These *_ord functions wrap core R functions with modifications
for use with 'tbl_ord' methods. Some parameters are hidden from the user
and set to settings required for these methods, some matrix outputs are
given row or column names to be used by them, and new '*_ord' S3 class
attributes are added to enable them.
eigen_ord(x, symmetric = isSymmetric.matrix(x))
svd_ord(x, nu = min(dim(x)), nv = min(dim(x)))
cmdscale_ord(d, k = 2, add = FALSE)
cancor_ord(x, y, xcenter = TRUE, ycenter = TRUE, scores = FALSE)a numeric or complex matrix whose spectral decomposition is to be computed. Logical matrices are coerced to numeric.
if TRUE, the matrix is assumed to be symmetric
(or Hermitian if complex) and only its lower triangle (diagonal
included) is used. If symmetric is not specified,
isSymmetric(x) is used.
the number of left singular vectors to be computed.
This must between 0 and n = nrow(x).
the number of right singular vectors to be computed.
This must be between 0 and p = ncol(x).
a distance structure such as that returned by dist
or a full symmetric matrix containing the dissimilarities.
the maximum dimension of the space which the data are to be represented in; must be in \(\{1, 2, \ldots, n-1\}\).
logical indicating if an additive constant \(c*\) should be computed, and added to the non-diagonal dissimilarities such that the modified dissimilarities are Euclidean.
numeric matrix (\(n \times p_2\)), containing the y coordinates.
logical or numeric vector of length \(p_1\),
describing any centering to be done on the x values before the
analysis. If TRUE (default), subtract the column means.
If FALSE, do not adjust the columns. Otherwise, a vector
of values to be subtracted from the columns.
analogous to xcenter, but for the y values.
Logical; whether to return canonical scores and structure correlations.
Objects slightly modified from the outputs of the original functions, with new '*-ord' classes.
The following table summarizes the wrapped functions:
| Original function | Hide params | New params | Add names | New class |
base::eigen() | Yes | No | Yes | Yes |
base::svd() | Yes | No | Yes | Yes |
stats::cmdscale() | Yes | No | No | Yes |
stats::cancor() | No | Yes | No | Yes |
By default, cancor_ord() returns the same data as stats::cancor(): the
canonical correlations (cor), the canonical coefficients ($xcoef and
$ycoef), and the variable means ($xcenter, $ycenter). If scores = TRUE, then cancor_ord() also returns the scores $xscores and $yscores
calculated from the (appropriately centered) data and the coefficients and
the intraset structure correlations $xstructure and $ystructure between
these and the data. These modifications are inspired by the cancor()
function in candisc, though two caveats should be noted: First, the
canonical coefficients (hence the canonical scores) are scaled by \(n - 1\)
compared to these, though the intraset structure correlations are the same.
Second, the interset structure correlations are not returned, as these may
be obtained by conferring inertia unto the intraset ones.
# glass composition data from one furnace
glass_banias <- subset(
glass,
Context == "L.15;B.166",
select = c("SiO2", "Na2O", "CaO", "Al2O3", "MgO", "K2O")
)
# eigendecomposition of a covariance matrix
(glass_cov <- cov(glass_banias))
#> SiO2 Na2O CaO Al2O3 MgO K2O
#> SiO2 2.6155367 0.6093667 -1.2869867 -0.45252 -0.46817333 -0.31149
#> Na2O 0.6093667 0.2559067 -0.3217067 -0.16542 -0.10587333 -0.10726
#> CaO -1.2869867 -0.3217067 0.7060267 0.24842 0.20559333 0.13220
#> Al2O3 -0.4525200 -0.1654200 0.2484200 0.12716 0.07972000 0.07230
#> MgO -0.4681733 -0.1058733 0.2055933 0.07972 0.09462667 0.06682
#> K2O -0.3114900 -0.1072600 0.1322000 0.07230 0.06682000 0.06131
eigen_ord(glass_cov)
#> eigen() decomposition
#> $values
#> [1] 3.617285e+00 1.467376e-01 8.282650e-02 1.360291e-02 1.141672e-04
#> [6] 6.230496e-19
#>
#> $vectors
#> EV1 EV2 EV3 EV4 EV5 EV6
#> SiO2 0.8469970 0.31716695 -0.25837288 -0.11577441 -0.2822267 0.1489597
#> Na2O 0.2099520 -0.79170694 -0.10021025 -0.51787194 0.1385212 0.1780413
#> CaO -0.4260986 0.04199369 -0.76882445 -0.05663831 -0.3233201 0.3432808
#> Al2O3 -0.1556273 0.45906193 -0.08066526 -0.77062798 0.2878426 -0.2860325
#> MgO -0.1492104 -0.07286372 0.38010592 -0.30504020 -0.8407925 -0.1672273
