{"id":9,"date":"2004-11-22T19:02:33","date_gmt":"2004-11-22T23:02:33","guid":{"rendered":"\/?p=9"},"modified":"2010-10-06T23:35:40","modified_gmt":"2010-10-07T04:35:40","slug":"pca-details","status":"publish","type":"post","link":"https:\/\/www.realclimate.org\/index.php\/archives\/2004\/11\/pca-details\/","title":{"rendered":"PCA details"},"content":{"rendered":"
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PCA of the 70 North American ITRDB Tree-ring Proxy Series used by Mann et al (1998)<\/b><\/p>\n

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

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\r\n                Rank          Explained Variance       Cumulative Variance\r\n                 1                 0.3818 \t  \t 0.3818\r\n                 2                 0.0976 \t\t 0.4795\r\n                 _______________________________________________\r\n                 3                 0.0491 \t\t 0.5286\r\n                 4                 0.0354  \t\t 0.5640\r\n<\/pre>\n<\/p>\n
First 2 PCs were retained based on application of the standard selection rules (see Figure 1) used by Mann et al (1998).<\/p>\n
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b. Eigenvalue spectrum for PCA analysis Based on Convention of MM  (1400-1971 zero reference period, data un-normalized)<\/p>\n
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\r\n                Rank          Explained Variance       Cumulative Variance\r\n                 1                 0.1946\t  \t 0.1946\r\n                 2                 0.0905\t\t 0.2851\r\n                 3                 0.0783\t\t 0.3634\r\n                 4                 0.0663 \t\t 0.4297\r\n                 5                 0.0549  \t\t 0.4846\r\n                 _______________________________________________\r\n                 6                 0.0373  \t\t 0.5219\r\n<\/pre>\n<\/p>\n
First 5 PCs should be retained in this case employing the standard selection rules (see Figure 1) used by Mann et al (1998). <\/p>\n
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<\/a><\/p>\n
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FIGURE 1<\/b>.
\nComparison 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.<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"
PCA of the 70 North American ITRDB Tree-ring Proxy Series used by Mann et al (1998)<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-9","post","type-post","status-publish","format-standard","category-supplemental-data","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t