Probabilistic Choice Models Research Articles

The residential location choice of the elderly in Korea: A multilevel logit model

The present study explores a residential movement of elderly households, which is postulated based on the probabilistic choice theory. This study intends to develop a residential location choice model integrating micro- and macro-approaches by adding regional factors to the probabilistic choice model in terms of the individual level. With the movement to rural areas being given more focus, the estimated results will have implications on local governments’ policies with regard to the shrinking population. The findings suggest that the propensities associated with the decision to move to rural areas vary in different regions. The unemployed elderly or the elderly who live with their children are most likely to move to urban areas, while elderly couples show more inclination to migrate to rural areas than the spouseless elderly. This study presents that the probability that the urban elderly will move to rural areas is lower than that of the rural elderly.

Response mode and stochastic choice together explain preference reversals

Informed by Grether and Plott (1979) and Cox and Grether (1996), we implement various preference elicitation procedures over a parameter grid. First, we find a lower incidence of preference reversals for probability equivalents from the dual‐to‐selling version of Becker, Degroot, and Marschak (1964; BDM) than for certainty equivalents from traditional BDM—consistent with conjectures regarding response mode. Second, the Blavatskyy (2009, 2012) model of probabilistic choice can explain the incidence of preference reversals when using probability equivalents. Thus, between response mode (outside the Blavatskyy model) and stochastic choice (as per Blavatskyy), preference reversals in the original certainty equivalent case seem to be explained. We also present estimates for risk and stochasticity parameters; the former are not correlated across mechanisms, but the latter are. Finally, relatively more error‐laden behavior (based on within‐mechanism checks) can be associated with fewer reversals across mechanisms. The data make clear, empirically, the logical proposition that reducing reversals requires only a better “match” with binary choice, not necessarily rational behavior at any deeper level. Preference reversals probabilistic choice mechanism design institutions C91 D47 D81

Considering perception errors in network efficiency measure: an application to bridge importance ranking in degradable transportation networks

In this paper, a new network efficiency measure that takes into account of traveller's perception errors as well as flows, behaviours, and costs is developed for assessing link importance in congested transportation networks. The core component of the network efficiency measure is a probabilistic route choice model embedded in a network equilibrium framework, which explicitly captures the interactions between travellers’ perception errors and link cost functions to produce a stochastic user equilibrium (SUE) flow pattern. The importance measure defined as the relative network efficiency drop is developed to rank the links in the network. The network efficiency and importance measures can work for both uncongested and congested transportation networks. To show proof of concept, we use two networks to demonstrate the features and applicability of the proposed measures. In the Braess network, we examine the value of link efficiency, link importance, and link ranking in comparison with the topological measure and the user equilibrium (UE) measure. In addition, we investigate the effects capacity degradation level, demand level, and degree of perception error. In the Winnipeg network, we apply the network efficiency and importance measures to assess the bridges in the city of Winnipeg, Manitoba, Canada. We compare the SUE importance with the localised volume to capacity (V/C) ratio method, and investigate the bridge importance measures in the context of a flooding scenario to examine the effect of providing information to drivers. The results demonstrate that the SUE network efficiency and importance measures are useful in both theory and applications.

Behavior in the centipede game: A decision-theoretical perspective

The centipede game is a two-player finite game of perfect information where a unique subgame perfect Nash equilibrium appears to be intuitively unappealing and descriptively inadequate. This paper analyzes behavior in the centipede game when a traditional game-theoretical assumption that players maximize expected utility is relaxed. We demonstrate the existence of a descriptively adequate subgame perfect equilibrium under two standard decision-theoretical assumptions. First, players choose under uncertainty in a probabilistic manner as captured by embedding a core deterministic decision theory in a model of probabilistic choice. Second, players adopt non-linear decision weights and overweight the likelihood of rare events as captured, for example, by rank-dependent utility or prospect theory.

Behavior in the Centipede Game: A Decision-Theoretical Perspective

The centipede game is a two-player finite game of perfect information where a unique subgame perfect Nash equilibrium appears to be intuitively unappealing and descriptively inadequate. This paper analyzes behavior in the centipede game when a traditional game-theoretical assumption that players maximize expected utility is relaxed. We demonstrate the existence of a descriptively adequate subgame perfect equilibrium under two standard decision-theoretical assumptions. First, players choose under uncertainty in a probabilistic manner as captured by embedding a core deterministic decision theory in a model of probabilistic choice. Second, players adopt non-linear decision weights and overweight the likelihood of rare events as captured, for example, by rank-dependent utility or prospect theory.

Contextual processing of brightness and color in Mongolian gerbils.

