varimax

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.

Regression and Varimax Rotation « Climate Audit 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.

Regression and Varimax Rotation « Climate Audit 2007

A rotated (varimax) PC analysis (Richman 1986) using the remaining 22 chronologies identified five principal components (PCs) with an eigenvalue greater than unity.

Wilson et al 2007 « Climate Audit 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.

Regression and Varimax Rotation « Climate Audit 2007

Houghton and Toure carried out a rotated varimax on their PCs.

Varimax Rotation and the AMM « Climate Audit 2007

The inverse regression of temperature on the rotated varimax PCs is denoted by equation 3 as follows:

Regression and Varimax Rotation « Climate Audit 2007

Denote the rotation operator by , dim(R) = (k,k), with the rotated varimax PCs obtained as per equation (2) as follows:

Regression and Varimax Rotation « Climate Audit 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.

North American Upper Treeline #3 « Climate Audit 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.

Regression and Varimax Rotation « Climate Audit 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.

Regression and Varimax Rotation « Climate Audit 2007