Wednesday, August 25, 2010

SILVER 2.0

Back in June I introduced SILVER as a metric to measure how partisan a member of congress is compared to the voting tendencies of their district or state. I did this by combining PVI and DW-Nominate and I scaled it (or attempted to) to the same -1 to 1 scale that DW-Nominate uses. Since that time I’ve been forced to give the issue some more thought because of a baseball stat called NERD.

Believe it or not when I first developed the SILVER stat I was not aware that Crisitunity from the excellent Swing State Project blog had already developed a similar thing. Crisitunity computed his version in a different way, ranking the PVI and DW-Nominate scores of all members of the house on a 1 to 435 scale and then using the difference between the two rankings as his score. This might be a better method than the one I employed in my first version, but in the end we’re trying to measure two different things.

The system that Crisitunity developed measures house members against each other without regard to party affiliation, the point is to measure the overall liberalness of a legislator in the context of their district against the house as a whole. SILVER is meant to measure a legislator against his or her own party, not the entire legislative body.

In the first version of SILVER I compared the PVI and DW-nominate scores for each legislator to the mean of their parties score. So for instance Jim Oberstar has a DW-Nominate score of -0.54 and the Democratic mean is -0.35, so Jim Oberstar is 0.19 points more liberal than the average Democratic representative. I than did the same for PVI, so Oberstar’s 8th district PVI is D+3 and Democratic average is D+9, so Oberstar’s district is 6 points more Republican than the average Democratic district.

Jim Oberstar would get credit for both being more liberal than average and for being from a district that is less liberal than average. Keith Ellison, on the other hand, gets credit for being more liberal than average, but gets a deduction for representing a district that is more Democratic than average.

It’s at this point that the first version of SILVER went off the tracks. In attempting to combine those two numbers and put the result on a -1 to 1 scale I used completely subjective values. What this means is that the weights for the two variables were uneven. I adjusted them to arrive at a result that was in the right scale and that looked right. This was not the correct way to do it. I’ll admit that I was a little uneasy about the method at first but could not think of a better way at the time so I just went with it.

So how does NERD fit in? NERD is a stat developed by Carson Cistulli at Fangraphs to measure the entertainment value of a pitching matchup for the baseball nerd. It’s not really that important what comprises the stat as much as the methodology that Carson used to compute it. Like my initial version of SILVER, NERD compares the component stats to league average; the difference is that NERD uses the correct formula to do this, a formula that scales the result at the same time that it compares it to the mean, NERD uses z-scores.

It was in reading about the methodology behind NERD that I realized how I had screwed up SILVER; z-score was the correct way to calculate what I was attempting to calculate. For those unfamiliar with the term, a z-score is a comparison with the mean divided by the standard deviation of the data set. In other words, z-score is a measure of how many standard deviations an individual is from the mean of the population. Using the standard deviation as the denominator instead of some random constant that looks correct to me ensures that the two values being added together, PVI and DW-Nominate, are given equal weight.

So here is the updated SILVER methodology; calculate the z-score of each legislator’s PVI and DW-Nominate scores within their party and add them together. The result is a less subjective relationship between PVI and DW-Nominate.

Here is an example using Leonard Boswell (D-IA):



Boswell has a DW-Nominate z-score of -.58, meaning that Boswell is .58 standard deviations less liberal than the average Democrat. The .58 PVI z-score means that the district Boswell represents is .58 standard deviation’s more conservative than the average democratic district. Adding these two scores together gives us a SILVER score of 0. Leonard Boswell would be considered an average democrat considering his districts partisan tilt.

Here is another example using Dennis Kucinich (D-OH):



What you can see here is that Dennis Kucinich is 2.45 standard deviations more liberal than the average democrat (meaning he’s really, really liberal, but we already knew that) and he represents a district that is right about average in terms of PVI, this results in a SILVER score of 2.49, the highest of any democrat.

Another difference between this version and the last is that a positive score is not an indicator of being more liberal and a negative score is not an indicator of being more conservative. A democrat with a positive score is more liberal than average and a republican with a positive score is more conservative than average. This is in keeping with the purpose of the metric, which is to measure a legislator’s partisan tendencies, not necessarily to measure their liberalness in and of itself.

The other, less important, change I’ve made is to drop any notion that SILVER is an acronym for something. In the initial version I tried to create an acronym out of SILVER that related to the metric, in the end it was nothing more than a bunch of gibberish, so no more of that. Now we can move on to the updated rankings.

First Minnesota’s delegation:



Jim Oberstar ranks 6th among house Democrats and Al Franken ranks 6th among Senate Democrats. Colin Peterson ranks just slightly below average, 0 is an average score, and the rest of Minnesota’s legislators are above average except for one, Amy Klobuchar.

You can also see how in the new version the positive to negative scores don't fall along a liberal - conservative spectrum, so you can directly compare legislator's of different parties against each other more readily.

These rankings didn’t change significantly compared to the previous iteration, except Keith Ellison comes out looking marginally better and Tim Walz and Colin Peterson marginally worse, meaning that in the last version I was over-weighting the PVI score.

I’ll have the SILVER rankings for the entire House and Senate up soon.

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