Hi all,
I read in a text book, that you can examine a variable that is colinear
with others, and giving different ANOVA output and explanatory power
when ordered differently in the model forula, by modelling that
explanatory variable, against the others colinear with it. Then, using
that information to split the vector (explanatory variable) in question,
into two new vectors, one should correspond to the fitted values and one
the residuals of the (I think you could call it nested) model. One
vector therefore should be aligned with the subspacespace defined by the
other variables colinear with it, and the other will be residual, and so
orthogonal to the subspace of the colinear variables. Then by including
these two variables in the origional model - the one that showed the
order dependency, you can see how much explanatory power the othogonal
part of the order dependent variable has, at different orders, and in
principle it shouldn't change, but the vector made from the part
co-aligned with the co-variates, will change as the order changes - it's
explanatory power should decreace in ANOVA is it moves away from being
the first explanatory variable in the model.
Obviously finding the fitted model values and residual required to split
the vector in two is a simple lm() with the right variables. But how
would I create two new vectors from this and append them to my
dataframe? Is there a package or function specially designed with this
sort of task in mind?
Thanks,
Ben Ward.
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