An Empirical Bayes Approach to Estimating Ordinal Treatment Effects

Ordinal variables — categorical variables with a defined order to the categories, but without equal spacing between them — are frequently used in social science applications. Although a good deal of research exists on the proper modeling of ordinal response variables, there is not a clear directive as to how to model ordinal treatment variables. The usual approaches found in the literature for using ordinal treatment variables are either to use fully unconstrained, though additive, ordinal group indicators or to use a numeric predictor constrained to be continuous. Generalized additive models are a useful exception to these assumptions (Beck and Jackman 1998). In contrast to the generalized additive modeling approach, we propose the use of a Bayesian shrinkage estimator to model ordinal treatment variables. The estimator we discuss in this paper allows the model to contain both individual group level indicators and a continuous predictor. In contrast to traditionally used shrinkage models that pull the data toward a common mean, we use a linear model as the basis. Thus, each individual effect can be arbitrary, but the model “shrinks” the estimates toward a linear ordinal framework according to the data. We demonstrate the estimator on two political science examples: the impact of voter identification requirements on turnout (Alvarez, Bailey, and Katz 2007), and the impact of the frequency of religious service attendance on the liberality of abortion attitudes (e.g., Singh and Leahy 1978, Tedrow and Mahoney 1979, Combs and Welch 1982)

The Effect of Voter Identification Laws on Turnout

Since the passage of the “Help America Vote Act” in 2002, nearly half of the states have adopted a variety of new identification requirements for voter registration and participation by the 2006 general election. There has been little analysis of whether these requirements reduce voter participation, especially among certain classes of voters. In this paper we document the effect of voter identification requirements on registered voters as they were imposed in states in the 2000 and 2004 presidential elections, and in the 2002 and 2006 midterm elections. Looking first at trends in the aggregate data, we find no evidence that voter identification requirements reduce participation. Using individual-level data from the Current Population Survey across these elections, however, we find that the strictest forms of voter identification requirements — combination requirements of presenting an identification card and positively matching one’s signature with a signature either on file or on the identification card, as well as requirements to show picture identification — have a negative impact on the participation of registered voters relative to the weakest requirement, stating one’s name. We also find evidence that the stricter voter identification requirements depress turnout to a greater extent for less educated and lower income populations, but no racial differences.Carnegie Corporation of New York; John S. and James L. Knight Foundatio

Is there an excess of black holes around 20M⊙20 M_{\odot}? Optimising the complexity of population models with the use of reversible jump MCMC

Some analyses of the third gravitational wave catalogue released by the LIGO-Virgo-KAGRA collaboration (LVK) suggest an excess of black holes around $15-20 M_{\odot}$. In order to investigate this feature, we introduce two flexible population models, a semi-parametric one and a non-parametric one. Both make use of reversible jump Markov chain Monte-Carlo to optimise their complexity. We also illustrate how the latter can be used to efficiently perform model selection. Our parametric model broadly agrees with the fiducial analysis of the LVK, but finds a peak of events at slightly larger masses. Our non-parametric model shows this same displacement. Moreover, it also suggests the existence of an excess of black holes around $20 M_{\odot}$. We assess the robustness of this prediction by performing mock injections and running hierarchical analyses on those. We find that such a feature might be due to statistical fluctuations, given the small number of events observed so far, with a $5\%$ probability. We estimate that with a few hundreds of observations, as expected for O4, our non-parametric model will, be able to robustly determine the presence of this excess. It will then allow for an efficient agnostic inference of the properties of black holes.Comment: correct typo in equation

Machines Versus Humans: The Counting and Recounting of Pre-Scored Punchcard Ballots