Brightness and color cues are essential for visually guided behavior. However, for rodents, little is known about how well they do use these cues. We used a virtual reality setup that offers a controlled environment for sensory testing to quantitatively investigate visually guided behavior for achromatic and chromatic stimuli in Mongolian gerbils (Meriones unguiculatus). In two-alternative forced choice tasks, animals had to select target stimuli based on relative intensity or color with respect to a contextual reference. Behavioral performance was characterized using psychometric analysis and probabilistic choice modeling. The analyses revealed that the gerbils learned to make decisions that required judging stimuli in relation to their visual context. Stimuli were successfully recognized down to Weber contrasts as low as 0.1. These results suggest that Mongolian gerbils have the perceptual capacity for brightness and color constancy.

Generalized outcome-based strategy classification: comparing deterministic and probabilistic choice models.

Model comparisons are a vital tool for disentangling which of several strategies a decision maker may have used--that is, which cognitive processes may have governed observable choice behavior. However, previous methodological approaches have been limited to models (i.e., decision strategies) with deterministic choice rules. As such, psychologically plausible choice models--such as evidence-accumulation and connectionist models--that entail probabilistic choice predictions could not be considered appropriately. To overcome this limitation, we propose a generalization of Bröder and Schiffer's (Journal of Behavioral Decision Making, 19, 361-380, 2003) choice-based classification method, relying on (1) parametric order constraints in the multinomial processing tree framework to implement probabilistic models and (2) minimum description length for model comparison. The advantages of the generalized approach are demonstrated through recovery simulations and an experiment. In explaining previous methods and our generalization, we maintain a nontechnical focus--so as to provide a practical guide for comparing both deterministic and probabilistic choice models.

Comment on “A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance” by Pavlo Blavatskyy

We present examples of existing evidence that lead us to be cautious about claims made in the original paper [Blavatskyy PR (2011) A model of probabilistic choice satisfying first-order stochastic dominance. Management Sci. 57(3):542–548] that the proposed model provides a better fit to experimental data than do existing models. We raise concerns about the accuracy of this and other assertions and about the adequacy of the comparisons made with alternative models in the existing literature. This paper was accepted by Rakesh Sarin, decision analysis.

Probabilistic choice models in health-state valuation research: background, theories, assumptions and applications

Interest is rising in measuring subjective health outcomes, such as treatment outcomes that are not directly quantifiable (functional disability, symptoms, complaints, side effects and health-related quality of life). Health economists in particular have applied probabilistic choice models in the area of health evaluation. They increasingly use discrete choice models based on random utility theory to derive values for healthcare goods or services. Recent attempts have been made to use discrete choice models as an alternative method to derive values for health states. In this article, various probabilistic choice models are described according to their underlying theory. A historical overview traces their development and applications in diverse fields. The discussion highlights some theoretical and technical aspects of the choice models and their similarity and dissimilarity. The objective of the article is to elucidate the position of each model and their applications for health-state valuation.

Probabilistic choice (models) as a result of balancing multiple goals

We conceptualize probabilistic choice as the result of the simultaneous pursuit of multiple goals in a vector optimization representation, which is reduced to a scalar optimization that implies goal balancing. The majority of prior theoretical and empirical work on such probabilistic choice is based on random utility models, the most basic of which assume that each choice option has a valuation that has a deterministic (systematic) component plus a random component determined by some specified distribution. An alternate approach to probabilistic choice has considered maximization of one quantity (e.g., utility), subject to constraints on one or more other quantities (e.g., cost). The multiple goal perspective integrates the results regarding the well-studied multinomial logit model of probabilistic choice that has been derived from each of the above approaches; extends the results to other models in the generalized extreme value (GEV) class; and relates them to recent axiomatic work on the utility of gambling.

Psychoco: Psychometric Computing inR

This special volume features eleven contributions to psychometric computing, a research area that integrates psychometrics and computational methods in statistics. Topics covered include structural equation modeling, item response theory, probabilistic choice modeling, and other modeling approaches prevalent in or useful for psychometric research. Each contributed paper is accompanied by a software package published on the Comprehensive R Archive Network. This introduction gives a brief overview of the volume.

A Reason for Unreason: Returns-Based Beliefs in Game Theory

Players cooperate in experiments more than game theory would predict. In order to explain this, we introduce the 'returns-based beliefs' approach: the expected returns of a particular strategy in proportion to the total expected returns of all strategies. Using a decision analytic solution concept, Luce's (1959) probabilistic choice model, and 'hyperpriors' for ambiguity in players' cooperability, our approach explains empirical observations in classic games such as the Prisoner's Dilemma. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2x2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts.

An alternative explanation for the logit form probabilistic choice model from the equal likelihood hypothesis

We present an alternative explanation of the logit probabilistic choice from the equal likelihood hypothesis without the Gumbel distribution. The hypothesis is that if the total utility values from combinations of actions are the same, all such combinations of actions are equally likely.

