How to use RSDA 3.3

RSDA Package version 3.3

Oldemar Rodríguez R.

Installing the package

CRAN

install.packages("RSDA", dependencies=TRUE)

Github

devtools::install_github("PROMiDAT/RSDA")

How to read a Symbolic Table from a CSV file with RSDA?

ex3 <- read.sym.table(file = 'tsym1.csv', header=TRUE, sep=';',dec='.', row.names=1)
ex3
#> # A tibble: 7 × 7
#>      F1              F2      F3    F4        F5               F6              F7
#>   <dbl>      <symblc_n> <symbl> <dbl> <symblc_>       <symblc_n>      <symblc_n>
#> 1   2.8   [1.00 : 2.00]  <hist>   6       {a,d}   [0.00 : 90.00]  [9.00 : 24.00]
#> 2   1.4   [3.00 : 9.00]  <hist>   8     {b,c,d} [-90.00 : 98.00]  [-9.00 : 9.00]
#> 3   3.2  [-1.00 : 4.00]  <hist>  -7       {a,b}  [65.00 : 90.00] [65.00 : 70.00]
#> 4  -2.1   [0.00 : 2.00]  <hist>   0   {a,b,c,d}  [45.00 : 89.00] [25.00 : 67.00]
#> 5  -3   [-4.00 : -2.00]  <hist>  -9.5       {b}  [20.00 : 40.00]  [9.00 : 40.00]
#> 6   0.1 [10.00 : 21.00]  <hist>  -1       {a,d}    [5.00 : 8.00]   [5.00 : 8.00]
#> 7   9    [4.00 : 21.00]  <hist>   0.5       {a}    [3.14 : 6.76]   [4.00 : 6.00]

##How to save a Symbolic Table in a CSV file with RSDA?

write.sym.table(ex3, file = 'tsymtemp.csv', sep = ';',dec = '.',
                row.names = TRUE, col.names = TRUE)

Symbolic Data Frame Example in RSDA

data(example3)
example3
#> # A tibble: 7 × 7
#>      F1              F2                      F3    F4        F5               F6
#>   <dbl>      <symblc_n>              <symblc_m> <dbl> <symblc_>       <symblc_n>
#> 1   2.8   [1.00 : 2.00] M1:0.10 M2:0.70 M3:0.20   6   {e,g,i,k}   [0.00 : 90.00]
#> 2   1.4   [3.00 : 9.00] M1:0.60 M2:0.30 M3:0.10   8   {a,b,c,d} [-90.00 : 98.00]
#> 3   3.2  [-1.00 : 4.00] M1:0.20 M2:0.20 M3:0.60  -7   {2,b,1,c}  [65.00 : 90.00]
#> 4  -2.1   [0.00 : 2.00] M1:0.90 M2:0.00 M3:0.10   0   {a,3,4,c}  [45.00 : 89.00]
#> 5  -3   [-4.00 : -2.00] M1:0.60 M2:0.00 M3:0.40  -9.5 {e,g,i,k}  [20.00 : 40.00]
#> 6   0.1 [10.00 : 21.00] M1:0.00 M2:0.70 M3:0.30  -1     {e,1,i}    [5.00 : 8.00]
#> 7   9    [4.00 : 21.00] M1:0.20 M2:0.20 M3:0.60   0.5   {e,a,2}    [3.14 : 6.76]
#> # ℹ 1 more variable: F7 <symblc_n>
example3[2,]
#> # A tibble: 1 × 7
#>      F1            F2                      F3    F4         F5               F6
#>   <dbl>    <symblc_n>              <symblc_m> <dbl> <symblc_s>       <symblc_n>
#> 1   1.4 [3.00 : 9.00] M1:0.60 M2:0.30 M3:0.10     8  {a,b,c,d} [-90.00 : 98.00]
#> # ℹ 1 more variable: F7 <symblc_n>
example3[,3]
#> # A tibble: 7 × 1
#>                        F3
#>                <symblc_m>
#> 1 M1:0.10 M2:0.70 M3:0.20
#> 2 M1:0.60 M2:0.30 M3:0.10
#> 3 M1:0.20 M2:0.20 M3:0.60
#> 4 M1:0.90 M2:0.00 M3:0.10
#> 5 M1:0.60 M2:0.00 M3:0.40
#> 6 M1:0.00 M2:0.70 M3:0.30
#> 7 M1:0.20 M2:0.20 M3:0.60
example3[2:3,5]
#> # A tibble: 2 × 1
#>           F5
#>   <symblc_s>
#> 1  {a,b,c,d}
#> 2  {2,b,1,c}
example3$F1
#> [1]  2.8  1.4  3.2 -2.1 -3.0  0.1  9.0

How to generated a symbolic data table from a classic data table in RSDA?

data(ex1_db2so)
ex1_db2so
#>         state sex county group age
#> 1     Florida   M      2     6   3
#> 2  California   F      4     3   4
#> 3       Texas   M     12     3   4
#> 4     Florida   F      2     3   4
#> 5       Texas   M      4     6   4
#> 6       Texas   F      2     3   3
#> 7     Florida   M      6     3   4
#> 8     Florida   F      2     6   4
#> 9  California   M      2     3   6
#> 10 California   F     21     3   4
#> 11 California   M      2     3   4
#> 12 California   M      2     6   7
#> 13      Texas   F     23     3   4
#> 14    Florida   M      2     3   4
#> 15    Florida   F     12     7   4
#> 16      Texas   M      2     3   8
#> 17 California   F      3     7   9
#> 18 California   M      2     3  11
#> 19 California   M      1     3  11

The classic.to.sym function allows to convert a traditional table into a symbolic one, to this we must indicate the following parameters.