The counting of ballots, especially punchcard ballots, has received a great deal of attention in the years following the 2000 presidential election in Florida. Much of the research literature has focused on various measures of how accurately voting machines record voter intentions, with studies of the relative accuracy rates across voting machines (e.g., Caltech/MIT Voting Technology Project 2001), studies of voting accuracy across groups of the electorate (Alvarez and Sinclair 2003), and studies that examine the variability in voting machine accuracy across both machine types and voter types (Alvarez, Sinclair and Wilson 2002; Ansolabehere 2002; Tomz and Van Houweling 2003).Carnegie Corporation of New York; John S. and James L. Knight Foundation; John Randolph Haynes and Dora Haynes Foundatio

Hidden Donors: The Censoring Problem in U.S. Federal Campaign Finance Data

Inferences about individual campaign contributors are limited by how the Federal Election Commission collects and reports data. Only transactions that exceed a cycle-to-date total of $200 are individually disclosed, so that contributions of many donors are unobserved. We contrast visible and "hidden" donors, i.e., small donors who are invisible due to censoring—and routinely ignored in existing research. We use the Sanders presidential campaign in 2016, whose unique campaign structure received money only through an intermediary/conduit committee. These are governed by stricter disclosure statutes, allowing us to study donors who are normally hidden. For Sanders, there were seven hidden donors for every visible donor, and altogether, hidden donors were responsible for 33.8% of Sanders' campaign funds. We show that hidden donors start giving relatively later, with contributions concentrated around early primaries. We suggest that as presidential campaign strategies change towards wooing smaller donors, more research on what motivates them is necessary

Government Partisanship, Labor Organization, and Macroeconomic Performance: A Corrigendum

Alvarez, Garrett and Lange (1991) used cross-national data panel data on the Organization for Economic Coordination and Development nations to show that countries with left governments and encompassing labor movements enjoyed superior economic performance. Here we show that the standard errors reported in that article are incorrect. Reestimation of the model using ordinary least squares and robust standard errors upholds the major finding of Alvarez, Garrett and Lange, regarding the political and institutional causes of economic growth but leaves the findings for unemployment and inflation open to question. We show that the model used by Alvarez, Garrett and Lange, feasible generalized least squares, cannot produce standard errors when the number of countries analyzed exceeds the length of the time period under analysis. Also, we argue that ordinary least squares with robust standard errors is superior to feasible generalized least square for typical cross-national panel studies

Measuring source properties and quasi-normal-mode frequencies of heavy massive black-hole binaries with LISA

The laser-interferometer space antenna (LISA) will be launched in the mid 2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR both in the inspiral and the merger-ringdown stages. Such signals are ideal for tests of General Relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA, and simulate their LISA signals using the newly developed parametrised, multipolar, aligned-spin effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins), and also on parameters that describe fractional deviations from the GR quasi-normal-mode frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within $10\%$ and in the best cases to within $1\%$. We also show that we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral: individual source-frame masses can typically be constrained to within $10\%$ and as precisely as $1\%$, and individual spins can typically be constrained to within $0.1$ and as precisely as $0.001$. Finally, we probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. For the source parameters considered, we measure erroneous deviations from GR due to systematics in the waveform model. These results confirm the need for improving waveform models to perform tests of GR with binary BHs at high SNR with LISA.Comment: 15 pages, 18 with appendices, 19 figure

Using small molecule probes to investigate aggregation of sunset yellow FCF: what are the concentration limits?

The assembly of small molecules into larger structures, often driven by non-covalent interactions such as hydrogen-bonding, aromatic stacking interactions and burial of hydrophobic surface, is of wide spread interest. The interaction of small molecules with aggregates also has a large range of application from fluorescence aggregation assays to gas storage in framework materials. Here we utilise nuclear magnetic resonance spectroscopy to investigate the interaction of a small molecule probe on the assembly state of sunset yellow across a wide range of relative concentrations. Information from both macroscopic (diffusion) and microscopic (chemical shifts) measurements allows the interaction to be studied and the binding mode to be interrogated. Using fluorophenol as the small molecule probe, we show that the aggregation behaviour of sunset yellow is broadly unaffected by the relative amount of fluorophenol added