Mathematically speaking, last weekend was wonderful. I saw the simple solution for simultaneously isolating and identifying linear dependence in a matrix. And I posted the simple solution last Monday.
I am, as you might expect, disappointed that I didn’t see the simple solution immediately… but there you have it: I’m a human being. I gladly give myself credit for seeing it at all.
I am, on the other hand, extremely optimistic that this simple solution can be used to isolate and identify multicollinearity… defined specifically as “near linear dependence”. (Many people seem to treat multicollinearity as though it were defined by its symptoms. That would be fine… if those symptoms were always caused by multicollinearity, but they’re not.)
In addition, I have decided that dealing with multicollinearity has two phases: isolation/identification, and assessing the severity. What do we have? And how serious is it?
So, I expect that the simple solution for finding a linear dependence will be equally effective for finding – but not for assessing – multicollinearity.
I am hoping that “variance inflation factors” combined with this simple solution can be used to determine whether multicollinearity is serious or not.
We’ll know more after we’ve seen a few examples. (I’ll know more after I’ve tried it on a few examples.)
Oh, I found another example out on the Internet. The Cobb-Douglas production function first appeared in 1928 — as a fit to data. That data is generally considered to be multicollinear — and I found it, too.
One of the ways in which I rewarded myself for seeing that simple solution last weekend – in time to publish it Monday evening, to boot – was to start watching the TV series “Babylon 5” again.
I think it is a great show… that is, the first four seasons. The less said about season five, the better. (Okay. Season five hinged on the commander of Babylon 5 being too stupid to see things that were happening. That wouldn’t have been a big deal, except that earlier seasons portrayed him as not merely alert, but actually brilliant.)
And no, I’m not getting any algebra done in the evenings.
Last week’s happenings post has gotten a fair number of hits. It occurs to me that, at the very least, I should add the LOGO code for the curves I displayed. (Done, in a comment to that post.) I’ve also seen some rather unintuitive Mathematica® code for the Koch curve. Yuck! That’s another reason to put out the LOGO code.
Regarding the other subject last week… the Mathematica notebooks for the dynamics package repeatedly referenced Strogatz’ “Nonlinear Dynamics and Chaos”… so I checked it out on Amazon and saw that it had a five star rating with 40 reviews.
That’s pretty impressive, so I bought it.
I’ve already read through it, and – what else? – I’m looking forward to working through it.
Okay. My alter ego the kid has already spent an hour on dynamics this morning; my other alter ego the grad student is going to put some time in on abstract algebra. Then I plan to continue looking at multicollinearity in the Hald data.