Jeff Masters on Mann and PCA
May 18, 2012
Bishop Hill in Books, Climate: Mann, Climate: Statistics

Jeff Masters, the meteorologist who blogs at wunderground.com, has written the standard-issue five star review of Mann's Hockey Stick and the Climate Wars.

I thought I'd highlight something Masters wrote about the infamous short-centred principal components analysis used in Mann's paper.

[Mann] takes the reader on a 5-page college-level discussion of the main technique used, Principal Component Analysis (PCA), and shows how his famed "hockey stick" graph came about. It's one of the best descriptions I've seen on how PCA works (though it will be too technical for some.)

Mann, rather hilariously, describes the short-centring technique he applied in MBH98 as "the modern centering convention", and Masters seems to have swallowed this story whole.

Let us defer here to Ian Jolliffe, an expert in principal components analysis. Here he is discussing a talk he had given, which was claimed to endorse short-centring (which he refers to as decentred PCA).

[T]here is a strong implication that I have endorsed ‘decentred PCA’. This is ‘just plain wrong’...

[My talk] certainly does not endorse decentred PCA. Indeed I had not understood what MBH had done until a few months ago. Furthermore, the talk is distinctly cool about anything other than the usual column-centred version of PCA. It gives situations where uncentred or doubly-centred versions might conceivably be of use, but especially for uncentred analyses, these are fairly restricted special cases. It is said that for all these different centrings ‘it’s less clear what we are optimising and how to interpret the results’.

I can’t claim to have read more than a tiny fraction of the vast amount written on the controversy surrounding decentred PCA (life is too short), but from what I’ve seen, this quote is entirely appropriate for that technique. There are an awful lot of red herrings, and a fair amount of bluster, out there in the discussion I’ve seen, but my main concern is that I don’t know how to interpret the results when such a strange centring is used? Does anyone? What are you optimising? A peculiar mixture of means and variances? An argument I’ve seen is that the standard PCA and decentred PCA are simply different ways of describing/decomposing the data, so decentring is OK. But equally, if both are OK, why be perverse and choose the technique whose results are hard to interpret? Of course, given that the data appear to be non-stationary, it’s arguable whether you should be using any type of PCA.

So the world's leading expert on principal components analysis says that data analysed through Mann's "modern-centring convention" are uninterpretable. They are meaningless. Dr Masters says, nevertheless, that Mann has given one of the best explanations of the technique he has ever seen.

Perhaps Dr Masters needs to find himself a friendly statistician.

 

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