0.000 0.000   0.053    0.000 0.000  0.00
perfumes    0.000 0.000   0.000    0.023 0.000  0.00
hobby       0.000 0.000   0.000    0.000 0.107  0.00
other       0.000 0.000   0.000    0.000 0.000  0.12

Column Weights: Jmass
M12<  M13   M16   M19   M25   M35   M45   M57  M65+
M12< 0.137 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M13  0.000 0.27 0.000 0.000 0.000 0.000 0.000 0.000 0.000
M16  0.000 0.00 0.171 0.000 0.000 0.000 0.000 0.000 0.000
M19  0.000 0.00 0.000 0.081 0.000 0.000 0.000 0.000 0.000
M25  0.000 0.00 0.000 0.000 0.166 0.000 0.000 0.000 0.000
M35  0.000 0.00 0.000 0.000 0.000 0.067 0.000 0.000 0.000
M45  0.000 0.00 0.000 0.000 0.000 0.000 0.039 0.000 0.000
M57  0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.045 0.000
M65+ 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.026

Total inertia  0.395

Inertias, percent inertias and cumulative percent inertias of the row space

inertia inertiapc cuminertiapc
value1   0.305    77.102       77.102
value2   0.045    11.448       88.551
value3   0.037     9.436       97.987
value4   0.004     0.992       98.979
value5   0.003     0.732       99.711
value6   0.001     0.203       99.913
value7   0.000     0.064       99.977
value8   0.000     0.023      100.000
Inertias, percent inertias and  cumulative percent inertias of the column space

inertia2 inertiapc2 cuminertiapc2
value1    0.235     59.532        59.532
value2    0.103     26.134        85.666
value3    0.031      7.774        93.440
value4    0.016      4.142        97.581
value5    0.004      0.940        98.521
value6    0.003      0.878        99.399
value7    0.002      0.382        99.781
value8    0.001      0.219       100.000

Polynomial Components of Inertia

** Column Components **
Component Value P-value
Location                           4897.563       0
Dispersion                         2149.966       0
Cubic                               639.561       0
Error                               539.706       0
** Chi-squared Statistic **        8226.796       0

Generalized correlation matrix of Hybrid Decomposition
v1     v2     v3     v4     v5     v6     v7     v8
m1 -0.474  0.268  0.028 -0.074  0.035  0.012 -0.016  0.007
m2 -0.071 -0.149  0.121 -0.040 -0.022  0.028 -0.024  0.006
m3 -0.074 -0.095 -0.120  0.083  0.015 -0.034  0.009  0.001
m4 -0.003  0.009  0.011  0.040 -0.037  0.024  0.001 -0.013
m5  0.000 -0.005 -0.027 -0.029 -0.019  0.026 -0.012 -0.013
m6 -0.001 -0.002  0.002 -0.004  0.001 -0.004  0.019 -0.020
m7  0.000  0.001  0.000 -0.002 -0.008 -0.012 -0.006 -0.004
m8  0.000  0.000  0.001  0.002  0.005  0.001 -0.005 -0.006
m9  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000

Column standard polynomial coordinates = column polynomial axes
Axis 1  Axis 2
M12<  -1.232   1.352
M13   -0.759   0.142
M16   -0.285  -0.652
M19    0.188  -1.029
M25    0.661  -0.991
M35    1.135  -0.536
M45    1.608   0.336
M57    2.081   1.624
M65+   2.554   3.328

Row principal polynomial coordinates
Axis 1  Axis 2
clothing      2.411  -0.890
accessories   1.675  -0.259
tobacco       2.866   1.837
stationary   -1.154   0.719
books         1.426  -0.054
records       0.490  -0.974
household     2.342   0.432
candy        -1.215   1.275
toys         -2.021   1.746
jewelry      -0.421  -0.179
perfumes      3.069   1.033
hobby         2.133   1.263
other         0.948  -0.437

Column distances from the origin of the plot
Axis 1  Axis 2
M12<   0.063   0.005
M13    0.026   0.001
M16    0.000   0.006
M19    0.025   0.000
M25    0.040   0.000
M35    0.037   0.002
M45    0.029   0.006
M57    0.021   0.008
M65+   0.011   0.015

Row distances from the origin of the plot
Axis 1  Axis 2
clothing      5.811   0.793
accessories   2.807   0.067
tobacco       8.212   3.375
stationary    1.332   0.517
books         2.032   0.003
records       0.240   0.948
household     5.486   0.187
candy         1.475   1.625
toys          4.084   3.049
jewelry       0.177   0.032
perfumes      9.420   1.066
hobby         4.550   1.596
other         0.899   0.191

Inner product of coordinates (first two axes when 'firstaxis=1' and 'lastaxis=2')
M12<    M13    M16    M19    M25     M35     M45    M57    M65+
clothing    -11.290 -3.763 -0.260  4.818  6.085  12.452  18.011 16.870  20.006
accessories  -6.529 -2.516 -0.749  2.044  3.353   7.906  13.126 14.485  21.405
tobacco      -2.829 -3.681 -4.878 -4.759  0.184   8.790  26.309 42.262  84.115
stationary    6.478  1.882 -0.338 -3.368 -3.628  -6.571  -8.129 -5.830  -3.474
books        -4.947 -2.096 -0.900  1.137  2.447   6.382  11.451 13.603  21.685
records      -5.195 -0.982  1.197  3.850  3.167   4.178   2.323 -2.646 -12.442
household    -6.225 -3.301 -2.299 -0.016  2.754   9.405  19.694 26.339  46.466
candy         8.710  2.122 -1.172 -5.419 -5.078  -7.989  -7.678 -2.164   7.132
toys         13.123  3.428 -1.359 -7.660 -7.537 -12.516 -13.410 -6.476   4.058
jewelry       0.750  0.566  0.573  0.368 -0.250  -1.481  -3.711 -5.509 -10.456
perfumes     -6.451 -4.198 -3.749 -1.710  2.474  11.356  26.596 38.091  70.606
hobby        -2.487 -2.768 -3.466 -3.165  0.391   6.759  19.405 30.656  60.436
other        -4.758 -1.504  0.035  2.210  2.605   5.078   6.937  5.969   6.059

Eccentricity of ellipses
[1] 0.749

Ellipse axes, Area, p-values of rows
HL Axis 1 HL Axis 2  Area P-value
clothing        0.161     0.107 0.054       0
accessories     0.243     0.161 0.123       0
tobacco         0.196     0.130 0.080       0
stationary      0.150     0.100 0.047       0
books           0.239     0.158 0.119       0
records         0.251     0.166 0.131       0
household       0.312     0.207 0.203       0
candy           0.220     0.146 0.101       0
toys            0.208     0.138 0.090       0
jewelry         0.252     0.167 0.132       0
perfumes        0.382     0.253 0.303       0
hobby           0.170     0.113 0.061       0
other           0.164     0.109 0.056       0

Ellipse axes, Area, p-values of columns
HL Axis 1 HL Axis 2  Area P-value
M12<     0.122     0.081 0.031   0.000
M13      0.074     0.049 0.011   0.000
M16      0.072     0.048 0.011   0.000
M19      0.085     0.056 0.015   0.000
M25      0.091     0.060 0.017   0.000
M35      0.094     0.062 0.018   0.000
M45      0.113     0.075 0.026   0.000
M57      0.165     0.109 0.057   0.000
M65+     0.252     0.167 0.133   0.761
```

CAvariants documentation built on May 30, 2017, 1:25 a.m.