Suppose there are n prinicipal components associated with an n-variable
multivariate data set ( ie where n>1). It's been
quoted that:-
Statement 1
If any principle component explains greater than 1/n *100% of the variance
then that principal component by itself accounts for a "significant amount
of the variance" in the data.
Statement 2
The "justification" is that if the data consists entirely of white noise
then each principal component would be expected to explain only 1/n * 100%
of the variance. If more than that is explained by any principal component
it therefore suggests that that prinicipal component is "explaining some
structure" in the data.
Clearly this is related to the problem of deciding what criterion
to use in discarding "insignificant" prinicipal components.
The question is: how accurate are Statements 1 and 2?
Many thanks,
Eric Grist
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|