Example 1

result <- classic.to.sym(x = ex1_db2so, 
                         concept = c(state, sex),
                         variables = c(county, group, age))
result
#> # A tibble: 6 × 3
#>           county         group            age
#>       <symblc_n>    <symblc_n>     <symblc_n>
#> 1 [3.00 : 21.00] [3.00 : 7.00]  [4.00 : 9.00]
#> 2  [1.00 : 2.00] [3.00 : 6.00] [4.00 : 11.00]
#> 3 [2.00 : 12.00] [3.00 : 7.00]  [4.00 : 4.00]
#> 4  [2.00 : 6.00] [3.00 : 6.00]  [3.00 : 4.00]
#> 5 [2.00 : 23.00] [3.00 : 3.00]  [3.00 : 4.00]
#> 6 [2.00 : 12.00] [3.00 : 6.00]  [4.00 : 8.00]

We can add new variables indicating the type we want them to be.

result <- classic.to.sym(x = ex1_db2so, 
                         concept = c("state", "sex"),
                         variables = c(county, group, age),
                         age_hist = sym.histogram(age, breaks = pretty(ex1_db2so$age, 5)))
result
#> # A tibble: 6 × 4
#>     age_hist         county         group            age
#>   <symblc_h>     <symblc_n>    <symblc_n>     <symblc_n>
#> 1     <hist> [3.00 : 21.00] [3.00 : 7.00]  [4.00 : 9.00]
#> 2     <hist>  [1.00 : 2.00] [3.00 : 6.00] [4.00 : 11.00]
#> 3     <hist> [2.00 : 12.00] [3.00 : 7.00]  [4.00 : 4.00]
#> 4     <hist>  [2.00 : 6.00] [3.00 : 6.00]  [3.00 : 4.00]
#> 5     <hist> [2.00 : 23.00] [3.00 : 3.00]  [3.00 : 4.00]
#> 6     <hist> [2.00 : 12.00] [3.00 : 6.00]  [4.00 : 8.00]

