I am a mathematically oriented person, and I am a little disappointed in one thing. Multicollinearity in regression is swept under the rug in the reading, which claims it is a problem that there is no good way to deal with theoretically, but this is not true. It is well dealt with in theory; it’s just that the math involved is too advanced for what CFA candidates are expected to know:
If the reading isn’t going to consider the error of the coefficients jointly as a positive-definite matrix and mention the Stein effect, etc., it should have one of those “beyond the scope of this reading” disclaimers rather than claiming, in effect, that there is no way to handle it.
…because multicollinearity is only a problem if that error matrix is nearly singular—and in that case, we can simply remove one of the independent variables as it says in the reading. (The reading doesn’t say what to do about ill-conditioned coefficients, and that’s another problem yet.)
That’s what I like about the CFA in general—and I think it’s comprehensive enough—but from the point of view of factual accuracy, I think it’s almost a little misleading (unintentionally of course) the way the reading shuts the door on this particular topic.
If you want to get into finite details of every topic, no one would ever pass the CFA exam. It’s a broad based exam, and goes into plenty of detail as is. What do think the pass rate would be if they started pulling in esoteric mathematical theory? I understand the point you’re making, but you’ve got to put it into perspective relative to goal of the program. They aren’t trying to mint PhD’s in mathematics.
Justin, what is theoretically ok in math may not be theoretically ok in economics - point being if you remove one of the offending independent variables, it is ok as far as math theory goes - but not ok as far as econ goes (why - because there is NO fundamental logic to randomly choose one of two or more highly correlated independent variables).
I agree with rest of the people, CFA is EXTREMELY broad on topical coverage and fairly shallow in any given topic
I’m only talking about removing it per the CFA reading if it is so highly correlated that it can effectively be determined by a linear combination of some of the remaining independent variables—in which case it offers no additional explanatory value, because said linear combination could be used equally well as a proxy for the one left out. In fact the regression fails—becomes indeterminate—if any independent variable is 100% explained as a linear combination of the remaining ones.