Friday, January 25, 2013

The George Costanza Paradox

One day, George Costanza realizes that all of his instincts are wrong. He decides to do the opposite. Here is a rhetorical question offered without further comment: If George has the instinct to do the opposite, what should he do?

Friday, January 4, 2013

Violent Crime in Twentieth Century America

I have previously remarked on the enormous increase in the incarceration rate in the United States. One thing I (crazily) didn't bother to look at in that discussion was the crime rate. And I probably wouldn't have thought about it at all except for an interesting Metafilter post from yesterday about the relation between criminal behavior -- especially violent crime -- and exposure to lead.

The main article linked from Metafilter was this piece by Kevin Drum in Mother Jones reviewing research on the relation between crime in the U.S. and atmospheric lead concentration primarily due to the use of leaded gasoline, which was phased out in the U.S. beginning in the 1970s and finally outright banned in 1996 under the Clean Air Act.

On some level I recognized that lead caused violent crime. (I said as much to my in-laws just a couple of weeks ago.) But at the same time, I had no real sense of the magnitude of the crime wave in the second half of the twentieth century. And that is the reason for this post: to give a simple picture of that crime wave.

Pictured above are graphs of the violent crime rates in the United States as a whole from 1960 to 2011, in the state of Illinois and the District of Columbia over the same period, and in New York City from 1965 to 2011. The U.S. data may be found here, and you can use the search box on that site to call up the other data (and data about other cities or states if you're interested).

What astounded me was the size of the increases in crime rate. From 1960 to its peak in 1991, the violent crime rate in the United States increased 471%. Soak that in for a second or two before going on with your day.

Wednesday, September 19, 2012

Almost Everything Causes Almost Everything Else

In this post, I give a simple argument to the effect that almost every variable (property universal) is a structural cause of almost every other variable (property universal).

First the background idea.  A variable X is a structural cause of another variable Y if there exists a setting for variables other than X and Y and a test pair <xT, xC> for X such that the value Y takes on when we set X to the value xT is not equal to the value Y takes on when we set X to the (different) value xC.  Call the first value yT, and call the second value yC.

Consider a pair of interacting variables.  What I have in mind here are the two variables that form interaction terms in regression equations.  For example, in the equation,
Z = β0 + β1*X + β2*Y + β3*XY + ε,
the XY term represents an interaction between X and Y.  Whenever an interaction occurs, both variables (in this case X and Y) will count as structural causes of the response variable (in this case Z), since there is some setting of each interacting variable for which the other variable matters to the response.

Let me illustrate with a simple case.  Simons et al. (2009) were interested in the effect of religiosity on risky sexual behaviors among college students.  They measured a half dozen variables and tested some structural equation models over those variables.  Among the variables they measured were Age at which the first intercourse experience occurred and Positive_Feelings about that first intercourse experience.  According to their study, Age was a cause of Positive_Feelings for females but not for males.  Assuming for the moment that their models are correct, whether a manipulation of Age at first intercourse would affect Positive_Feelings about that first intercourse experience depends on Sex.  Specifically, delaying one's first intercourse experience would increase the positive feelings a woman has with respect to that experience.  But for men, delaying or hastening would have no effect on positive feelings about the experience.  Hence, Sex and Age are interactive causes of Positive_Feelings.  If you set Sex to male (assuming that makes sense), then manipulating Age makes no difference to Positive_Feelings.  If you set Sex to female, then manipulating Age does make a difference to Positive_Feelings: increasing Age increases Positive_Feelings.

Here is the problem.  Consider the class of things that humans could in principle manipulate, even if humans do not regularly (or ever) actually manipulate them.  Then consider the class of things that humans could in principle observe, even if humans do not regularly (or ever) actually observe them.  Pick a representative member from each class: call them M and O.  Let the variable A represent whether or not some human agent decides to manipulate M to different values corresponding to possible observations of the values of O.  For example, one might decide to open (or close) a window based on whether or not the temperature is over (or under) a specific value.  Now, although O may have no direct, independent power to bring about M, it counts as a cause of M in virtue of its interaction with A.  But O and M are entirely arbitrary.  Hence, for every variable that is in principle manipulable by humans and for every variable that is in principle observable by humans, there is a setting of the other variables (specifically a setting for the variable A) such that setting O to different values would result in M taking on different values.  Therefore, every variable that is in principle observable by humans is a structural cause of every variable that is in principle manipulable by humans.

That's a lot of causation!

I don't know yet how disastrous this result is for theorizing about causation.  What I think it shows (at least) is that causal modelers are not interested in the metaphysical sense of causation expressed by pure structural causation -- that despite the fact that the basic idea of structural causation is what makes causal modeling work.  Instead, causal modelers appear to want something less than all of the structural causes.