Example 2

data(USCrime)
head(USCrime)
#>   state fold population householdsize racepctblack racePctWhite racePctAsian
#> 1     8    1       0.19          0.33         0.02         0.90         0.12
#> 2    53    1       0.00          0.16         0.12         0.74         0.45
#> 3    24    1       0.00          0.42         0.49         0.56         0.17
#> 4    34    1       0.04          0.77         1.00         0.08         0.12
#> 5    42    1       0.01          0.55         0.02         0.95         0.09
#> 6     6    1       0.02          0.28         0.06         0.54         1.00
#>   racePctHisp agePct12t21 agePct12t29 agePct16t24 agePct65up numbUrban pctUrban
#> 1        0.17        0.34        0.47        0.29       0.32      0.20      1.0
#> 2        0.07        0.26        0.59        0.35       0.27      0.02      1.0
#> 3        0.04        0.39        0.47        0.28       0.32      0.00      0.0
#> 4        0.10        0.51        0.50        0.34       0.21      0.06      1.0
#> 5        0.05        0.38        0.38        0.23       0.36      0.02      0.9
#> 6        0.25        0.31        0.48        0.27       0.37      0.04      1.0
#>   medIncome pctWWage pctWFarmSelf pctWInvInc pctWSocSec pctWPubAsst pctWRetire
#> 1      0.37     0.72         0.34       0.60       0.29        0.15       0.43
#> 2      0.31     0.72         0.11       0.45       0.25        0.29       0.39
#> 3      0.30     0.58         0.19       0.39       0.38        0.40       0.84
#> 4      0.58     0.89         0.21       0.43       0.36        0.20       0.82
#> 5      0.50     0.72         0.16       0.68       0.44        0.11       0.71
#> 6      0.52     0.68         0.20       0.61       0.28        0.15       0.25
#>   medFamInc perCapInc whitePerCap blackPerCap indianPerCap AsianPerCap
#> 1      0.39      0.40        0.39        0.32         0.27        0.27
#> 2      0.29      0.37        0.38        0.33         0.16        0.30
#> 3      0.28      0.27        0.29        0.27         0.07        0.29
#> 4      0.51      0.36        0.40        0.39         0.16        0.25
#> 5      0.46      0.43        0.41        0.28         0.00        0.74
#> 6      0.62      0.72        0.76        0.77         0.28        0.52
#>   OtherPerCap HispPerCap NumUnderPov PctPopUnderPov PctLess9thGrade
#> 1        0.36       0.41        0.08           0.19            0.10
#> 2        0.22       0.35        0.01           0.24            0.14
#> 3        0.28       0.39        0.01           0.27            0.27
#> 4        0.36       0.44        0.01           0.10            0.09
#> 5        0.51       0.48        0.00           0.06            0.25
#> 6        0.48       0.60        0.01           0.12            0.13
#>   PctNotHSGrad PctBSorMore PctUnemployed PctEmploy PctEmplManu PctEmplProfServ
#> 1         0.18        0.48          0.27      0.68        0.23            0.41
#> 2         0.24        0.30          0.27      0.73        0.57            0.15
#> 3         0.43        0.19          0.36      0.58        0.32            0.29
#> 4         0.25        0.31          0.33      0.71        0.36            0.45
#> 5         0.30        0.33          0.12      0.65        0.67            0.38
#> 6         0.12        0.80          0.10      0.65        0.19            0.77
#>   PctOccupManu PctOccupMgmtProf MalePctDivorce MalePctNevMarr FemalePctDiv
#> 1         0.25             0.52           0.68           0.40         0.75
#> 2         0.42             0.36           1.00           0.63         0.91
#> 3         0.49             0.32           0.63           0.41         0.71
#> 4         0.37             0.39           0.34           0.45         0.49
#> 5         0.42             0.46           0.22           0.27         0.20
#> 6         0.06             0.91           0.49           0.57         0.61
#>   TotalPctDiv PersPerFam PctFam2Par PctKids2Par PctYoungKids2Par PctTeen2Par
#> 1        0.75       0.35       0.55        0.59             0.61        0.56
#> 2        1.00       0.29       0.43        0.47             0.60        0.39
#> 3        0.70       0.45       0.42        0.44             0.43        0.43
#> 4        0.44       0.75       0.65        0.54             0.83        0.65
#> 5        0.21       0.51       0.91        0.91             0.89        0.85
#> 6        0.58       0.44       0.62        0.69             0.87        0.53
#>   PctWorkMomYoungKids PctWorkMom NumIlleg PctIlleg NumImmig PctImmigRecent
#> 1                0.74       0.76     0.04     0.14     0.03           0.24
#> 2                0.46       0.53     0.00     0.24     0.01           0.52
#> 3                0.71       0.67     0.01     0.46     0.00           0.07
#> 4                0.85       0.86     0.03     0.33     0.02           0.11
#> 5                0.40       0.60     0.00     0.06     0.00           0.03
#> 6                0.30       0.43     0.00     0.11     0.04           0.30
#>   PctImmigRec5 PctImmigRec8 PctImmigRec10 PctRecentImmig PctRecImmig5
#> 1         0.27         0.37          0.39           0.07         0.07
#> 2         0.62         0.64          0.63           0.25         0.27
#> 3         0.06         0.15          0.19           0.02         0.02
#> 4         0.20         0.30          0.31           0.05         0.08
#> 5         0.07         0.20          0.27           0.01         0.02
#> 6         0.35         0.43          0.47           0.50         0.50
#>   PctRecImmig8 PctRecImmig10 PctSpeakEnglOnly PctNotSpeakEnglWell
#> 1         0.08          0.08             0.89                0.06
#> 2         0.25          0.23             0.84                0.10
#> 3         0.04          0.05             0.88                0.04
#> 4         0.11          0.11             0.81                0.08
#> 5         0.04          0.05             0.88                0.05
#> 6         0.56          0.57             0.45                0.28
#>   PctLargHouseFam PctLargHouseOccup PersPerOccupHous PersPerOwnOccHous
#> 1            0.14              0.13             0.33              0.39
#> 2            0.16              0.10             0.17              0.29
#> 3            0.20              0.20             0.46              0.52
#> 4            0.56              0.62             0.85              0.77
#> 5            0.16              0.19             0.59              0.60
#> 6            0.25              0.19             0.29              0.53
#>   PersPerRentOccHous PctPersOwnOccup PctPersDenseHous PctHousLess3BR MedNumBR
#> 1               0.28            0.55             0.09           0.51      0.5
#> 2               0.17            0.26             0.20           0.82      0.0
#> 3               0.43            0.42             0.15           0.51      0.5
#> 4               1.00            0.94             0.12           0.01      0.5
#> 5               0.37            0.89             0.02           0.19      0.5
#> 6               0.18            0.39             0.26           0.73      0.0
#>   HousVacant PctHousOccup PctHousOwnOcc PctVacantBoarded PctVacMore6Mos
#> 1       0.21         0.71          0.52             0.05           0.26
#> 2       0.02         0.79          0.24             0.02           0.25
#> 3       0.01         0.86          0.41             0.29           0.30
#> 4       0.01         0.97          0.96             0.60           0.47
#> 5       0.01         0.89          0.87             0.04           0.55
#> 6       0.02         0.84          0.30             0.16           0.28
#>   MedYrHousBuilt PctHousNoPhone PctWOFullPlumb OwnOccLowQuart OwnOccMedVal
#> 1           0.65           0.14           0.06           0.22         0.19
#> 2           0.65           0.16           0.00           0.21         0.20
#> 3           0.52           0.47           0.45           0.18         0.17
#> 4           0.52           0.11           0.11           0.24         0.21
#> 5           0.73           0.05           0.14           0.31         0.31
#> 6           0.25           0.02           0.05           0.94         1.00
#>   OwnOccHiQuart RentLowQ RentMedian RentHighQ MedRent MedRentPctHousInc
#> 1          0.18     0.36       0.35      0.38    0.34              0.38
#> 2          0.21     0.42       0.38      0.40    0.37              0.29
#> 3          0.16     0.27       0.29      0.27    0.31              0.48
#> 4          0.19     0.75       0.70      0.77    0.89              0.63
#> 5          0.30     0.40       0.36      0.38    0.38              0.22
#> 6          1.00     0.67       0.63      0.68    0.62              0.47
#>   MedOwnCostPctInc MedOwnCostPctIncNoMtg NumInShelters NumStreet PctForeignBorn
#> 1             0.46                  0.25          0.04         0           0.12
#> 2             0.32                  0.18          0.00         0           0.21
#> 3             0.39                  0.28          0.00         0           0.14
#> 4             0.51                  0.47          0.00         0           0.19
#> 5             0.51                  0.21          0.00         0           0.11
#> 6             0.59                  0.11          0.00         0           0.70
#>   PctBornSameState PctSameHouse85 PctSameCity85 PctSameState85 LandArea PopDens
#> 1             0.42           0.50          0.51           0.64     0.12    0.26
#> 2             0.50           0.34          0.60           0.52     0.02    0.12
#> 3             0.49           0.54          0.67           0.56     0.01    0.21
#> 4             0.30           0.73          0.64           0.65     0.02    0.39
#> 5             0.72           0.64          0.61           0.53     0.04    0.09
#> 6             0.42           0.49          0.73           0.64     0.01    0.58
#>   PctUsePubTrans LemasPctOfficDrugUn ViolentCrimesPerPop
#> 1           0.20                0.32                0.20
#> 2           0.45                0.00                0.67
#> 3           0.02                0.00                0.43
#> 4           0.28                0.00                0.12
#> 5           0.02                0.00                0.03
#> 6           0.10                0.00                0.14
result  <- classic.to.sym(x = USCrime,
                          concept = state, 
                          variables= c(NumInShelters,
                                       NumImmig,
                                       ViolentCrimesPerPop),
                          ViolentCrimesPerPop_hist = sym.histogram(ViolentCrimesPerPop,
                                                                   breaks = pretty(USCrime$ViolentCrimesPerPop,5)))
result
#> # A tibble: 46 × 4
#>    ViolentCrimesPerPop_hist NumInShelters      NumImmig ViolentCrimesPerPop
#>                  <symblc_h>    <symblc_n>    <symblc_n>          <symblc_n>
#>  1                   <hist> [0.00 : 0.32] [0.00 : 0.04]       [0.01 : 1.00]
#>  2                   <hist> [0.01 : 0.18] [0.01 : 0.09]       [0.05 : 0.36]
#>  3                   <hist> [0.00 : 1.00] [0.00 : 0.57]       [0.05 : 0.57]
#>  4                   <hist> [0.00 : 0.08] [0.00 : 0.02]       [0.02 : 1.00]
#>  5                   <hist> [0.00 : 1.00] [0.00 : 1.00]       [0.01 : 1.00]
#>  6                   <hist> [0.00 : 0.68] [0.00 : 0.23]       [0.07 : 0.75]
#>  7                   <hist> [0.00 : 0.79] [0.00 : 0.14]       [0.00 : 0.94]
#>  8                   <hist> [0.01 : 0.01] [0.01 : 0.01]       [0.37 : 0.37]
#>  9                   <hist> [1.00 : 1.00] [0.39 : 0.39]       [1.00 : 1.00]
#> 10                   <hist> [0.00 : 0.52] [0.00 : 1.00]       [0.06 : 1.00]
#> # ℹ 36 more rows

