Category Archives: Multivariate

Ian Jolliffe Comments at Tamino

Ian Jolliffe, a noted principal components authority, has posted a comment at Tamino’s, which repudiates Tamino’s (and Mann’s) citation of Jolliffe as a supposed authority for Mannian PCA. He wrote to me separately, notifying me of the posting and authorizing me to cross-post his comment and stating that we had correctly understood and described his […]

Conflict and Confidence: MBH99

Here’s a first attempt at applying the techniques of Brown and Sundberg 1987 to MBH99. The results shown here are very experimental, as I’m learning the techniques, but the results appear very intriguing and to hold some possibility for linking temperature reconstructions to known statistical methodologies – something that seems more scientifically useful than “PR […]

Squared Weights in MBH98

A couple of weeks ago, I said that I would document (at least for Jean S and UC) an observation about the use of squared weights in MBH98. I realize that most readers won’t be fascinated with this particular exposition, but indulge us a little since this sort of entry is actually a very useful […]

PC Weights on a Square Region

A few days ago, I showed some plots showing distribution of weights arising from principal components carried out on data from a region arranged as a line segment (think Chile). Today I’ve done a similar analysis for a square shaped region again assuming spatial autocorrelation governed by distance. In this case, I made a regular […]

Toeplitz Matrices and the Stahle Tree Ring Network

One of the most ridiculous aspects and most misleading aspects of MBH (and efforts to rehabilitate it) is the assumption that principal components applied to geographically heterogeneous networks necessarily yield time series of climatic interest. Preisendorfer (and others) state explicitly that principal components should be used as an exploratory method – and disavowed any notion […]

More on "Naturally Orthogonal"

I realize that not all CA readers are interested in multivariate methods and that dendroclimatologists want to “forget the math”, but I find it interesting to try to relate dendro and paleoclimate recipes to known statistical methodologies that you can read about in texts. I commented the other day on the form of Principal Components […]

Nature's Style: "Naturally Orthogonal"?

Wilson and Luckman 2003 observe: The first PCs from the RW and MXD PCA are naturally orthogonal (r = —0.006) over the 1900—1991 period suggesting the in’?fluence of different forcing mechanisms upon these parameters. They move on without pausing here, but this point should not be left without a commentary. The issue here is one […]

Regression and Varimax Rotation

I’ve been reading through some articles on altitudinal reconstructions by Rob Wilson and other Luckman students. The studies all follow a similar strategy as Wilson et al 2007 – principal components analysis; truncation to eigenvalues 1, varimax rotation and regression. It’s pretty obvious that these operations are all linear and if the linear algebra were […]

Varimax Rotation and the AMM

While I was reading about rotated varimax PCA in connection with Rob Wilson’s article, I came across R.W. Houghton and Y.M. Tourre, 1992, Characteristics of Low-Frequency Sea Surface Temperature Fluctuations in the Tropical Atlantic, Journal of Climate Volume 5, Issue 7 (July 1992) pp. 765—772 url. They observed that a PC analysis applied to Atlantic […]

Wilson et al 2007

Rob Wilson has referred us to Wilson et al 2007. In addition to being an example of site selection, Wilson et al 2007 uses a type of principal components on a tree ring network – something that should be of interest to many CA readers – and an interesting illustration of non-Mannian statistical methods within […]

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