  The cos-max method is a little-known method of identifying collinearities. It
is based on the cos-max transformation [4], which makes minimal adjustment to a
set of vectors to create orthogonal components with a one-to-one correspondence
between the original vectors and the components. The aim of the transformation
is that each vector should be close to the orthogonal component with which it
is paired. Vectors involved in a collinearity must be adjusted substantially in
order to create orthogonal components, while other vectors will typically be
adjusted far less. The cos-max method uses the size of adjustments to identify
collinearities. It gives a coherent relationship between collinear sets of
variables and variance inflation factors (VIFs), and identifies collinear sets
using more information than traditional methods. In this paper we describe
these features of the method and examine its performance in examples, comparing
it with alternative methods. In each example the collinearities identified by
the cos-max method only contained variables with high VIFs and contained all
variables with high VIFs. The collinearities identified by other methods did
not have such a close link to VIFs. Also, the collinearities identified by the
cos-max method were as simple or simpler than those given by other methods,
with less overlap between collinearities in the variables that they contained.