Example 3

data("ex_mcfa1") 
head(ex_mcfa1)
#>   suspect age     hair    eyes    region
#> 1       1  42    h_red e_brown     Bronx
#> 2       2  20  h_black e_green     Bronx
#> 3       3  64  h_brown e_brown  Brooklyn
#> 4       4  55 h_blonde e_brown     Bronx
#> 5       5   4  h_brown e_green Manhattan
#> 6       6  61 h_blonde e_green     Bronx
sym.table <- classic.to.sym(x = ex_mcfa1, 
                            concept = suspect, 
                            variables=c(hair,
                                        eyes,
                                        region),
                            default.categorical = sym.set)
sym.table
#> # A tibble: 100 × 3
#>                  hair              eyes               region
#>            <symblc_s>        <symblc_s>           <symblc_s>
#>  1            {h_red} {e_brown,e_black}              {Bronx}
#>  2 {h_black,h_blonde} {e_green,e_black}    {Bronx,Manhattan}
#>  3  {h_brown,h_white} {e_brown,e_green}    {Brooklyn,Queens}
#>  4         {h_blonde} {e_brown,e_black}    {Bronx,Manhattan}
#>  5    {h_brown,h_red}         {e_green}    {Manhattan,Bronx}
#>  6 {h_blonde,h_white}  {e_green,e_blue}       {Bronx,Queens}
#>  7    {h_white,h_red}  {e_black,e_blue}       {Queens,Bronx}
#>  8 {h_blonde,h_white} {e_brown,e_black} {Manhattan,Brooklyn}
#>  9 {h_blonde,h_white} {e_black,e_brown}     {Brooklyn,Bronx}
#> 10  {h_brown,h_black} {e_brown,e_green}    {Manhattan,Bronx}
#> # ℹ 90 more rows

Example 4

We can modify the function that will be applied by default to the categorical variables

sym.table <- classic.to.sym(x = ex_mcfa1, 
                            concept = suspect,
                            default.categorical = sym.set)
sym.table
#> # A tibble: 100 × 4
#>                age               hair              eyes               region
#>         <symblc_n>         <symblc_s>        <symblc_s>           <symblc_s>
#>  1 [22.00 : 42.00]            {h_red} {e_brown,e_black}              {Bronx}
#>  2 [20.00 : 57.00] {h_black,h_blonde} {e_green,e_black}    {Bronx,Manhattan}
#>  3 [29.00 : 64.00]  {h_brown,h_white} {e_brown,e_green}    {Brooklyn,Queens}
#>  4 [14.00 : 55.00]         {h_blonde} {e_brown,e_black}    {Bronx,Manhattan}
#>  5  [4.00 : 47.00]    {h_brown,h_red}         {e_green}    {Manhattan,Bronx}
#>  6 [32.00 : 61.00] {h_blonde,h_white}  {e_green,e_blue}       {Bronx,Queens}
#>  7 [49.00 : 61.00]    {h_white,h_red}  {e_black,e_blue}       {Queens,Bronx}
#>  8  [8.00 : 32.00] {h_blonde,h_white} {e_brown,e_black} {Manhattan,Brooklyn}
#>  9 [39.00 : 67.00] {h_blonde,h_white} {e_black,e_brown}     {Brooklyn,Bronx}
#> 10 [50.00 : 68.00]  {h_brown,h_black} {e_brown,e_green}    {Manhattan,Bronx}
#> # ℹ 90 more rows

Converting a SODAS 1.0 *.SDS files to RSDA files

hani3101 <- SDS.to.RSDA(file.path = "hani3101.sds")
#> Preprocessing file
#> Converting data to JSON format
#> Processing variable 1: R3101
#> Processing variable 2: RNINO12
#> Processing variable 3: RNINO3
#> Processing variable 4: RNINO4
#> Processing variable 5: RNINO34
#> Processing variable 6: RSOI
hani3101
#> # A tibble: 32 × 6
#>                             R3101                 RNINO12
#>                        <symblc_m>              <symblc_m>
#>  1 X2:0.21 X4:0.18 X3:0.15 X5:... X1:0.17 X2:0.83 X3:0.00
#>  2 X2:0.30 X4:0.14 X3:0.19 X5:... X1:0.00 X2:0.25 X3:0.75
#>  3 X2:0.16 X4:0.12 X3:0.20 X5:... X1:0.67 X2:0.33 X3:0.00
#>  4 X2:0.13 X4:0.15 X3:0.22 X5:... X1:0.17 X2:0.83 X3:0.00
#>  5 X2:0.14 X4:0.14 X3:0.18 X5:... X1:0.42 X2:0.58 X3:0.00
#>  6 X2:0.26 X4:0.06 X3:0.23 X5:... X1:0.00 X2:0.67 X3:0.33
#>  7 X2:0.28 X4:0.14 X3:0.10 X5:... X1:0.00 X2:1.00 X3:0.00
#>  8 X2:0.25 X4:0.15 X3:0.19 X5:... X1:0.00 X2:1.00 X3:0.00
#>  9 X2:0.20 X4:0.15 X3:0.19 X5:... X1:0.00 X2:1.00 X3:0.00
#> 10 X2:0.21 X4:0.16 X3:0.31 X5:... X1:0.08 X2:0.92 X3:0.00
#> # ℹ 22 more rows
#> # ℹ 4 more variables: RNINO3 <symblc_m>, RNINO4 <symblc_m>, RNINO34 <symblc_m>,
#> #   RSOI <symblc_m>
# We can save the file in CSV to RSDA format as follows:
write.sym.table(hani3101,
                file='hani3101.csv',
                sep=';',
                dec='.',
                row.names=TRUE,
                col.names=TRUE)

