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This graph shows the estimate that Kenny Shirley and I have of support for the death penalty by sex and race in the U.S. since 1955:

We also found that capital punishment used to be more popular in the Northeast than in the South, but now it’s the other way around.

Here’s the abstract to our paper:

One of the longest running questions that has been regularly included in Gallup’s national public opinion poll is “Do you favor or oppose the death penalty for persons convicted of murder?” Because the death penalty is governed by state laws rather than federal laws, it is of special interest to know how public opinion varies by state, and how it has changed over time within each state. In this paper we combine dozens of national polls taken over a fifty-year span and fit a Bayesian multilevel logistic regression model to individual response data to estimate changes in state-level public opinion over time. Such a long span of polls has not been analyzed this way before, partly because doing so requires a suitable model for the overall national time trend of death penalty public opinion, which is challenging to formulate.

In the context of the death penalty example, we develop here a suite of methods, largely graphical, for manipulating and understanding a fitted hierarchical model. In the death penalty problem we resolve the issue of modeling the national trend of support by using redundant parametrization and a structured prior distribution for the yearly effects. The resulting model can be fit using standard MCMC techniques, but the output of the model-fitting process is difficult to analyze immediately, as it is for many large hierarchical Bayesian models. The fitted model analyses we discuss in this paper include computing finite population contrasts and average predictive comparisons, and plotting posterior intervals of within-group standard deviations to compare different sources of variation within the data. We discuss inferences about the changing nature of death penalty support across time, states, and demographic groups that could not be made without using a variety of advanced tools for model understanding.

The analysis is an example of Mr. T (multilevel regression and poststratification over time).

P.S. To clarify the graph above: The parallelness of the lines (that they all jump up and down together) arises from our additive model. The true trends could not possibly be so clean. We did, however, look at residuals over time by sex and ethnicity and did not see any big patterns, so I think the picture above is basically accurate.

P.P.S. The estimates that we have that are readily available right now are for a slightly more detailed set of interactions than state*year. We computed interval estimates for the probability of support for an individual in each of the (51, 54, 2, 2, 5, 4) (states, years, race, sex, degree, age) cells. From this, you could post-stratify (if you have census data that gives you cell probabilities for these variables) to get state*year effects.

Here is the (51, 54, 2, 2, 5, 4) array (it’s about 8 MB as an .RData object). This other file is just a list of the variable names in the array. Both are as described on page 50 of the paper.


  1. Pete says:

    Thanks for the 50 page worked example of a multilevel Bayesian model!. The paper talks about suplemental materials; will you be making them available too?



  2. Nameless says:

    It seems to me that you would find that support of death penalty (from the plot above) correlates quite strongly with murder rates within each race.

    Which raises an interesting question, is there a causal relationship here, and which way does it run?

    • The murder rate within African-Americans is considerably higher than in the general population. But the approval of the DP seems to be lowest in that group. So the correlation is negative.

      Why? I don’t know.

      • krippendorf says:

        One guess: immediacy. African American men are roughly seven times more likely to have been incarcerated at least once by age 30 than white men — 22% vs. 3%. (See, e.g., Western & Pettit’s life table analyses, in “Punishment and Inequality in America” [table 1.3, p. 29].) And, racial homophily & residential segregation being what they are, African American women are much more likely than white women to have a male friend or family member who has been incarcerated.

        African Americans are also much less likely than whites to trust the justice system. I’d guess that this plays out, in part, in the belief that the death penalty is occasionally (often?) applied to innocent people.

  3. EmilyKennedy says:

    This is really interesting within the context of the rise of Three Strikes laws in the ’90’s. And obviously all the research and scholarly work on the prison industrial complex in the U.S.

  4. Dan Simpson says:

    This is quite cool.

    Did you consider using a Besag-type CAR model over the states to model state-state interactions? To me (with very little thought), it seems that nearby states should have similar opinions (especially when you remove the effects of the covariates considered in the model), so a structured spatial effect would be appropriate. There’s a little of this in the ‘region’ designation, but is it enough?

  5. Gregory Petrow says:

    Nice data and modeling, but is there any theory behind any of this? Shouldn’t the hypotheses be front and center?

    • Andrew says:

      Theory is great, but it can also be a contribution to just describe what’s out there. When a good description is available, maybe others can use it to motivate or test theories, in a social-science division of labor.

  6. Great study and extremely useful as a learning resource as well!
    One remark: the recent book by Frank Baumgartner, Suzanna De Boef and Amber Boydstun (which you cite) argues that the rise of the ‘innocence’ policy frame can account for the changing media tone towards the death penalty and, indirectly, for the changing public opinion as well. Looking at your Figures 8 and 9 it would appear that support for the death penalty is falling much more rapidly among blacks and remains relatively stable among non-blacks. So are only black people sensitive to the cluster of arguments about ‘innocence’ that Baumgartner et al. isolate as the single most importnat drive behind policy change? Is it possible that since many of people exonerated from death row have been black, blacks are more likely to respond to the changing media tone and framing?

    btw, I have a more extensive review of their book here:

  7. Dimiter Toshkov says:

    Frank Baumgartner et al. (2009) argue that the major drive behind changes in media tone and public opinion on the death penalty since the mid-1990s is the rise of the ‘innocence’ policy frame. So why does the ‘innocence’ frame seem to influence black people only (or at least much stronger)? You mention the study early in the paper but it would be nice to discuss how your findings square (or not) with their argument (which is supported only by national level time-series data)…
    from a methodological point of view: is it possible in your framework to model more directly the national time trend (using variables that have been previously identified as important, like murder rates, public opinion, media tone, etc.)?

  8. Muiren says:

    [ “In all, we modeled data from 34 polls, all of which were taken in distinct years between 1953 and 2006, where the maximum number of years between consecutive polls was 5 years (between the 1960 and 1965 Gallup polls). The number of respondents per poll ranged from 445 to 3085, and the total number of responses was N = 58, 253 “]


    No mention of Response/Non-Response rates in the survey samples ?

    That information is critical to the basic validity of specific original survey-research polls.

    Suspect actual response-rates were fairly high in the 1950’s (over 60%) … and very low (under 20%) in the last decade or so of the selected polls.

    • Andrew says:

      We follow standard practice, which is to ignore the nonrespondents and consider the people who do respond as a random sample conditional on poststratification cells.

      • muiren says:

        [“We follow standard practice, which is to ignore the non-respondents and consider the people who do respond as a random sample conditional on post-stratification cells.”]

        Fully agree this is ‘standard-practice’ in the commercial polling business.

        Gallup has always generally claimed to conduct scientific polling, but in recent years is usually quite vague in stating what they actually “measure” and deliver. The core issue is random sampling.

        A very low response-rate in survey research is prima facie evidence of a non-random sample, which is immune from paper conversion/manipulation into an actual random sample of the population under study.

  9. mike says:

    I’m confused by why the national average line is above all but the non-black male line. Doesn’t this mean the the population of non-black men is greater than all black men&women and non-black women combined?

  10. anon says:

    You might want to research the effect of single crimes on public opinion. I noticed a spike at around 1966 and googled “major crimes 1966 america” and found a horrific murder and torture case happened in Indiana then.

  11. Joanna says:

    Why is the pdf file of the paper no longer working?

  12. […] an interesting graph from a new paper by Kenny Shirley and Andrew […]