Probabilistic models of set-dependent and attribute-level best-worst choice

We characterize a class of probabilistic choice models where the choice probabilities depend on two scales, one with a value for each available option and the other with a value for the set of available options. Then, we develop similar results for a task in which a person is presented with a profile of attributes, each at a pre-specified level, and chooses the best or the best and the worst of those attribute-levels. The latter design is an important variant on previous designs using best-worst choice to elicit preference information, and there is various evidence that it yields reliable interpretable data. Nonetheless, the data from a single such task cannot yield separate measures of the "importance" of an attribute and the "utility" of an attribute-level. We discuss various empirical designs, involving more than one task of the above general type, that may allow such separation of importance and utility. © 2008 Elsevier Inc. All rights reserved

Modeling the choices of individual decision-makers by combining efficient choice experiment designs with extra preference information

We show how to combine statistically efficient ways to design discrete choice experiments based on random utility theory with new ways of collecting additional information that can be used to expand the amount of available choice information for modeling the choices of individual decision makers. Here we limit ourselves to problems involving generic choice options and linear and additive indirect utility functions, but the approach potentially can be extended to include choice problems with non-additive utility functions and non-generic/labeled options/attributes. The paper provides several simulated examples, a small empirical example to demonstrate proof of concept, and a larger empirical example based on many experimental conditions and large samples that demonstrates that the individual models capture virtually all the variance in aggregate first choices traditionally modeled in discrete choice experiments

Estimating preferences for a dermatology consultation using Best-Worst Scaling: Comparison of various methods of analysis

Background: Additional insights into patient preferences can be gained by supplementing discrete choice experiments with best-worst choice tasks. However, there are no empirical studies illustrating the relative advantages of the various methods of analysis within a random utility framework. Methods: Multinomial and weighted least squares regression models were estimated for a discrete choice experiment. The discrete choice experiment incorporated a best-worst study and was conducted in a UK NHS dermatology context. Waiting time, expertise of doctor, convenience of attending and perceived thoroughness of care were varied across 16 hypothetical appointments. Sample level preferences were estimated for all models and differences between patient subgroups were investigated using ovariateadjusted multinomial logistic regression. Results: A high level of agreement was observed between results from the paired model (which is theoretically consistent with the 'maxdiff' choice model) and the marginal model (which is only an approximation to it). Adjusting for covariates showed that patients who felt particularly affected by their skin condition during the previous week displayed extreme preference for short/no waiting time and were less concerned about other aspects of the appointment. Higher levels of educational attainment were associated with larger differences in utility between the levels of all attributes, although the attributes per use had the same impact upon choices as those with lower levels of attainment. The study also demonstrated the high levels of agreement between summary analyses using weighted least squares and estimates from multinomial models. Conclusion: Robust policy-relevant information on preferences can be obtained from discrete choice experiments incorporating best-worst questions with relatively small sample sizes. The separation of the effects due to attribute impact from the position of levels on the latent utility scale is not possible using traditional discrete choice experiments. This separation is important because health policies to change the levels of attributes in health care may be very different from those aiming to change the attribute impact per se. The good approximation of summary analyses to the multinomial model is a useful finding, because weighted least squares choice totals give better insights into the choice model and promote greater familiarity with the preference data

Radiative Transfer for Exoplanet Atmospheres

Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer calculation and predict the spectrum of an exoplanet atmosphere, including solving the radiative transfer equation, calculating opacities (and chemistry), iterating for radiative equilibrium (or not), and adapting the output of the calculations to the astronomical observations. A review of the state of the art is performed, focusing on selected milestone papers. Outstanding issues, including the need to understand aerosols or clouds and elucidating the assumptions and caveats behind inversion methods, are discussed. A checklist is provided to assist referees/reviewers in their scrutiny of works involving radiative transfer. A table summarizing the methodology employed by past studies is provided.Comment: 7 pages, no figures, 1 table. Filled in missing information in references, main text unchange

Rescaling quality of life values from discrete choice experiments for use as QALYs: a cautionary tale

Background: Researchers are increasingly investigating the potential for ordinal tasks such as ranking and discrete choice experiments to estimate QALY health state values. However, the assumptions of random utility theory, which underpin the statistical models used to provide these estimates, have received insufficient attention. In particular, the assumptions made about the decisions between living states and the death state are not satisfied, at least for some people. Estimated values are likely to be incorrectly anchored with respect to death (zero) in such circumstances. Methods: Data from the Investigating Choice Experiments for the preferences of older people CAPability instrument (ICECAP) valuation exercise were analysed. The values (previously anchored to the worst possible state) were rescaled using an ordinal model proposed previously to estimate QALY-like values. Bootstrapping was conducted to vary artificially the proportion of people who conformed to the conventional random utility model underpinning the analyses. Results: Only 26% of respondents conformed unequivocally to the assumptions of conventional random utility theory. At least 14% of respondents unequivocally violated the assumptions. Varying the relative proportions of conforming respondents in sensitivity analyses led to large changes in the estimated QALY values, particularly for lower-valued states. As a result these values could be either positive (considered to be better than death) or negative (considered to be worse than death). Conclusion: Use of a statistical model such as conditional (multinomial) regression to anchor quality of life values from ordinal data to death is inappropriate in the presence of respondents who do not conform to the assumptions of conventional random utility theory. This is clearest when estimating values for that group of respondents observed in valuation samples who refuse to consider any living state to be worse than death: in such circumstances the model cannot be estimated. Only a valuation task requiring respondents to make choices in which both length and quality of life vary can produce estimates that properly reflect the preferences of all respondents

