The personal standards subscale of the Sport-MPS-2--considered by many perfectionism theorists as a central indicator of perfectionistic strivings in sport (see Stoeber & Madigan, 2016)--had moderate to strong positive loadings on both perfectionism variates
To interpret a characteristic root, Tabachnick and Fidell (2013) recommended assessing (a) the composition of each of the variates--and the variance shared between the original variables and the variates
on which they load--by examining the raw canonical correlation coefficients, (b) the percentage of variance in the dependent variate
explained by the independent variate
, (c) the standardized canonical correlation coefficients of the skills variate
to ascertain the relative contributions of each of the skills to the interrelated skills set, and (d) the cross-canonical correlation coefficients to ascertain contributions of each of the skills as they individually predicted the dependent variate
(Hair, Anderson, Tatham, & Black, 1998).
[M.sub.(p)kj] is the kth band MAD variate
of the pth pair of fused images for pixel j.
(1936) Relations between Two Sets of Variates
. Biometrika 28, 312-377.
Therefore, in order to generate [alpha]-[mu] complex variates
, one can simply generate Nakagami-m complex variates
and use the relation between the envelopes of the two processes.
The extended matrix variate
beta function, denoted by [B.sub.m](a, b; [summation]), is defined as
By replacing etr(-[[OMEGA].sup.-1] X/d) by the confluent hypergeometric function of matrix argument [sub.1] [F.sub.1]([alpha]; [beta];-[[OMEGA].sup.-1] X/[theta]), a generalization of the matrix variate
gamma distribution can be defined by the p.d.f.:
Table 3: Interlandmark distances with the highest PCA loading values FEMALE MALE Interlandmark Values Interlandmark Values Distances Distances 9-19 0.467995671 5-15 0.467656118 9-17 0.464656038 9-19 0.472865700 5-15 0.459180650 9-17 0.467191420 7-17 0.454574732 7-15 0.466876458 7-15 0.454574732 9-18 0.452874771 9-16 0.454539315 7-16 0.451470110 8-17 0.453854942 5-13 0.451087999 9-18 0.451114477 8-17 0.449943458 5-16 0.446761918 8-16 0.448657419 8-16 0.446739520 8-15 0.446786093 11-19 0.446026845 7-17 0.446475302 8-19 0.440943604 5-14 0.440513243 8-18 0.438755866 5-16 0.438528035 Table 4: Canonical variate
analysis of the Relative warp scores between sexes of P.
where [[R.sup.2].sub.(U,Lu)] and [[R.sup.2].sub.(V,LV)] are the proportion of explained variance in set U and set V that are accounted for by a particular canonical variate
[U.sup.*.sub.i] and [V.sup.*.sub.j] respectively.
Structural Coefficients, Canonical Correlations, Percentage of Variances, and Redundancies Between the Predictor Variables and ADMS, and Their Canonical Variates
Predicator Canonical variates
[chi].sup.1] [chi square] [chi].sup.3] AGQ-R Mastery approach .66 # -.19 -.44 Mastery avoidance .29 .80 # .15 Performance approach .87 # .01 -.29 Performance avoidance .57 # .50 # -.45 WRADS Report classmates .37 .13 .46 Report friends .53 # -.16 .67 # Variance percentage 33.74 16.17 19.31 Redundancy 4.57 0.99 0.77 [rho] (canonical [[rho].sub [[rho].sub [[rho].sup correlation) .1] = .37 .2] = .25 .3] = .20 [[rho].sup.2] .14 0.06 0.04 [rho] .001 .001 0.04 Criterion variables Canonical variates
We organized the 257 specimens into one sample for a principal components analysis (PCA) and 13 samples for a canonical variate
analysis (CVA) to search for patterns of geographic variation.
With the boundary condition, an analytic formula for the option with geometric average starting at any time before maturity is derived by solving the PDE, and the option with arithmetic average is evaluated in Monte Carlo simulation using control variate
technique with the help of the above analytic solution.