Gay marriage: a tipping point?

Fancy statistical analysis can indeed lead to better understanding.

Jeff Lax and Justin Phillips used the method of multilevel regression and poststratification (“Mister P”; see here and here) to estimate attitudes toward gay rights in the states. They put together a dataset using national opinion polls from 1994 through 2009 and analyzed several different opinion questions on gay rights.

Policy on gay rights in the U.S. is mostly set at the state level, and Lax and Phillips’s main substantive finding is that state policies are strongly responsive to public opinion. However, in some areas, policies are lagging behind opinion somewhat.

A fascinating trend

Here I’ll focus on the coolest thing Lax and Phillips found, which is a graph of state-by-state trends in public support for gay marriage. In the past fifteen years, gay marriage has increased in popularity in all fifty states. No news there, but what was a surprise to me is where the largest changes have occurred. The popularity of gay marriage has increased fastest in the states where gay rights were already relatively popular in the 1990s.

In 1995, support for gay marriage exceeded 30% in only six states: New York, Rhode Island, Connecticut, Massachusetts, California, and Vermont. In these states, support for gay marriage has increased by an average of almost 20 percentage points. In contrast, support has increased by less than 10 percentage points in the six states that in 1995 were most anti-gay-marriage–Utah, Oklahoma, Alabama, Mississippi, Arkansas, and Idaho.

Here’s the picture showing all 50 states:


I was stunned when I saw this picture. I generally expect to see uniform swing, or maybe even some “regression to the mean,” with the lowest values increasing the most and the highest values declining, relative to the average. But that’s not what’s happening at all. What’s going on?

Some possible explanations:

– A “tipping point”: As gay rights become more accepted in a state, more gay people come out of the closet. And once straight people realize how many of their friends and relatives are gay, they’re more likely to be supportive of gay rights. Recall that the average American knows something like 700 people. So if 5% of your friends and acquaintances are gay, that’s 35 people you know–if they come out and let you know they’re gay. Even accounting for variation in social networks–some people know 100 gay people, others may only know 10–there’s the real potential for increased awareness leading to increased acceptance.

Conversely, in states where gay rights are highly unpopular, gay people will be slower to reveal themselves, and thus the knowing-and-accepting process will go slower.

– The role of politics: As gay rights become more popular in “blue states” such as New York, Massachusetts, California, etc., it becomes more in the interest of liberal politicians to push the issue (consider Governor David Paterson’s recent efforts in New York). Conversely, in states where gay marriage is highly unpopular, it’s in the interest of social conservatives to bring the issue to the forefront of public discussion. So the general public is likely to get the liberal spin on gay rights in liberal states and the conservative spin in conservative states. Perhaps this could help explain the divergence.

Where do we go next in studying this?

– We can look at other issues, not just on gay rights, to see where this sort of divergence occurs, and where we see the more expected uniform swing or regression-to-the-mean patterns.

– For the gay rights questions, we can break up the analysis by demographic factors–in particular, religion and age–to see where opinions are changing the fastest.

– To study the “tipping point” model, we could look at survey data on “Do you know any gay people?” and “How many gay people do you know?” over time and by state.

– To study the role of politics, we could gather data on the involvement of state politicians and political groups on gay issues.

I’m sure there are lots of other good ideas we haven’t thought of.

P.S. More here.

Gay marriage and civil unions

Lax and Phillips look at a bunch of issues. Here’s their graph showing the proportions of people in each state who favor gay marriage, and those who favor civil unions. The patterns are pretty consistent, which is no surprise. What is more interesting here is that policies on gay marriage are highly congruent with preferences–pretty much, gay marriage is legal where more than 50% of the people support it, and illegal where the policy has less than 50% support. In contrast, policies for civil unions lag behind attitudes, with several states having a majority in favor of civil unions but with no such policy enacted.


