Binary Choice Data Research Articles

SIMPLE SEMIPARAMETRIC ESTIMATION OF ORDERED RESPONSE MODELS

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameters, and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite-dimensional parameters in the model, we construct nonparametric maximum likelihood estimates for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite-dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. The advantages of our methods are borne out in simulation studies and a real data application.

How sociolinguistic factors shape children's subjective impressions of teacher quality.

When university students are asked to rate their instructors, their evaluations are often influenced by the demographic characteristics of the instructor-such as the instructor's race, gender, or language background. These influences can manifest in unfair systematic biases against particular groups of teachers and hamper movements to promote diversity in higher education. When and how do these biases develop? Here, we begin to address these questions by examining children's sociolinguistic biases against teachers who speak with different accents. To do this, we presented 5-year-old Canadian English-speaking children with pairs of adult talkers. Children were asked to select "who they'd like to be their teacher" then they rated "how good of a teacher" they thought each talker would be on a 5-point scale. In each trial, one talker spoke in the locally dominant variety of Canadian English, and the other spoke in a different accent. Children strongly preferred Canadian-accented teachers over teachers who spoke with non-native (i.e., French or Dutch) accents, but also demonstrated a preference for Canadian teachers over teachers who spoke with non-local regional accents (i.e., Australian or British). In line with the binary choice data, children rated the Canadian talkers more favourably. The relationship between the gender of the teacher and the gender of the child also impacted ratings. This work demonstrates that even at the onset of formal education, children may already exhibit signs of accent-based biases. We discuss these findings in relation to the growing literature on implicit bias in higher education.

A multidimensional pairwise comparison model for heterogeneous perceptions with an application to modelling the perceived truthfulness of public statements on COVID-19.

Pairwise comparison models are an important type of latent attribute measurement model with broad applications in the social and behavioural sciences. Current pairwise comparison models are typically unidimensional. The existing multidimensional pairwise comparison models tend to be difficult to interpret and they are unable to identify groups of raters that share the same rater‐specific parameters. To fill this gap, we propose a new multidimensional pairwise comparison model with enhanced interpretability which explicitly models how object attributes on different dimensions are differentially perceived by raters. Moreover, we add a Dirichlet process prior on rater‐specific parameters which allows us to flexibly cluster raters into groups with similar perceptual orientations. We conduct simulation studies to show that the new model is able to recover the true latent variable values from the observed binary choice data. We use the new model to analyse original survey data regarding the perceived truthfulness of statements on COVID‐19 collected in the summer of 2020. By leveraging the strengths of the new model, we find that the partisanship of the speaker and the partisanship of the respondent account for the majority of the variation in perceived truthfulness, with statements made by co‐partisans being viewed as more truthful.

Voluntary Disclosure of GRI and CSR Environmental Criteria in Colombian Companies

The study analysed the asymmetry in the disclosure of environmental criteria of the Global Reporting Initiative (GRI) standard based on financial and non-financial information in 37 companies in 19 sub-sectors of the Colombian economy that were assessed by MERCO (Business Monitor of Corporate Reputation) in 2017 and 2018 in terms of corporate reputation, responsibility, and corporate governance. It is based on the theories of agency, stakeholders, and legitimacy, whereby six hypotheses were postulated. The indicators of environmental criteria were retrieved from the website and sustainability reports of each company, using a dichotomous approach for collecting information on environmental activities. The hypotheses were contrasted with a binary choice and panel data models. The results showed that increasing quality and transparency in voluntarily disclosed information decreases its asymmetry, thereby meeting the information needs of stakeholders, providing confidence, and strengthening corporate social responsibility (CSR) activities. In addition, the most indebted and largest companies disclose less information on environmental activities, in contrast to companies with higher solvency. Overall, the study contributed with the calculation of an asymmetry ratio with the MERCO indicators and the use of the insolvency risk variable as an explanatory variable for disclosure. Additionally, it contributed to the field of study of CSR from the Latin American context.

