ABSTRACT
This chapter examines several situations in which the multivariate relationships among the variables give the analysis special properties or introduce particular complications. It treats four such situations. The first special relationship occurs when the predictor variables are not a linearly independent set, a state known as multicollinearity. Multicollinearity involves multiple vectors. Near multicollinearity, probably the greatest bane of multivariate analysis, is the second topic discussed here. The final two sections describe configurations that are, in a sense, the opposite of multicollinearity, where certain variables are orthogonal. A researcher almost never chooses a linearly dependent set of variables intentionally, but can do so when unaware of the constraints. There are substantial advantages to working with orthogonal predictors such as computational and statistical. In multiple regression, a variable (suppressor variable) that is of little use as a predictor, by itself becomes important when it is combined with another predictor.