Statistical methods matter

Again, I’d like to emphasize the role of the statistics here. If you knew to look for the pattern in the top graph above, it wouldn’t be too hard to show it using standard statistical methods, for example by pooling the data and regressing individual opinions on a state-level liberal-conservative score interacted with time. But . . . I doubt the pattern would’ve been seen without the fancy multilevel modeling. This and other advanced statistical tools allow us to look at data from more angles without being overwhelmed by sampling variability.

This illustrates a key convergence between statistical modeling and exploratory data analysis: better modeling allows for more exploration. Conversely, the patterns we see in exploration can inform our models. (For example, in an earlier version of their analysis, Lax and Phillips noted that Utah was an outlier. Their model already had a state-level predictor %evangelical Christian, and they changed it to %Mormon or evangelical Christian, which made sense in this context and fixed the problem with the outlier.)

27 thoughts on “Gay marriage: a tipping point?

  1. My wife, who's known Lax for 15-20 years, suggests that maybe gay people, out gay people and the sort of the people who might be more likely to support same-sex marriage have been moving to more supportive states.

  2. I thought of that, but my impression was that, if anything, that particular trend went in the other direction: in the old days, gays would cluster in supportive environments such as New York and San Francisco, whereas nowadays they can live anywhere. But, at the level of states (rather than cities), maybe you're right.

  3. Those look like the state-level shifts that would result from a constant shift for all individuals on a probit scale. Given that there is an underlying individual-level probit model lurking under "Mister P", shouldn't we be just a tad worried about seeing this at the aggregate level? Are these shifts identified by the model/priors or the data?

  4. Ben:

    They estimate each set of years separately, so it's not an artifact of the model.

    I'll take your comment to be suggesting that, if the popularity of an issue is low (as in Alabama, Oklahoma, etc.), there will be fewer people on the cusp of changing their opinions, while if the popularity is closer to 50%, there will be more people who are persuadable.

    That's a fine argument, and I'm not saying it's wrong, but I'd just point out that it contradicts another fine-sounding argument, which is that in a controversial issue such as gay rights, you might expect popularity to grow quickly through a core group and then slow down as it reaches the general population. Such reasoning would suggest an opposite pattern of less change in the states where gay marriage is already popular.

  5. Just a quick question on causality. You note that the gay marriage policy and majority support line up pretty closely. Your comment seems to be written in a way that gently implies something like "where people support gay marriage – it happens" so that the causal relationship runs from popular support to policy. On the other hand, I have heard the claim that in several of the New England states, at least part of the reason people support gay marriage is because they have seen what their state is like once it is legal (no massive breakdown of families, minimal impact on education, slight benefit to "marriage-tourism" industry, etc.) – i.e., that the causal relationship may run the other direction. At a crude level – that makes Iowa (where the policy decision is quite recent, and general public support is relatively low for a gay marriage state) an interesting case study. Is there any additional data to weigh in on the causal direction question?

  6. I would be interested to see the % of people in these states under the age of 30 (or conversely the % of people over 55). Or better yet, the percentage of outbound migration of the under 30 crowd.

  7. I'd be curious to know if the shifts in the first graph are partially explained by changing demographics. For example, here in New Hampshire a popular belief is that the "blue" trend of the last several years is due largely to people moving north from Massachusetts. Not sure how much of the change (on gay marriage or more generally) I'd attribute to that, but it seems plausible that there might a meaningful effect there.

  8. Since New Hampshire is one of the states in the top (7-9 ish) for polling in favor of gay marriage in all three years (93, 03, 09) and its rank didn't really go down or up, then I don't think changing demographics had much of an effect.

  9. Thanks for all the feedback:

    Ceolaf: That probably plays some role. I'm sure some such movement occurs, but I doubt it's a new trend or a large part of the explanation for opinion change.

    Ben: The model does do some of the work, but, as Andy said, in the time graphs we are using separate models for the 3 periods (in the paper's analysis, we use all the data partially pooled and taking weights from the later years). We do see states moving past each other so it's not just an aggregate shift. Some of the change is do to changes in demographic correlations and some of it to changes in the state-level intercepts beyond that. We're going to do further work to parse this out.