Converting a SODAS 2.0 *.XML files to RSDA files

abalone <- SODAS.to.RSDA("abalone.xml")
#> Processing variable 1: LENGTH
#> Processing variable 2: DIAMETER
#> Processing variable 3: HEIGHT
#> Processing variable 4: WHOLE_WEIGHT
#> Processing variable 5: SHUCKED_WEIGHT
#> Processing variable 6: VISCERA_WEIGHT
#> Processing variable 7: SHELL_WEIGHT
abalone
#> # A tibble: 24 × 7
#>           LENGTH      DIAMETER        HEIGHT  WHOLE_WEIGHT SHUCKED_WEIGHT
#>       <symblc_n>    <symblc_n>    <symblc_n>    <symblc_n>     <symblc_n>
#>  1 [0.28 : 0.66] [0.20 : 0.48] [0.07 : 0.18] [0.08 : 1.37]  [0.03 : 0.64]
#>  2 [0.30 : 0.74] [0.22 : 0.58] [0.02 : 1.13] [0.15 : 2.25]  [0.06 : 1.16]
#>  3 [0.34 : 0.78] [0.26 : 0.63] [0.06 : 0.23] [0.20 : 2.66]  [0.07 : 1.49]
#>  4 [0.39 : 0.82] [0.30 : 0.65] [0.10 : 0.25] [0.26 : 2.51]  [0.11 : 1.23]
#>  5 [0.40 : 0.74] [0.32 : 0.60] [0.10 : 0.24] [0.35 : 2.20]  [0.12 : 0.84]
#>  6 [0.45 : 0.80] [0.38 : 0.63] [0.14 : 0.22] [0.64 : 2.53]  [0.16 : 0.93]
#>  7 [0.49 : 0.72] [0.36 : 0.58] [0.12 : 0.21] [0.68 : 2.12]  [0.16 : 0.82]
#>  8 [0.55 : 0.70] [0.46 : 0.58] [0.18 : 0.22] [1.21 : 1.81]  [0.32 : 0.71]
#>  9 [0.08 : 0.24] [0.06 : 0.18] [0.01 : 0.06] [0.00 : 0.07]  [0.00 : 0.03]
#> 10 [0.13 : 0.58] [0.10 : 0.45] [0.00 : 0.15] [0.01 : 0.89]  [0.00 : 0.50]
#> # ℹ 14 more rows
#> # ℹ 2 more variables: VISCERA_WEIGHT <symblc_n>, SHELL_WEIGHT <symblc_n>
write.sym.table(abalone,
                file='abalone.csv',
                sep=';',
                dec='.',
                row.names = TRUE,
                col.names = TRUE)

Basic statistics

Symbolic Mean

data(example3)
mean(example3$F1)
#> [1] 1.628571
mean(example3[,1])
#> [1] 1.628571
mean(example3$F2)
#> [1] 5
mean(example3[,2])
#> [1] 5
mean(example3$F2,method = "interval")
#> <symbolic_interval[1]>
#> [1] [1.86 : 8.14]
mean(example3[,2],method = "interval")
#> <symbolic_interval[1]>
#> [1] [1.86 : 8.14]

Symbolic median

median(example3$F1)
#> [1] 1.4
median(example3[,1])
#> [1] 1.4
median(example3$F2)
#> [1] 1.5
median(example3[,2])
#> [1] 1.5
median(example3$F6, method = 'interval')
#> <symbolic_interval[1]>
#> [1] [5.00 : 89.00]
median(example3[,6], method = 'interval')
#> <symbolic_interval[1]>
#> [1] [5.00 : 89.00]

Variance and standard deviation

var(example3[,1])
#> [1] 15.98238
var(example3[,2])
#> [1] 90.66667
var(example3$F6)
#> [1] 1872.358
var(example3$F6, method = 'interval')
#> <symbolic_interval[1]>
#> [1] [2,408.97 : 1,670.51]
var(example3$F6, method = 'billard')
#> [1] 1355.143
sd(example3$F1)
#> [1] 3.997797
sd(example3$F2)
#> [1] 6.733003
sd(example3$F6)
#> [1] 30.59704
sd(example3$F6, method = 'interval')
#> <symbolic_interval[1]>
#> [1] [49.08 : 40.87]
sd(example3$F6, method = 'billard')
#> [1] 36.81226

Symbolic correlation

cor(example3$F1, example3$F4)
#> [1] 0.2864553
cor(example3[,1], example3[,4])
#>           [,1]
#> [1,] 0.2864553
cor(example3$F2, example3$F6, method = 'centers')
#> [1] -0.6693648
cor(example3$F2, example3$F6, method = 'billard')
#> [1] -0.6020041

Radar plot for intervals

library(ggpolypath)
#> Loading required package: ggplot2

data(oils)
oils <- RSDA:::to.v3(RSDA:::to.v2(oils))
sym.radar.plot(oils[2:3,])
#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

sym.radar.plot(oils[2:5,])
#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE

#> Warning in type.convert.default(X[[i]], ...): 'as.is' should be specified by
#> the caller; using TRUE


res <- interval.histogram.plot(oils[,2],
                               n.bins = 4,
                               col = c(2,3,4,5))

res
#> $frequency
#> [1] 25 49  1 25
#> 
#> $histogram
#>      [,1]
#> [1,]  0.7
#> [2,]  1.9
#> [3,]  3.1
#> [4,]  4.3

res <- interval.histogram.plot(oils[,3],
                               n.bins = 3,
                               main = "Histogram",
                               col = c(2, 3, 4))

res
#> $frequency
#> [1] 50 25 25
#> 
#> $histogram
#>      [,1]
#> [1,]  0.7
#> [2,]  1.9
#> [3,]  3.1

Distances for intervals

Gowda-Diday

data("oils")
DM <- sym.dist.interval(sym.data = oils[,1:4],
                        method = "Gowda.Diday")
model <- hclust(DM)
plot(model, hang = -1)

Ichino

DM <- sym.dist.interval(sym.data= oils[,1:4],
                        method = "Ichino")
model <- hclust(DM)
plot(model, hang = -1)

Hausdorff

DM <- sym.dist.interval(sym.data = oils[,c(1,2,4)],
                        gamma = 0.5,
                        method = "Hausdorff",
                        normalize = FALSE,
                        SpanNormalize = TRUE,
                        euclidea = TRUE,
                        q = 2)
model <- hclust(DM)
plot(model, hang = -1)

Linear regression for intervals

Training

data(int_prost_train)
data(int_prost_test)
res.cm <- sym.lm(formula = lpsa~., sym.data = int_prost_train, method = 'cm')
res.cm
#> 
#> Call:
#> stats::lm(formula = formula, data = centers)
#> 
#> Coefficients:
#> (Intercept)       lcavol      lweight          age         lbph          svi  
#>    0.411537     0.579327     0.614128    -0.018659     0.143918     0.730937  
#>         lcp      gleason        pgg45  
#>   -0.205536    -0.030924     0.009507