Correlated racing evidence accumulator models

Many models of response time that base choices on the first evidence accumulator to win a race to threshold rely on statistical independence between accumulators to achieve mathematical tractability (e.g., Brown and Heathcote, 2008; Logan et al., 2014; Van Zandt et al., 2000). However, it is psychologically plausible that trial-to-trial fluctuations can cause both positive correlations (e.g., variability in arousal, attention or response caution that affect accumulators in the same way) and negative correlations (e.g., when evidence for each accumulator is computed relative to a criterion). We examine the effects of such correlations in a racing accumulator model that remains tractable when they are present, the log-normal race (LNR Heathcote and Love, 2012). We first show that correlations are hard to estimate in binary choice data, and that their presence does not noticeably improve model fit to lexical-decision data (Wagenmakers et al., 2008) that is well fit by an independent LNR model. Poor estimation is attributable to the fact that estimation of correlation requires information about the relationship between accumulator states but only the state of the winning accumulator is directly observed in binary choice. We then show that this problem is remedied when discrete confidence judgments are modeled by an extension of Vickers’s (1979) “balance-of-evidence” hypothesis proposed by Reynolds et al. (submitted). In this “multiple-threshold race” model confidence is based on the state of the losing accumulator judged relative to one or more extra thresholds. We show that not only is correlation well estimated in a multiple-threshold log-normal race (MTLNR) model with as few as two confidence levels, but that it also resulted in clearly better fits to Ratcliff et al.’s (1994) recognition memory data than an independent mode. We conclude that the MTLNR provides a mathematically tractable tool that is useful both for investigating correlations between accumulators and for modeling confidence judgments.

Use of a choice survey to identify adult, adolescent and parent preferences for vaccination in the United States

BackgroundAdult and adolescent vaccination rates are far below coverage targets in the United States. Our objective was to identify the most influential factors related to vaccine uptake among adults, adolescents, and parents of adolescents (parents) in the United States.MethodsWe used a fractional factorial design to create a binary choice survey to evaluate preferences for vaccination. The national survey was fielded to a sample of adults, adolescents ages 13–17 years, and parents, using a national probability-based online research panel in November 2015. Respondents were presented with 5 profiles of a hypothetical vaccine and asked in a series of questions whether they would accept each vaccine. We analyzed the binary choice data using logistic regression in STATA v13 (College Station, TX) to calculate the odds that a participant would choose to accept the vaccine.ResultsWe received completed responses from 334 (51%) of 652 adults, 316 (21%) of 1516 adolescents, and 339 (33%) of 1030 parents. Respondents were generally representative of the U.S. population. Vaccine effectiveness was the most influential factor in the choice to vaccinate for all groups. Other most influential factors were primary care provider (PCP) recommendation and the out-of-pocket cost of the vaccine. Other factors such as risk of illness, risk of vaccine side effects, vaccination location, and time for vaccination were not important in the decision to get vaccinated.ConclusionsAdults, adolescents, and parents are most sensitive to vaccine effectiveness, PCP recommendation, and out-of-pocket cost for vaccination in their decision to get vaccinated. Strong PCP recommendations that focus on vaccine effectiveness and health care policies that minimize out-of-pocket costs for vaccinations may increase vaccine uptake by adults and adolescents.

Simple Semiparametric Estimation of Ordered Response Models: With an Application to the Interdependent Durations Model

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameter and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite dimensional parameters in the model, we construct nonparametric maximum likelihood estimates (NPMLE) for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. We apply our methods to the interdependent durations model in Honore and de Paula (2010), where the social interaction effect is directly related to the threshold parameter in the corresponding ordered response model. The advantages of our methods are borne out in simulation studies and a real data application to the joint retirement decision of married couples.

A Bayesian approach to discriminating between biased responding and sequential dependencies in binary choice data.

A Bayesian approach to discriminating between biased responding and sequential dependencies in binary choice data.

Unbounded evidence accumulation characterizes subjective visual vertical forced-choice perceptual choice and confidence.