    Don: I bet you're right that some change occurs due to "reverse" causality, but I do think the stronger causal arrow runs from opinion to policy, tempered by the forces we study in the paper (salience, interest groups, etc.). We have a section on this in the paper (p28-9) where we present evidence against "reverse" causality (the state level intercepts which correct for demographic correlations should, under reverse causality, correlate with having the pro-gay policy and do not; replications of findings using only early poll data, etc.).

    Aaron: We too are very curious about subgroup trends but haven't gotten that far yet in our analysis. So far, we've been focusing more on the issues of policy responsiveness and congruence.

    Jared: For now, we're using the same census weights for all periods, so we cannot answer that question yet — we will update our findings using census weights that capture such demographic trends.

    For other versions of the trends graph, here's one that shows the states ordered
    by change and here is one by final.

  10. I think at least part of what you are seeing is a consequence of plotting on a percent scale, which undoubtedly seems natural, but is nevertheless unlikely to be the best metric to bring out the underlying dynamics.

    A crude but not ridiculous first approximation model to changes over time would just be a logistic trend that is necessarily asymptotic to (a value near) 0 and (a value near) 100 and steepest near 50%, or at least somewhere in the middle.

    There presumably are small liberal areas within states where the shift is 98 to 99% and small conservative areas where the shift is 1 to 2% — both a big deal in terms of halving doubters or doubling believers. But only around 50% are large shifts on the percent scale possible at all (unless there are reversals of opinion).

    So, I suggest plotting on logit or (if anyone prefers) probit scale. The axis labels could and should still be percents. Among many other people, Tukey was making this kind of point in the 1950s.

    Oddly enough, most statistically minded people seem to think, since Berkson, of logit as the link function that you apply with binary data. Many seem to have forgotten that this grew out of thinking of logistic trends in continuous variables over time in biology, demography, chemistry, etc. going back hundreds of years.

    That aside, this thought seems totally consistent with tipping point ideas, although I think they have been a little oversold and only catch part of a process that is likely to be susceptible to more exact analysis.

  11. Nick: We may have to wait until we have future data far over the 50% mark to see how trends play out for support levels in that region, but so far the trends are consistent with both a tipping point story and a logistic trend story and no doubt others.

    Some correlations of possible interest from simple linear models of the trends:

    A. Change from 1994 to 2008 does correlate to the 1994 level. The marginal "effect" of 1 point of state support in 1994 is an extra 1.88 points of support in 2008.

    B. That growth is roughly split between the two time periods even though the second time period is half as long.

    C. Even holding constant 1994 levels, higher levels of period 1 change correlate to higher period 2 change.

  12. I hate belabor the point, and the problem is clearly HRC's information, but Colorado's designated beneficiary agreements provide the identical rights that Hawaii's reciprocal beneficiary agreements provide, and was indeed crafted to mirror Hawaii's status. The only functional distinction between the two is that Hawaii's law requires individuals entering into the agreement to not be eligible to to enter into marriage.

    Forgive me for continuing to force the issue, and you can be sure I will be sending an e-mail to HRC, but I've got to stand up for my home state, and it's slow but steady push for equality.

  13. One factor that hasn't been looked at is the % of parents who are for and against gay marriage. I suspect this plays a factor, though I cannot prove it. But those Republicans always turn a debate on gay marriage into "what do I tell my children" and the word "marriage" and "family" for that matter make you think of children.. anyway its just a thought.

    Also a counter-thought: Yes, let's think of the children. What do you tell them… if they are gay? No, when you grow up you can't be a scout leader or get married etc. etc.

  14. Naturally I agree that there is as yet very little evidence on what will happen beyond 50%. Some might speculate that in some states the asymptote would be way short of 100%.

    But my main point is not to speculate about a logistic trend but to say that part of what you are seeing is just how percents behave, on almost any model, static as well as dynamic. So you need not wait for anything to try plotting on a logit scale to see what else such a graph reveals.