Prediction

pred.cm <- sym.predict(model = res.cm, new.sym.data = int_prost_test)

Testing

RMSE.L(int_prost_test$lpsa, pred.cm$Fitted)
#> [1] 0.7229999
RMSE.U(int_prost_test$lpsa, pred.cm$Fitted)
#> [1] 0.7192467
R2.L(int_prost_test$lpsa, pred.cm$Fitted)
#> [1] 0.501419
R2.U(int_prost_test$lpsa, pred.cm$Fitted)
#> [1] 0.5058389
deter.coefficient(int_prost_test$lpsa, pred.cm$Fitted)
#> [1] 0.4962964

LASSO regression for intervals

data(int_prost_train)
data(int_prost_test)

Training

res.cm.lasso <- sym.glm(sym.data = int_prost_train,
                        response = 9,
                        method = 'cm',
                        alpha = 1,
                        nfolds = 10,
                        grouped = TRUE)

Prediction

pred.cm.lasso <- sym.predict(res.cm.lasso,
                             response = 9,
                             int_prost_test,
                             method = 'cm')

Testing

plot(res.cm.lasso)

plot(res.cm.lasso$glmnet.fit, "lambda", label=TRUE)

RMSE.L(int_prost_test$lpsa,pred.cm.lasso)
#> [1] 0.7014621
RMSE.U(int_prost_test$lpsa,pred.cm.lasso) 
#> [1] 0.6982014
R2.L(int_prost_test$lpsa,pred.cm.lasso) 
#> [1] 0.531049
R2.U(int_prost_test$lpsa,pred.cm.lasso) 
#> [1] 0.5348845
deter.coefficient(int_prost_test$lpsa, pred.cm.lasso)
#> [1] 0.4896842

RIDGE regression for intervals

Training

data(int_prost_train)
data(int_prost_test)

res.cm.ridge <- sym.glm(sym.data = int_prost_train,
                        response = 9,
                        method = 'cm',
                        alpha = 0,
                        nfolds = 10,
                        grouped = TRUE)

Prediction

pred.cm.ridge <- sym.predict(res.cm.ridge,
                             response = 9,
                             int_prost_test,
                             method = 'cm')

Testing

plot(res.cm.ridge)

plot(res.cm.ridge$glmnet.fit, "lambda", label=TRUE)

RMSE.L(int_prost_test$lpsa, pred.cm.ridge)
#> [1] 0.703543
RMSE.U(int_prost_test$lpsa, pred.cm.ridge)
#> [1] 0.7004145
R2.L(int_prost_test$lpsa, pred.cm.ridge)
#> [1] 0.5286114
R2.U(int_prost_test$lpsa, pred.cm.ridge)
#> [1] 0.5322683
deter.coefficient(int_prost_test$lpsa, pred.cm.ridge)
#> [1] 0.4808652

PCA for intervals

Example 1

data("oils")
res <- sym.pca(oils,'centers')
plot(res, choix = "ind")

plot(res, choix = "var")

Example 2

res <- sym.pca(oils,'tops')
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
plot(res, choix = "ind")

Example 3

res <- sym.pca(oils, 'principal.curves')
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
plot(res, choix = "ind")

Example 4

res <- sym.pca(oils,'optimized.distance')
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
plot(res, choix = "ind")

plot(res, choix = "var")

Example 5

res <- sym.pca(oils,'optimized.variance')
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
#> tcltk DLL is linked to '/opt/X11/lib/libX11.6.dylib'
plot(res, choix = "ind")

plot(res, choix = "var")

