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 comments in our response here: :
I looked at the reference you made to my presentation at http://www.uoguelph.ca/~rmckitri/research/MM-W05-background.pdf *after* I drafted my contribution and I can see that you actually read the presentation. You have accurately reflected my views there, but I
guess it’s better to have it ‘from the horse’s mouth’.
Here is Jolliffe’s comment in full:
Apologies if this is not the correct place to make these comments. I am a complete newcomer to this largely anonymous mode of communication. I’d be grateful if my comments could be displayed wherever it is appropriate for them to appear.
It has recently come to my notice that on the following website, http://tamino.wordpress.com/2008/03/06/pca-part-4-non-centered-hockey-sticks/ .. , my views have been misrepresented, and I would therefore like to correct any wrong impression that has been given.
An apology from the person who wrote the page would be nice.
In reacting to Wegman’s criticism of ‘decentred’ PCA, the author says that Wegman is ‘just plain wrong’ and goes on to say ‘You shouldn’t just take my word for it, but you *should* take the word of Ian Jolliffe, one of the world’s foremost experts on PCA, author of a seminal book on the subject. He takes an interesting look at the centering issue in this presentation.’ It is flattering to be recognised as a world expert, and I’d like to think that the final sentence is true, though only ‘toy’ examples were given. However there is a strong implication that I have endorsed ‘decentred PCA’. This is ‘just plain wrong’.
The link to the presentation fails, as I changed my affiliation 18 months ago, and the website where the talk lived was closed down. The talk, although no longer very recent – it was given at 9IMSC in 2004 – is still accessible as talk 6 at http://www.secamlocal.ex.ac.uk/people/staff/itj201/RecentTalks.html
It 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.
I am by no means a climate change denier. My strong impressive is that the evidence rests on much much more than the hockey stick. It therefore seems crazy that the MBH hockey stick has been given such prominence and that a group of influential climate scientists have doggedly defended a piece of dubious statistics. Misrepresenting the views of an independent scientist does little for their case either. It gives ammunition to those who wish to discredit climate change research more generally. It is possible that there are good reasons for decentred PCA to be the technique of choice for some types of analyses and that it has some virtues that I have so far failed to grasp, but I remain sceptical.
As an editorial comment, the validity of Mannian PCA is only one layer of the various issues.
For example, Wahl and Ammann approach the salvaging of Mann overboard from a slightly different perspective than Tamino. Their approach was to argue that Mannian PCA was vindicated by the fact that it yielded a high RE statistic and thus, regardless of how the reconstruction was obtained, it was therefore “validated”. I don’t see how this particular approach circumvents Wegman’s: “Method Wrong + Answer ‘Right’ = Incorrect Science”, but that’s a different argument and issue. Also if you read the fine print of Wahl and Ammann, the RE of reconstructions with centered PCA are much lower than the RE using incorrect Mannian PCA, but, again, that is an issue for another day.
It would be nice if Jolliffe’s intervention were sufficient to end the conceit that Mann used an “alternate” centering convention and to finally take this issue off the table.