Two of the three reconstructions (WL03 REG (short) and WL02) start with the calculation of varimax principal components. ❋ Unknown (2007)
Both carry out principal components analyses of tree ring networks – MBH using Mannian principal components; Wilson et al 2007 using rotated varimax PCs. ❋ Unknown (2007)
A rotated (varimax) PC analysis (Richman 1986) using the remaining 22 chronologies identified five principal components (PCs) with an eigenvalue greater than unity. ❋ Unknown (2007)
If (say) 5 PCs are selected (truncation) – 5 is the number chosen in Wilson et al without saying why, factor analysis (varimax rotation) attempts to find an orthogonal rotation within the subspace that loads the weights as much as possible on groups. ❋ Unknown (2007)
My point is that the authors of these studies forget that the PCs can be expressed in terms of the original proxies; and that weights assigned to the original series are independent of the varimax rotation – that says nothing about whether the weights are concentrted or not. ❋ Unknown (2007)
In a second step, the goal of varimax rotation is to identify meaningful patterns- in some subjective sense- , which are then use for the regression. ❋ Unknown (2007)
PS I nearly always use oblimin rotations since varimax can assume orthogonality when humans are rarely so ; ❋ Unknown (2007)
Denote the rotation operator by , dim(R) = (k,k), with the rotated varimax PCs obtained as per equation (2) as follows: ❋ Unknown (2007)
The “rotated varimax PC analysis” appears to be the same procedure as factor analysis . ❋ Unknown (2007)
Houghton and Toure carried out a rotated varimax on their PCs. ❋ Unknown (2007)
In this case, “rotated varimax PCs” boil down to being a high-falutin way of simply making 5 “regional” averages. ❋ Unknown (2007)
I also think that in general the varimax rotation- and indeed any linear rotation- will not affect the final reconstruction, but in my opinion the critical step is the truncation. ❋ Unknown (2007)
Some readers will probably wonder what the difference is between the “rotated varimax PCs” and correlation/covariance PCs. ❋ Unknown (2007)
The inverse regression of temperature on the rotated varimax PCs is denoted by equation 3 as follows: ❋ Unknown (2007)
The studies all follow a similar strategy as Wilson et al 2007 – principal components analysis; truncation to eigenvalues ' title=' ' class='latex' / 1, varimax rotation and regression. ❋ Unknown (2007)
Their reconstruction follows the typical of the Luckman school: principal components analysis of the tree ring network; truncation to 3 or so PCs with eigenvalues greater than 1; varimax rotation; inverse multiple regression of temperature against the rotated PCs. ❋ Unknown (2007)
The resulting varimax-rotated vectors would look different and one may be lead to apply a different truncation, depending on the subjective judgement whether a certain vector is physically reasonable or not. ❋ Unknown (2007)
Posted Apr 3, 2007 at 4:51 PM | Permalink | Reply bernie, my point here is that the rotation matrix R in the varimax rotation appears to be cancelled out in the regression phase – so whatever the original motive for the varimax rotation, the weights that are finally assigned to the individual sites appear to be the same, whether or not the varimax rotation is done prior to the linear regression. ❋ Unknown (2007)
I think that the point here is interesting intellectually and may illustrate something interesting about the combination of varimax rotated PCs and regression – which is why I asked for a statistical reference for this combination of techniques. ❋ Unknown (2007)