Humans can subjectively yet quantitatively assess choice confidence based on perceptual precision even when a perceptual decision is made without an immediate reward or feedback. However, surprisingly little is known about choice confidence. Here we investigate the dynamics of choice confidence by merging two parallel conceptual frameworks of decision making, signal detection theory and sequential analyses (i.e., drift-diffusion modeling). Specifically, to capture end-point statistics of binary choice and confidence, we built on a previous study that defined choice confidence in terms of psychophysics derived from signal detection theory. At the same time, we augmented this mathematical model to include accumulator dynamics of a drift-diffusion model to characterize the time dependence of the choice behaviors in a standard forced-choice paradigm in which stimulus duration is controlled by the operator. Human subjects performed a subjective visual vertical task, simultaneously reporting binary orientation choice and probabilistic confidence. Both binary choice and confidence experimental data displayed statistics and dynamics consistent with both signal detection theory and evidence accumulation, respectively. Specifically, the computational simulations showed that the unbounded evidence accumulator model fits the confidence data better than the classical bounded model, while bounded and unbounded models were indistinguishable for binary choice data. These results suggest that the brain can utilize mechanisms consistent with signal detection theory-especially when judging confidence without time pressure.NEW & NOTEWORTHY We found that choice confidence data show dynamics consistent with evidence accumulation for a forced-choice subjective visual vertical task. We also found that the evidence accumulation appeared unbounded when judging confidence, which suggests that the brain utilizes mechanisms consistent with signal detection theory to determine choice confidence.

The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call Voting

The purpose of this paper is to show how the geometry of the quadratic utility function in the standard spatial model of choice can be exploited to estimate a model of Parliamentary roll call voting. In a standard spatial model of Parliamentary roll call voting, the legislator votes for the policy outcome corresponding to Yea if her utility for Yea is greater than her utility for Nay. The voting decision of the legislator is modeled as a function of the difference between these two utilities. With quadratic utility, this difference has a simple geometric interpretation that can be exploited to estimate legislator ideal points and roll call parameters in a standard framework where the stochastic portion of the utility function is normally distributed. The geometry is almost identical to that used in Poole (2000) to develop a non-parametric unfolding of binary choice data and the algorithms developed by Poole (2000) can be easily modified to implement the standard maximum likelihood model.

Primary facets of order polytopes

Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all order relations of a chosen type. The five prominent types of order relations are linear orders, weak orders, semiorders, interval orders and partial orders. For each of them, the problem of finding a complete, workable characterization of the vectors of probabilities is crucial—but it is reputably inaccessible. Under a geometric reformulation, the problem asks for a linear description of a convex polytope whose vertices are known. As for any convex polytope, a shortest linear description comprises one linear inequality per facet. Getting all of the facet-defining inequalities of any of the five order polytopes seems presently out of reach. Here we search for the facet-defining inequalities which we call primary because their coefficients take only the values −1, 0 or 1. We provide a classification of all primary, facet-defining inequalities of three of the five order polytopes. Moreover, we elaborate on the intricacy of the primary facet-defining inequalities of the linear order and the weak order polytopes.

Supplemental Material for A Bayesian Approach to Discriminating Between Biased Responding and Sequential Dependencies in Binary Choice Data

Supplemental Material for A Bayesian Approach to Discriminating Between Biased Responding and Sequential Dependencies in Binary Choice Data

Thurstonian Scaling of Compositional Questionnaire Data

ABSTRACTTo prevent response bias, personality questionnaires may use comparative response formats. These include forced choice, where respondents choose among a number of items, and quantitative comparisons, where respondents indicate the extent to which items are preferred to each other. The present article extends Thurstonian modeling of binary choice data to “proportion-of-total” (compositional) formats. Following the seminal work of Aitchison, compositional item data are transformed into log ratios, conceptualized as differences of latent item utilities. The mean and covariance structure of the log ratios is modeled using confirmatory factor analysis (CFA), where the item utilities are first-order factors, and personal attributes measured by a questionnaire are second-order factors. A simulation study with two sample sizes, N = 300 and N = 1,000, shows that the method provides very good recovery of true parameters and near-nominal rejection rates. The approach is illustrated with empirical data from N = 317 students, comparing model parameters obtained with compositional and Likert-scale versions of a Big Five measure. The results show that the proposed model successfully captures the latent structures and person scores on the measured traits.

