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We tested whether shape across the seven independent sub-elements covaried similarly by comparing the variance-covariance matrices using Mantel's test of matrix correlation in MANTEL version 1.15 [27] with 10,000 random row permutations of one of the matrices.
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MRM is derived from partial Mantel tests of matrix correlations, in which predictor matrices (in this case, landscape variables, see paragraph below and Appendix A) are used to explain variation in a response matrix (genetic distance).
The top matrix correlation is shown in Figure 1.
For this purpose, we employ the matrix correlation distance proposed in our previous works [ 20] which is a distance measure for matrix data.
Peramelia shows an intermediate pattern between Dasyuromorphia and Diprotodontia, with marginally significant correlations in matrix correlation analysis when size is included, but not when it is removed.
Matrix correlations were calculated in GenAlex v6.5 [ 117] and XLStat (v2013, Addinsoft) with 1000 random permutations.
Small but significant matrix correlations were also found in a study of macaque skulls [20].
Variance/covariance matrix correlations are consistently higher that correlation matrix comparisons, except in comparisons between the syndactylous digits.
A correlation matrix revealed correlations in 12 out of 15 pairs, three factors were extracted that accounted for over 80% of the variance, communality was 0.79 0.89, sampling adequacy was 78%, and factor structure simplicity was satisfactory.
Models were constructed with the SAS GENMOD procedure, which uses generalized estimating equations, with an exchangeable working correlation matrix to account for correlation in the data.
The MTMM correlation matrix described in detail the inter-scale correlation patterns within either instrument, and more importantly across different instruments.
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