Symbolic Multiple Correspondence Analysis

Example 1

data("ex_mcfa1") 
ex_mcfa1
#>     suspect age     hair    eyes    region
#> 1         1  42    h_red e_brown     Bronx
#> 2         2  20  h_black e_green     Bronx
#> 3         3  64  h_brown e_brown  Brooklyn
#> 4         4  55 h_blonde e_brown     Bronx
#> 5         5   4  h_brown e_green Manhattan
#> 6         6  61 h_blonde e_green     Bronx
#> 7         7  61  h_white e_black    Queens
#> 8         8  32 h_blonde e_brown Manhattan
#> 9         9  39 h_blonde e_black  Brooklyn
#> 10       10  50  h_brown e_brown Manhattan
#> 11       11  41    h_red  e_blue Manhattan
#> 12       12  35 h_blonde e_green  Brooklyn
#> 13       13  56 h_blonde e_brown     Bronx
#> 14       14  52    h_red e_brown    Queens
#> 15       15  55    h_red e_green  Brooklyn
#> 16       16  25  h_brown e_brown    Queens
#> 17       17  52 h_blonde e_brown  Brooklyn
#> 18       18  28    h_red e_brown Manhattan
#> 19       19  21  h_white  e_blue Manhattan
#> 20       20  66  h_black e_black  Brooklyn
#> 21       21  67 h_blonde e_brown    Queens
#> 22       22  13  h_white  e_blue  Brooklyn
#> 23       23  39  h_brown e_green Manhattan
#> 24       24  47  h_black e_green  Brooklyn
#> 25       25  54 h_blonde e_brown     Bronx
#> 26       26  75  h_brown  e_blue  Brooklyn
#> 27       27   3  h_white e_green Manhattan
#> 28       28  40  h_white e_green Manhattan
#> 29       29  58    h_red  e_blue    Queens
#> 30       30  41  h_brown e_green     Bronx
#> 31       31  25  h_white e_black  Brooklyn
#> 32       32  75 h_blonde  e_blue Manhattan
#> 33       33  58  h_white e_brown     Bronx
#> 34       34  61  h_white e_brown Manhattan
#> 35       35  52  h_white  e_blue     Bronx
#> 36       36  19    h_red e_black    Queens
#> 37       37  58    h_red e_black     Bronx
#> 38       38  46  h_black e_green Manhattan
#> 39       39  74  h_brown e_black Manhattan
#> 40       40  26 h_blonde e_brown  Brooklyn
#> 41       41  63 h_blonde  e_blue    Queens
#> 42       42  40  h_brown e_black    Queens
#> 43       43  65  h_black e_brown  Brooklyn
#> 44       44  51 h_blonde e_brown  Brooklyn
#> 45       45  15  h_white e_black  Brooklyn
#> 46       46  32 h_blonde e_brown     Bronx
#> 47       47  68  h_white e_black Manhattan
#> 48       48  51  h_white e_black    Queens
#> 49       49  14    h_red e_green    Queens
#> 50       50  72  h_white e_brown  Brooklyn
#> 51       51   7    h_red  e_blue  Brooklyn
#> 52       52  22    h_red e_brown     Bronx
#> 53       53  52    h_red e_brown  Brooklyn
#> 54       54  62  h_brown e_green     Bronx
#> 55       55  41  h_black e_brown    Queens
#> 56       56  32  h_black e_black Manhattan
#> 57       57  58  h_brown e_brown    Queens
#> 58       58  25  h_black e_brown    Queens
#> 59       59  70 h_blonde e_green  Brooklyn
#> 60       60  64  h_brown  e_blue    Queens
#> 61       61  25  h_white  e_blue     Bronx
#> 62       62  42  h_black e_black  Brooklyn
#> 63       63  56    h_red e_black  Brooklyn
#> 64       64  41 h_blonde e_black  Brooklyn
#> 65       65   8  h_white e_black Manhattan
#> 66       66   7  h_black e_green  Brooklyn
#> 67       67  42  h_white e_brown    Queens
#> 68       68  10  h_white  e_blue Manhattan
#> 69       69  60  h_brown e_black     Bronx
#> 70       70  52 h_blonde e_brown  Brooklyn
#> 71       71  39  h_brown  e_blue Manhattan
#> 72       72  69  h_brown e_green    Queens
#> 73       73  67 h_blonde e_green Manhattan
#> 74       74  46    h_red e_black  Brooklyn
#> 75       75  72  h_black e_black    Queens
#> 76       76  66    h_red  e_blue    Queens
#> 77       77   4  h_black  e_blue Manhattan
#> 78       78  62  h_black e_green  Brooklyn
#> 79       79  10 h_blonde  e_blue     Bronx
#> 80       80  16 h_blonde e_black Manhattan
#> 81       81  59 h_blonde e_brown     Bronx
#> 82       82  63 h_blonde  e_blue Manhattan
#> 83       83  54    h_red  e_blue    Queens
#> 84       84  14  h_brown  e_blue  Brooklyn
#> 85       85  48  h_black e_green Manhattan
#> 86       86  59 h_blonde e_black     Bronx
#> 87       87  73 h_blonde e_black     Bronx
#> 88       88  51  h_brown e_brown     Bronx
#> 89       89  14  h_white e_black     Bronx
#> 90       90  58 h_blonde e_black    Queens
#> 91       91  56    h_red e_green Manhattan
#> 92       92  26    h_red  e_blue  Brooklyn
#> 93       93  59  h_brown e_black Manhattan
#> 94       94  27  h_white e_green Manhattan
#> 95       95  38  h_black e_green Manhattan
#> 96       96   5 h_blonde e_green     Bronx
#> 97       97  14  h_black  e_blue    Queens
#> 98       98  13  h_black e_brown Manhattan
#> 99       99  54  h_white  e_blue  Brooklyn
#> 100     100  66  h_white e_green Manhattan
#> 101       1  22    h_red e_black     Bronx
#> 102       2  57 h_blonde e_black Manhattan
#> 103       3  29  h_white e_green    Queens
#> 104       4  14 h_blonde e_black Manhattan
#> 105       5  47    h_red e_green     Bronx
#> 106       6  32  h_white  e_blue    Queens
#> 107       7  49    h_red  e_blue     Bronx
#> 108       8   8  h_white e_black  Brooklyn
#> 109       9  67  h_white e_brown     Bronx
#> 110      10  68  h_black e_green     Bronx
#> 111      11  15  h_black e_brown Manhattan
#> 112      12  46  h_white e_brown     Bronx
#> 113      13  68  h_white e_black Manhattan
#> 114      14  55 h_blonde  e_blue Manhattan
#> 115      15   7  h_white e_green     Bronx
#> 116      16  10  h_black e_brown  Brooklyn
#> 117      17  49    h_red  e_blue Manhattan
#> 118      18  12  h_brown  e_blue  Brooklyn
#> 119      19  41  h_white  e_blue     Bronx
#> 120      20  10  h_brown  e_blue     Bronx
#> 121      21  12  h_white e_green Manhattan
#> 122      22  53  h_white  e_blue Manhattan
#> 123      23   5  h_black e_black Manhattan
#> 124      24  46  h_brown e_black    Queens
#> 125      25  14  h_brown e_black    Queens
#> 126      26  55  h_white e_green  Brooklyn
#> 127      27  53    h_red e_brown Manhattan
#> 128      28  31  h_black e_brown Manhattan
#> 129      29  31 h_blonde e_brown    Queens
#> 130      30  55  h_brown e_black  Brooklyn
sym.table <- classic.to.sym(x = ex_mcfa1, 
                            concept = suspect, 
                            default.categorical = sym.set)
sym.table
#> # A tibble: 100 × 4
#>                age               hair              eyes               region
#>         <symblc_n>         <symblc_s>        <symblc_s>           <symblc_s>
#>  1 [22.00 : 42.00]            {h_red} {e_brown,e_black}              {Bronx}
#>  2 [20.00 : 57.00] {h_black,h_blonde} {e_green,e_black}    {Bronx,Manhattan}
#>  3 [29.00 : 64.00]  {h_brown,h_white} {e_brown,e_green}    {Brooklyn,Queens}
#>  4 [14.00 : 55.00]         {h_blonde} {e_brown,e_black}    {Bronx,Manhattan}
#>  5  [4.00 : 47.00]    {h_brown,h_red}         {e_green}    {Manhattan,Bronx}
#>  6 [32.00 : 61.00] {h_blonde,h_white}  {e_green,e_blue}       {Bronx,Queens}
#>  7 [49.00 : 61.00]    {h_white,h_red}  {e_black,e_blue}       {Queens,Bronx}
#>  8  [8.00 : 32.00] {h_blonde,h_white} {e_brown,e_black} {Manhattan,Brooklyn}
#>  9 [39.00 : 67.00] {h_blonde,h_white} {e_black,e_brown}     {Brooklyn,Bronx}
#> 10 [50.00 : 68.00]  {h_brown,h_black} {e_brown,e_green}    {Manhattan,Bronx}
#> # ℹ 90 more rows
res <- sym.mcfa(sym.table, c(2,3))
mcfa.scatterplot(res[,2], res[,3], sym.data = sym.table, pos.var = c(2,3))

res <- sym.mcfa(sym.table, c(2,3,4))
mcfa.scatterplot(res[,2], res[,3], sym.data = sym.table, pos.var = c(2,3,4))