Layered convection as the origin of Saturn's luminosity anomaly

As they keep cooling and contracting, Solar System giant planets radiate more energy than they receive from the Sun. Applying the first and second principles of thermodynamics, one can determine their cooling rate, luminosity, and temperature at a given age. Measurements of Saturn's infrared intrinsic luminosity, however, reveal that this planet is significantly brighter than predicted for its age. This excess luminosity is usually attributed to the immiscibility of helium in the hydrogen-rich envelope, leading to "rains" of helium-rich droplets. Existing evolution calculations, however, suggest that the energy released by this sedimentation process may not be sufficient to resolve the puzzle. Here, we demonstrate using planetary evolution models that the presence of layered convection in Saturn's interior, generated, like in some parts of Earth oceans, by the presence of a compositional gradient, significantly reduces its cooling. It can explain the planet's present luminosity for a wide range of configurations without invoking any additional source of energy. This suggests a revision of the conventional homogeneous adiabatic interior paradigm for giant planets, and questions our ability to assess their heavy element content. This reinforces the possibility for layered convection to help explaining the anomalously large observed radii of extrasolar giant planets.Comment: Published in Nature Geoscience. Online publication date: April 21st, 2013. Accepted version before journal editing and with Supplementary Informatio

Into the UV: The Atmosphere of the Hot Jupiter HAT-P-41b Revealed

For solar system objects, ultraviolet spectroscopy has been critical in identifying sources of stratospheric heating and measuring the abundances of a variety of hydrocarbon and sulfur-bearing species, produced via photochemical mechanisms, as well as oxygen and ozone. To date, fewer than 20 exoplanets have been probed in this critical wavelength range (0.2–0.4 μm). Here we use data from Hubble's newly implemented WFC3 UVIS G280 grism to probe the atmosphere of the hot Jupiter HAT-P-41b in the ultraviolet through optical in combination with observations at infrared wavelengths. We analyze and interpret HAT-P-41b's 0.2–5.0 μm transmission spectrum using a broad range of methodologies including multiple treatments of data systematics as well as comparisons with atmospheric forward, cloud microphysical, and multiple atmospheric retrieval models. Although some analysis and interpretation methods favor the presence of clouds or potentially a combination of Na, VO, AlO, and CrH to explain the ultraviolet through optical portions of HAT-P-41b's transmission spectrum, we find that the presence of a significant H− opacity provides the most robust explanation. We obtain a constraint for the abundance of H−, $\mathrm{log}({{\rm{H}}}^{-})=-8.65\pm 0.62$, in HAT-P-41b's atmosphere, which is several orders of magnitude larger than predictions from equilibrium chemistry for a ~1700–1950 K hot Jupiter. We show that a combination of photochemical and collisional processes on hot hydrogen-dominated exoplanets can readily supply the necessary amount of H− and suggest that such processes are at work in HAT-P-41b and the atmospheres of many other hot Jupiters

A Systematic Review Comparing the Acceptability, Validity and Concordance of Discrete Choice Experiments and Best–Worst Scaling for Eliciting Preferences in Healthcare

Objective: The aim of this study was to compare the acceptability, validity and concordance of discrete choice experiment (DCE) and best–worst scaling (BWS) stated preference approaches in health. Methods: A systematic search of EMBASE, Medline, AMED, PubMed, CINAHL, Cochrane Library and EconLit databases was undertaken in October to December 2016 without date restriction. Studies were included if they were published in English, presented empirical data related to the administration or findings of traditional format DCE and object-, profile- or multiprofile-case BWS, and were related to health. Study quality was assessed using the PREFS checklist. Results: Fourteen articles describing 12 studies were included, comparing DCE with profile-case BWS (9 studies), DCE and multiprofile-case BWS (1 study), and profile- and multiprofile-case BWS (2 studies). Although limited and inconsistent, the balance of evidence suggests that preferences derived from DCE and profile-case BWS may not be concordant, regardless of the decision context. Preferences estimated from DCE and multiprofile-case BWS may be concordant (single study). Profile- and multiprofile-case BWS appear more statistically efficient than DCE, but no evidence is available to suggest they have a greater response efficiency. Little evidence suggests superior validity for one format over another. Participant acceptability may favour DCE, which had a lower self-reported task difficulty and was preferred over profile-case BWS in a priority setting but not necessarily in other decision contexts. Conclusion: DCE and profile-case BWS may be of equal validity but give different preference estimates regardless of the health context; thus, they may be measuring different constructs. Therefore, choice between methods is likely to be based on normative considerations related to coherence with theoretical frameworks and on pragmatic considerations related to ease of data collection

Atmospheric retrieval of exoplanets

Exoplanetary atmospheric retrieval refers to the inference of atmospheric properties of an exoplanet given an observed spectrum. The atmospheric properties include the chemical compositions, temperature profiles, clouds/hazes, and energy circulation. These properties, in turn, can provide key insights into the atmospheric physicochemical processes of exoplanets as well as their formation mechanisms. Major advancements in atmospheric retrieval have been made in the last decade, thanks to a combination of state-of-the-art spectroscopic observations and advanced atmospheric modeling and statistical inference methods. These developments have already resulted in key constraints on the atmospheric H2O abundances, temperature profiles, and other properties for several exoplanets. Upcoming facilities such as the JWST will further advance this area. The present chapter is a pedagogical review of this exciting frontier of exoplanetary science. The principles of atmospheric retrievals of exoplanets are discussed in detail, including parametric models and statistical inference methods, along with a review of key results in the field. Some of the main challenges in retrievals with current observations are discussed along with new directions and the future landscape