    In any decent statistical software that's at most a few lines. I gave an extended Stata example, with historical references on logits, in

    Cox, N.J. 2008.
    Stata tip 59: Plotting on any transformed scale
    The Stata Journal 8(1): 142-145.

  15. I have done some stats on sexual issues before, in grad school (for math). I suggest you control for population density as an explanatory factor. It turns out to be the biggest factor by far in determining underage teenage (13-16) pregnancy in Texas counties, for example; rising as we approach the population density (persons per square mile) of Austin and then leveling off. It beat religiosity, parental income, school quality, parental education levels, county average income, and academic achievement of the underage mother, all by a mile.

    In that case, I speculated that underage teen pregnancy was strongly controlled by simple opportunity. Meaning, a relatively constant percentage of underage girls could be lured into intercourse with the right guy, but with low population density, the right guy doesn't show up. (For 12-16 year olds, btw, the average age of the father is 22, and this study excludes incest and rape and focuses only on pregnancy due to voluntary intercourse with non-relatives living outside the child's home. Much of teen sex is predatory, statutory rape.)

    Anyway, I suspect population density can play a similar role here; the more people there are around the more likely one is to encounter homosexuals and public displays of homosexual affection or attitude.

    Some teen girls can be prey for just the right predator; and a saturation of choice increases the chances she will meet just the right jerk.

    But higher population density also broadens the range of exposure to people and attitudes, and makes it more likely somebody is working with (and friends with) open homosexuals, or to be exposed to situations involving them. Social attitudes are based largely on what one is "used to," and although population density is an obscure statistic, it is actually a potent descriptor of social phenomenon.

  16. Aaron: thanks for the information about Colorado — we'll look into that rather than rely only on HRC when we move further on this.

    MadProfessah: A graph of opinion on anti-discrimination laws and policy is here, but it does not yet show years of adoption.

    Nick: Thanks. We see your point, but these percents do not come from a single regression model. Rather, they come from predictions for each demographic-geographic type that are then weighted using census data. They need not have this pattern at all and do not for other issues I think. Nor, I think, would change have to occur in that pattern. There is no reason that opinion would have to shift the most at the state level near the 50% mark as in a logistic regression curve.

    Tony: I bet you're right that population density could serve as an addition state level predictor in our estimation process — though we do find that results are robust to sparser models therefor. See this.

  17. Neil: I was considering the change within the state over the period, not the change in its rank relative to other states (although your point is a good one, and unsurprising to me given NH's libertarian tendencies). Referring to the reordered graphs Jeff posted the change is one of the larger ones.

    Anyhow, my example was probably not the best but rather the one with which I was most familiar!

  18. Jeff- HRC is definitely wrong about Colorado. See my posts on the Colorado law here:
    Also, you've got a problem with the adoption graph. Some states are just wrong (eg, PA). For states that have some judges that grant second parent adoptions but no appellate court decision on the subject (or clear statute), you mark some as positive and others as negative. I can't figure out why.

  19. Nancy: Thank you for the feedback. We fully respect that you disagree about how some have coded state policy, but clearly the HRC has reasons for coding Colorado as not having full civil unions. Drawing the line for dichotomous policies can be difficult, and we wanted to avoid looking like we were cherry-picking. So we relied on that single source wherever possible. Our general conclusions in the paper will not rely on the coding on one particular data point.

    We coded 2nd parent adoption in states based on whether such adoptions were allowed in all jurisdictions within the state, again based on HRC.….

    We regret that we cannot include all these details in the chart, but please do see our paper for more information. And we do appreciate the feedback, which will be helpful as we move forward with this research program.
    or directly:

  20. I think our experience in Canada might support "reverse causality." Gay marriage became legal here in 2003, through numerous court decisions. There followed about a year of mass hysteria and hand-wringing, after which, of course, no damage whatever occurred to marriage, children, or family. Now the issue has completely fallen off the radar, as same sex couples continue to get happily married.

    thanks for a great study and interesting discussion.


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