#> K2O -0.1023356 0.23408287 0.42558539 -0.16816668 0.0826960 0.8476385
#>
# singular value decomposition of a data matrix
svd_ord(glass_banias)
#> $d
#> [1] 177.16843535 2.56375788 0.82468871 0.51400398 0.21898181
#> [6] 0.01400983
#>
#> $u
#> SV1 SV2 SV3 SV4 SV5 SV6
#> 1 -0.4114474 0.268953258 0.54464383 -0.4529219 0.4351102 0.25938230
#> 2 -0.4099492 0.124966122 0.51481370 0.3162816 -0.6000110 -0.30206743
#> 3 -0.4097327 -0.103523503 -0.13351247 0.5115444 0.6162163 -0.40271096
#> 4 -0.3914429 -0.815275824 -0.07487103 -0.3907913 -0.1362392 -0.07220201
#> 5 -0.4168814 0.486413365 -0.59131457 -0.3710452 -0.1857274 -0.26036475
#> 6 -0.4095779 -0.007607042 -0.25543255 0.3778329 -0.1337444 0.77865078
#>
#> $v
#> SV1 SV2 SV3 SV4 SV5 SV6
#> SiO2 -0.97757835 0.09992541 -0.16303444 0.046753453 -0.05969843 -0.04500518
#> Na2O -0.16869103 0.14528933 0.81605152 -0.238508341 0.42108755 0.22426170
#> CaO -0.11569079 -0.87296399 0.28883998 0.323881874 -0.16853953 0.08840776
#> Al2O3 -0.01665686 -0.29609746 -0.38102381 0.008014293 0.87323378 -0.06533172
#> MgO -0.03775856 -0.28137368 0.06285458 -0.713218748 -0.10916969 -0.62837365
#> K2O -0.02822033 -0.19998734 -0.27371758 -0.572086712 -0.12751682 0.73535272
#>
#> attr(,"class")
#> [1] "svd_ord"
# classical multidimensional scaling of a distance matrix
cmdscale_ord(dist(glass_banias))
#> $points
#> [,1] [,2]
#> [1,] -0.87986198 0.53544035
#> [2,] -0.45244074 0.40907498
#> [3,] -0.08144239 -0.26484655
#> [4,] 3.61567304 -0.04227923
#> [5,] -1.99639680 -0.36657720
#> [6,] -0.20553113 -0.27081236
#>
#> $eig
#> [1] 1.808643e+01 7.336881e-01 4.141325e-01 6.801456e-02 5.708361e-04
#> [6] 2.355381e-16
#>
#> $x
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] -2.207855556 -1.12728889 0.22354444 6.3455444 -3.2300556 -0.003888889
#> [2,] -1.127288889 -0.87692222 0.03611111 3.3851111 -1.3678889 -0.049122222
#> [3,] 0.223544444 0.03611111 -0.47385556 0.7213444 -0.2278556 -0.279288889
#> [4,] 6.345544444 3.38511111 0.72134444 -26.2322556 14.2529444 1.527311111
#> [5,] -3.230055556 -1.36788889 -0.22785556 14.2529444 -8.5234556 -0.903688889
#> [6,] -0.003888889 -0.04912222 -0.27928889 1.5273111 -0.9036889 -0.291322222
#>
#> $ac
#> [1] 0
#>
#> $GOF
#> [1] 0.9749924 0.9749924
#>
#> attr(,"class")
#> [1] "cmds_ord"
# canonical correlation analysis with trace components
glass_banias_minor <- subset(
glass,
Context == "L.15;B.166",
select = c("TiO2", "FeO", "MnO", "P2O5", "Cl", "SO3")
)
# impute half of detection threshold
glass_banias_minor$TiO2[[1L]] <- 0.5
cancor_ord(glass_banias, glass_banias_minor)
#> $cor
#> [1] 1 1 1 1 1
#>
#> $xcoef
#> [,1] [,2] [,3] [,4] [,5]
#> SiO2 1.5208338 -11.442468 0.24637620 -3.6336531 -2.879401
#> Na2O 0.6162264 4.530578 0.49288317 0.9782368 2.843217
#> CaO 1.9784095 -13.380217 -0.02445709 -5.2899746 -3.775547
#> Al2O3 0.9152174 11.763052 1.76949275 4.7132684 4.535237
#> MgO 3.8891975 -32.462610 -0.81337485 -8.8720942 -6.686017
#>
#> $ycoef
#> [,1] [,2] [,3] [,4] [,5]
#> TiO2 1.726017 -2.948854 1.0731891 1.910721 2.960014
#> FeO 1.644821 1.607463 -0.7174584 -7.612725 0.000000
#> MnO -2.274981 3.129723 -3.8589747 -4.606006 0.000000
#> P2O5 2.274901 -22.265078 2.1204758 5.301190 0.000000
#> Cl -10.072183 10.842238 -9.3884609 -23.471152 0.000000
#>
#> $xcenter
#> SiO2 Na2O CaO Al2O3 MgO K2O
#> 70.691667 12.196667 8.383333 1.210000 2.736667 2.045000
#>
#> $ycenter
#> TiO2 FeO MnO P2O5 Cl SO3
#> 0.1933333 0.4300000 0.9666667 0.2700000 0.8100000 0.3483333
#>
#> attr(,"class")
#> [1] "cancor_ord"
# calculate canonical scores and structure correlations
glass_cca <-
cancor_ord(glass_banias[, 1:3], glass_banias_minor[, 1:3], scores = TRUE)
# scores
glass_cca$xscores
#> [,1] [,2] [,3]
#> [1,] 0.08625757 -0.564009626 -0.5086737
#> [2,] -0.06325679 -0.009686013 -0.4449230
#> [3,] -0.31243762 0.589123478 -0.1458326
#> [4,] 0.85114073 0.156299524 0.2733283
#> [5,] -0.34697599 -0.470284132 0.6433738
#> [6,] -0.21472789 0.298556769 0.1827271
# intraset correlations
glass_cca$xstructure
#> [,1] [,2] [,3]
#> SiO2 -0.9261925 -0.3749912 -0.03935800
#> Na2O -0.5467957 -0.5715073 -0.61187732
#> CaO 0.7639885 0.6435255 -0.04686735
# interset correlations
glass_cca$xstructure %*% diag(glass_cca$cor)
#> [,1] [,2] [,3]
#> SiO2 -0.9261925 -0.3594308 -0.02748688
#> Na2O -0.5467957 -0.5477923 -0.42732349
#> CaO 0.7639885 0.6168220 -0.03273126