Symbolic UMAP

Ejemplo Oils

datos <- oils
datos
#> # A tibble: 8 × 4
#>             GRA               FRE               IOD               SAP
#> *    <symblc_n>        <symblc_n>        <symblc_n>        <symblc_n>
#> 1 [0.93 : 0.94] [-27.00 : -18.00] [170.00 : 204.00] [118.00 : 196.00]
#> 2 [0.93 : 0.94]   [-5.00 : -4.00] [192.00 : 208.00] [188.00 : 197.00]
#> 3 [0.92 : 0.92]   [-6.00 : -1.00]  [99.00 : 113.00] [189.00 : 198.00]
#> 4 [0.92 : 0.93]   [-6.00 : -4.00] [104.00 : 116.00] [187.00 : 193.00]
#> 5 [0.92 : 0.92] [-25.00 : -15.00]   [80.00 : 82.00] [189.00 : 193.00]
#> 6 [0.91 : 0.92]     [0.00 : 6.00]   [79.00 : 90.00] [187.00 : 196.00]
#> 7 [0.86 : 0.87]   [30.00 : 38.00]   [40.00 : 48.00] [190.00 : 199.00]
#> 8 [0.86 : 0.86]   [22.00 : 32.00]   [53.00 : 77.00] [190.00 : 202.00]
x <- sym.umap(datos)
x
#>             V1        V2          V3         V4
#> 1    -9.486419 -2.437560 11.09450514  3.8597450
#> 2    -9.291773 -2.242912 11.28922078  3.6651031
#> 3    -9.322376 -2.273513 11.25873422  3.6957040
#> 4    -9.240148 -2.191262 11.34096205  3.6134746
#> 5    -9.497748 -2.448876 11.08339404  3.8710728
#> 6    -9.645452 -2.596570 10.93580344  4.0187760
#> 7    -9.306796 -2.257918 11.27452456  3.6801182
#> 8    -9.328169 -2.279298 11.25315937  3.7014873
#> 9    -1.235054  1.836879 -2.94972019 -5.7066594
#> 10   -1.151552  1.838129 -2.93052399 -5.7656798
#> 11   -1.233733  1.799005 -3.05162192 -5.5995454
#> 12   -1.109717  1.527585 -3.05026821 -5.5966663
#> 13   -1.115887  1.974561 -2.87027101 -5.7007239
#> 14   -1.084133  2.008087 -2.94475355 -5.6159948
#> 15   -1.332376  1.902570 -2.90051234 -5.6109137
#> 16   -1.234441  1.818597 -3.13425707 -5.7771997
#> 17   -1.943464  2.224879 -3.87359369 -5.8978057
#> 18   -2.260242  1.959183 -3.50008662 -5.8856918
#> 19   -1.991149  2.264097 -3.81272396 -5.8480879
#> 20   -2.084464  1.864579 -3.65592624 -6.1601024
#> 21   -2.058150  2.248290 -3.76852481 -5.5536431
#> 22   -2.201742  2.108917 -3.69485394 -5.8168247
#> 23   -2.146909  2.212785 -3.88390350 -5.7021996
#> 24   -2.359044  2.007334 -3.72549972 -5.9458950
#> 25   -2.016807  2.218834 -3.18711095 -5.7165063
#> 26   -1.842308  1.829503 -3.41755379 -5.7894437
#> 27   -2.027974  1.980831 -3.41816637 -5.5431891
#> 28   -1.967136  2.020815 -3.32940908 -5.7332410
#> 29   -2.133592  1.903024 -3.52063772 -5.3200989
#> 30   -2.335501  1.954604 -3.58358895 -5.6684793
#> 31   -2.045006  1.683916 -3.47629672 -5.5372667
#> 32   -2.319471  1.800426 -3.48923740 -5.5594852
#> 33   -9.836918 -2.530528 -1.09181973  3.6016449
#> 34   -9.976300 -2.481613 -1.19294984  3.4584848
#> 35   -9.731401 -2.726910 -1.42070558  3.5256548
#> 36   -9.557896 -2.815222 -1.60457834  3.6888385
#> 37  -10.203365 -2.534262 -1.06815875  3.2857082
#> 38  -10.186821 -2.528668 -0.89248767  3.1737354
#> 39  -10.023885 -2.754892 -1.22478957  3.0948667
#> 40   -9.893945 -2.722448 -1.09201864  3.1092877
#> 41   -8.886738 -2.925786 -0.10866759  3.2194084
#> 42   -8.894895 -2.918994 -0.04656192  3.1817061
#> 43   -8.558576 -3.108756 -0.15292170  3.5209042
#> 44   -8.553762 -3.119990 -0.12832467  3.4020375
#> 45   -9.045744 -2.795375  0.04350897  3.0364241
#> 46   -9.132956 -2.710859  0.06946699  2.9646078
#> 47   -8.798646 -2.957939  0.23781326  2.9099614
#> 48   -8.907719 -2.834238  0.16215991  2.9779378
#> 49  -10.089641 -2.271160 -1.31993117  3.4227533
#> 50  -10.326117 -2.056373 -1.07295955  3.2034754
#> 51  -10.108617 -2.445900 -1.24756434  3.4866513
#> 52  -10.391770 -2.104110 -1.04970560  3.1561217
#> 53  -10.331175 -2.375337 -1.04743462  3.0492796
#> 54  -10.403801 -2.049200 -0.87999277  2.8163371
#> 55  -10.367941 -2.559443 -1.05958357  2.9863523
#> 56  -10.344861 -2.181893 -0.97013310  2.9003257
#> 57   -9.652443 -2.475703 -0.40052757  3.1934088
#> 58   -9.889868 -2.140432 -0.38851591  3.1232234
#> 59   -9.556867 -2.601785 -0.56241976  3.2800251
#> 60   -9.762875 -2.136516 -0.39710383  3.4568988
#> 61   -9.799112