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PCA details

Filed under: — mike @ 22 November 2004

PCA of the 70 North American ITRDB Tree-ring Proxy Series used by Mann et al (1998)

a. Eigenvalue spectrum for Mann et al (1998) PCA analysis (1902-1980 zero reference period, data normalized by detrended 1902-1980 standard deviation):

                Rank          Explained Variance       Cumulative Variance
                 1                 0.3818 	  	 0.3818
                 2                 0.0976 		 0.4795
                 _______________________________________________
                 3                 0.0491 		 0.5286
                 4                 0.0354  		 0.5640

First 2 PCs were retained based on application of the standard selection rules (see Figure 1) used by Mann et al (1998).

b. Eigenvalue spectrum for PCA analysis Based on Convention of MM (1400-1971 zero reference period, data un-normalized)

                Rank          Explained Variance       Cumulative Variance
                 1                 0.1946	  	 0.1946
                 2                 0.0905		 0.2851
                 3                 0.0783		 0.3634
                 4                 0.0663 		 0.4297
                 5                 0.0549  		 0.4846
                 _______________________________________________
                 6                 0.0373  		 0.5219

First 5 PCs should be retained in this case employing the standard selection rules (see Figure 1) used by Mann et al (1998).

FIGURE 1.
Comparison of eigenvalue spectrum resulting from a Principal Components Analysis (PCA) of the 70 North American ITRDB data used by Mann et al (1998) back to AD 1400 based on Mann et al (1998) centering/normalization convention (blue circles) and MM centering/normalization convention (red crosses). Shown also is the null distribution based on Monte Carlo simulations with 70 independent red noise series of the same length and same lag-one autocorrelation structure as the actual ITRDB data using the respective centering and normalization conventions (blue curve for MBH98 convention, red curve for MM convention). In the former case, 2 (or perhaps 3) eigenvalues are distinct from the noise eigenvalue continuum. In the latter case, 5 (or perhaps 6) eigenvalues are distinct from the noise eigenvalue continuum.


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