19 thoughts on “Damn, I was off by a factor of 2!

  1. I think an even better calculation would be calculated on a rate of months-since-marriage. The method of dividing by 2 (or 4) is premised on a constant hazard rate of divorce across years of marriage. But….

    According to, (wait for it) DivorceInfo.com*, divorce rates are increasing between date of marriage and four years out. So those people that came in later not only have been exposed for less time, they’ve been exposed for less time at a lower hazard rate. What you would want to do is compare survival probabilities across opposite/same-sex marriages at each year (or month, or whatever).

    But whatever you want, calculating the average yearly rate of divorce by dividing the divorce rate over X years by X is much less meaningful if the hazard is changing over time. And if the distribution of marriage dates (meaning length of marriage prior to end of study given the data collection process) is different from opposite/same-sex couples, then the comparison doesn’t make sense at all.

    * http://www.divorceinfo.com/statistics.htm

    • Jrc:

      Yes, I agree, and I discussed this issue (in general terms) in my first post on the topic. But, if we’re going to take a constant rate as a starting point, at least we should remember to divide by 2.

      Really there’s enough missing information (data on only a few states, different numbers of years in different states, different definitions of same-sex partnerships, lots of selection in who happens to be an early adopter of same-sex marriage) that I think any calculations at this point will be approximate.

      A good little research project, maybe, to lay out a bunch of assumptions and do the inference. Stan awaits!

    • Bravo, you beat me to it. I suspect (with ThM below) that the pent-up demand meant there were a LOT of marriages right at the beginning, meaning the average duration is longer than 1/2 the period. On the other hand, a factor of 2 isn’t that bad really, plenty of hard-core engineering problems where we’d be happy to estimate within a factor of 2 ;-)

  2. I would have assumed that more same-sex marriages occured at the beginning of legalization than after, since there was a lot of accumulated demand, so the doubling might be a bit harsh.

    • On the other hand, the quality of the relationships in that accumulated demand, many of which have already weathered some of the more difficult hazards that present in early stages of marriage, is almost certainly different than the average relationship certified by the state afterwards.

      There will be so much noise in these preliminary data (the first few years) that, because this is a politically charged topic, any analysis will likely have at least as much to do with posturing as it will with an honest pursuit of knowledge, even when there are individual researchers who are better at separating their own feelings on the matter from their analysis.

  3. Well the most important thing if you are making a comparison is to do the calculations the same way on comparable data. Comparing state data to national data is totally wrong, there is a lot of variation across states not to mention some year to year (which impacts that person-year issue). In their report they don’t actually say what the comparison is based on, though, they just say “compared to.” In fact I don’t know how they would do a comparison given that the lasted CDC state level data seems to be 2011.

    I doubt that same sex marriage is evenly distributed over the first few years. There was a lot of pent up demand in the early days. So I think dividing by 2 would probably not be quite right.

    • There is consensus among the commentators that there must have been pent-up demand. But, surprisingly, it appears that the number of marriages in NH and VT are rather evenly distributed over time. See

      http://williamsinstitute.law.ucla.edu/research/census-lgbt-demographics-studies/relationship-data-2014/

      So, for example, in VT, one gets about 9000 person years of exposure if one sums up the exposure contributed by each marriage cohort. This takes into account the different number of marriages in each year. If you assume a uniform distribution of marriage over time, and use the approach of calculating person years from the total number of marriages times half the period of time, then you get about 8,000 person years of exposure.

      Not bad. (And certainly not a factor of 2).

      • My impression is that in the early days people would travel between states to get married, so the pent up demand theory probably holds for the first year or so after the FIRST state, which was what? MA in 2003 I think. So marriage rates were probably pretty high in MA for 2004-2005, and again in say CA 2008-2011 or so. The data you link even shows a strong decline in rate for CT. The period 2010-2014 is probably already starting to be post-transient considering this national travel effect.

        • Are the stats based on reported marriages in each state and then getting divorced or number of reported same sex married couples in each state getting ?

          We used to have same-sex couples coming to Canada to get married (no idea of the numbers) which might distort the time-line for divorces.

      • Interesting!
        There is always danger with vital statistics data of doing too much hand waving i.e. assuming uniform. I’m just kind of puzzled by where “the annual divorce rate for married different-sex couples (2%)” is coming from. ACS has the overall divorce/ever married in Vermont at about 1%

        DIVORCES IN THE LAST YEAR BY SEX BY MARITAL STATUS FOR THE POPULATION 15 YEARS AND OVER
        Universe: Population 15 years and over more information
        2013 American Community Survey 1-Year Estimates
        http://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_13_1YR_B12503&prodType=table

  4. I seem to remember a result from renewal theory that demonstrated that sampling lifetimes via random sampling at time t resulted in an overestimation of average lifetime by a factor of two (say grabbing a bunch of light bulbs and then using the average lifetime of this sample–some wouldn’t burn out until the future, of course). Karlin would be the reference.

  5. The comparison is invalid anyway. The married homosexual population is composed of relatively newly married couples, it must have a very different age profile, it is a non-random sample of those who would get married in the long run, it is composed of male-male and female-female marriages with probably very different divorce rates, it is composed of very different kinds of people in ways other than sexual preference but relevant to divorce likelihood and no doubt many other differences.

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