Methodological challenges in modelling the choice of mode for a new travel alternative using binary stated choice data – The case of high speed rail in Norway

Binary stated choices between traveller’s current travel mode and a not-yet-existing mode might be used to build a forecasting model with all (current and future) travel alternatives. One challenge with this approach is the identification of the most appropriate inter-alternative error structure of the forecasting model.By critically assessing the practise of translating estimated group scale parameters into nest parameters, we illustrate the inherent limitations of such binary choice data. To overcome some of the problems, we use information from both stated and revealed choice data and propose a model with a cross-nested logit specification, which is estimated on the pooled data set.

Relative advantage maximisation as a model of context dependence for binary choice data

In recent years we have seen a burgeoning literature, within a discrete choice modelling setting, focussing on capturing increased behavioural realism in decision making through the use of alternative specifications of the utility function. One notable example is the increasing popularity of the random regret minimisation (RRM) model, in which respondents are assumed to choose the alternative that minimises the negative emotions associated with decision making.In this paper, we discuss a ‘relative advantage maximisation’ (RAM) model, which shares some similar characteristics to the RRM model in terms of how contextual effects in the choice set are accounted for. The key feature of the RAM model is the relative advantage component which frames the comparison of an attribute against its counterparts in all other alternatives in the choice set as either an advantage or a disadvantage. The relative advantage is so named because of the assumption that it is the advantage of an alternative relative to the sum of its advantage and disadvantage that matters in the utility function.Although the RRM model has been successfully applied to choice sets with three or more alternatives, with binary choice data, one significant limitation to its scope is that the RRM model collapses to the standard RUM model. This is not the case with the RAM model, and so the notion of context dependency is still meaningfully preserved under RAM. Using the MNL model, we find that the RAM model performs no worse than the RUM model in all six binary choice datasets analysed. In some cases, a small but significant improvement in model fit is observed. However, more advanced models such as the error components and random parameters logit present a more empirically mixed picture for the RAM model. Marginal willingness to pay (WTP) measures derived from the RAM model are also discussed. Differences may be negligible in the MNL case, but not necessarily so for the random parameter logit.

QTest: Quantitative Testing of Theories of Binary Choice.

The goal of this paper is to make modeling and quantitative testing accessible to behavioral decision researchers interested in substantive questions. We provide a novel, rigorous, yet very general, quantitative diagnostic framework for testing theories of binary choice. This permits the nontechnical scholar to proceed far beyond traditionally rather superficial methods of analysis, and it permits the quantitatively savvy scholar to triage theoretical proposals before investing effort into complex and specialized quantitative analyses. Our theoretical framework links static algebraic decision theory with observed variability in behavioral binary choice data. The paper is supplemented with a custom-designed public-domain statistical analysis package, the QTest software. We illustrate our approach with a quantitative analysis using published laboratory data, including tests of novel versions of "Random Cumulative Prospect Theory." A major asset of the approach is the potential to distinguish decision makers who have a fixed preference and commit errors in observed choices from decision makers who waver in their preferences.

