Dear all,
I'm studying Multivariate Analysis, in order to understand Factor Analysis,
Principal Component Analysis and Canonical Variate Analysis, and I'm a bit
puzzled by the concept of variate.
In fact, some authors use the term variate in the sense of random variable,
others use the term variate in the sense of linear combination of a set of
random variables... and some relate variates to factors.
I also found some definitions online:
«A random variable with a numerical value that is defined on a given sample
space» (The American Heritage® Dictionary of the English Language: Fourth
Edition, in http://www.bartleby.com/61/88/V0028800.html)
«A variate is a generalization of the concept of a random variable that is
defined without reference to a particular type of probabilistic experiment. It
is defined as the set of all random variables that obey a given probabilistic
law.» (http://mathworld.wolfram.com/Variate.html)
«Canonical variable or variate: A canonical variable, also called a variate, is
a linear combination of a set of original variables in which the within-set
correlation has been controlled (that is, the variance of each variable
accounted for by other variables in the set has been removed). It is a form of
latent variable. There are two canonical variables per canonical correlation
(function). One is the dependent canonical variable, while the one for the
independents may be called the covariate canonical variable. »
(http://www2.chass.ncsu.edu/garson/pa765/canonic.htm#variate)
So... my questions are:
1. What is exactly a variate?
2. What is a canonical variate?
3. What is the relation of variates to factors (or to principal components)?
Could anyone help me out with this? Thanks in advance.
Best regards,
Catarina Delgado
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