Quantifying response shift or adaptation effects in quality of life by synthesising best-worst scaling and discrete choice data

Older people's valuation of health-related aspects of quality of life may be altered by response shift, where they lower expectations of aspects of well-being that are believed to naturally deteriorate with age. Policy-makers may wish to adjust estimated preferences if these reflect past inequities in health funding rather than the true production possibilities. Response shift might be quantified by changing the context of the choice task. The ICECAP-O valuation exercise achieved this by asking a binary choice holistic decision of respondents, in addition to the case 2 best-worst choice task among the five attributes. Answers to the former are more likely to be subject to response shift since they involve traditional trade-offs. Answers to the latter reflect only ‘relative disutility’ of various impairments.Individual level estimates for the latter were substituted into the design matrix in a series of latent class analyses of the binary choice data. The five attribute mean estimates from the conditional logit regressions are the attribute importance parameters and represent the (internal) scaling factors that respondents use in transforming their case 2 BWS utilities into ones relevant in multi-profile decision-making. The principal hypothesis was that there were classes of respondents who used identical attribute importance weights. Rejection of this hypothesis prompted testing of secondary hypotheses that respondents placed lower importance on control (independence) and role (doing things that make you feel valued), those attributes thought to be most vulnerable to response shift. Results showed that 17% of respondents never traded, in most cases illogically given their own ICECAP-O responses, and were dropped. Tests of parameter-equality suggested at least 30% and possibly as many as 53% of respondents for whom there is a single statistically significant attribute importance factor and 64 (21%) of respondents for whom there is a single statistically non-significant attribute importance factor. The remaining 9% of respondents had a moderate status-quo bias (preference for own life). These results do not provide strong support for response shift in the ICECAP-O valuation sample. There is only very limited support for differential weights for the five attributes when moving into a traditional DCE framework.

Modelling Heterogeneity in Response Behaviour Towards a Sequence of Discrete Choice Questions: A Probabilistic Decision Process Model

There is a growing body of evidence in the non-market valuation literature suggesting that responses to a sequence of discrete choice questions tend to violate the assumptions typically made by analysts regarding independence of responses and stability of preferences. Decision processes (or heuristics) such as value learning and strategic misrepresentation have been offered as explanations for these results. While a few studies have tested these heuristics as competing hypotheses, none has investigated the possibility that each explains the response behaviour of a subgroup of the population. In this paper, we make a contribution towards addressing this research gap by presenting a probabilistic decision process model designed to estimate the proportion of respondents employing defined heuristics. We demonstrate the model on binary and multinomial choice data sources and find three distinct types of response behaviour. The results suggest that accounting for heterogeneity in response behaviour may be a better way forward than attempting to identify a single heuristic to explain the behaviour of all respondents.

UK OC OK? Interpreting Optimal Classification Scores for the U.K. House of Commons

Poole's (2000, Non-parametric unfolding of binary choice data. Political Analysis 8:211–37) nonparametric Optimal Classification procedure for binary data produces misleading rank orderings when applied to the modern House of Commons. With simulations and qualitative evidence, we show that the problem arises from the government-versus-opposition nature of British (Westminster) parliamentary politics and the strategic voting that is entailed therein. We suggest that political scientists think seriously about strategic voting in legislatures when interpreting results from such techniques.

A Gravity-Based Multidimensional Scaling Model for Deriving Spatial Structures Underlying Consumer Preference/Choice Judgments

In multidimensional unfolding multidimensional scaling (MDS) procedures, the predicted utility of a brand for a consumer is inversely related to the distance between that consumer's ideal point and the brand position in the derived space. Most MDS models treat all brands the same regardless of their respective market share. In many product categories, however, consumer preferences are heavily influenced by the size of the existing market share (i.e., the brand mass). This article presents two versions of a new spatial methodology that incorporates the effects of brand as well as consumer mass via a spatial gravity model of consumer utility; that is, the attraction of a brand for a consumer depends not only on the distance of the brand from a consumer's ideal point but also on the current market size of the brand, as well as the consumer purchase pattern and volume. One version of the proposed model estimates brand positions and individual ideal points with two-way or three-way pick any/N binary choice data. The second version we develop provides the same spatial decomposition for two-way or three-way metric preference/dominance data. We also develop a series of nested MDS models to estimate, test, and compare four different model structures with respect to any common data set. We illustrate the proposed methodology using an actual commercial application involving physician prescription behavior and examine competing model fits.