The impact of client choice on preventive healthcare facility network design

In contrast with sick people who need urgent medical attention, the clientele of preventive healthcare have a choice in whether to participate in the programs offered in their region. In order to maximize the total participation to a preventive care program, it is important to incorporate how potential clients choose the facilities to patronize. We study the impact of client choice behavior on the configuration of a preventive care facility network and the resulting level of participation. To this end, we present two alternative models: in the "probabilistic-choice model" a client may patronize each facility with a certain probability, which increases with the attractiveness of the available facilities. In contrast, the "optimal-choice model" stipulates that each client will go to the most attractive facility. In this paper, we assume that the proximity to a facility is the only attractiveness attribute considered by clients. To ensure the quality of care, we impose a bound on the mean waiting time as well as a minimum workload requirement at each open facility. Subject to a total capacity limit, the number of open facilities as well as the location and the capacity (number of servers) of each open facility is the main determinant of the configuration of a facility network. Both models are formulated as a mixed-integer program. To solve the problems efficiently, we propose a probabilistic search algorithm and a genetic algorithm. Finally, we use the models to analyze the network of mammography centers in Montreal.

Probabilistic subjective expected utility

This paper develops the first model of probabilistic choice under subjective uncertainty (when probabilities of events are not objectively known). The model is characterized by seven standard axioms (probabilistic completeness, weak stochastic transitivity, nontriviality, event-wise dominance, probabilistic continuity, existence of an essential event, and probabilistic independence) as well as one new axiom. The model has an intuitive econometric interpretation as a Fechner model of (relative) random errors. The baseline model is extended from binary choice to decisions among m > 2 alternatives using a new method, which is also applicable to other models of binary choice.

Capturing Competitive, Cannibalistic, And Variety-Seeking Influences On Market Share: An Asymmetric Modeling Approach

<span>This paper attempts to focus on the asymmetric source-of-share issue by building and calibrating a probabilistic choice model which estimates market share at the consumer level while also capturing the asymmetric influence of inter-brand competition, intra-brand cannibalism, and cross-form variety-seeking. The results suggest that the inclusion of asymmetric influences improves the fit to the data. Asymmetric variety-seeking is demonstrated to be a function of the dissimilarity between offerings. Managers who ignore asymmetric variety-seeking may be ignoring some of their closest competitors. The importance of asymmetric competition and symmetric cannibalism must also be taken into account. Both are demonstrated to be functions of the similarity between offerings. Managers who ignore asymmetric cannibalism may introduce offering extensions that leave the firm no better off financially. These extensions conceivably could have a negative impact on the financial viability of the firm given the extra cost of expanding their offering mix. In addition, asymmetric competition provides new insights as to the competitors most likely to be affected by a given firms actions.</span>

Dominance and innovation: a returns‐based beliefs approach

Do dominant or less dominant firms innovate more? There is considerable research on this question, with theoretical studies based on game theory and empirical evidence often divided. We provide a new theory that the decisions that concern strategic choice in innovation may be influenced by expected relative returns. Our approach, which we call the returns‐based beliefs approach, is based upon subjective probabilities. It combines a decision analytic solution concept and Luce's (Individual Choice Behavior, Wiley: New York, 1959) probabilistic choice model. We show that the returns‐based beliefs approach provides support for the thesis that dominant firms invest more in research and development (R&D) within an asymmetric mixed‐strategy game. Consequently, the returns‐based beliefs approach accords better with recent empirical studies of innovation. Using R&D data across a range of industries in the UK from 2001 to 2006, we show that firms’ spending on R&D is related more to their own profitability than to that of their competitors, which is consistent with the returns‐based beliefs approach. Copyright © 2011 John Wiley & Sons, Ltd.

A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance

This paper presents a new model of probabilistic binary choice under risk. In this model, a decision maker always satisfies first-order stochastic dominance. If neither lottery stochastically dominates the other alternative, a decision maker chooses in a probabilistic manner. The proposed model is derived from four standard axioms (completeness, weak stochastic transitivity, continuity, and common consequence independence) and two relatively new axioms. The proposed model provides a better fit to experimental data than do existing models. The baseline model can be extended to other domains such as modeling variable consumer demand. This paper was accepted by Peter Wakker, decision analysis.

A Review On Some Alternative Specifications Of The Logit Model

The logit model, perhaps the simplest and the best possible probabilistic choice model in the discrete choice modeling literature. As a matter of fact, it has been extensively used in many statistical and economic applications. Unfortunately, a very unattractive property of this model in its multinomial situation is independence of irrelevant alternative (IIA) property. Due to such limitation, a number of alternative possible specifications have been proposed in the literature. This paper investigates some of the important alternative specifications of the logit model along with their merits, demerits, estimation techniques, testing procedures and attempts to advocate about the superiority of the existing specifications for the users. Interestingly, we found no such absolutely superior model to be used as an alternative to the logit model. However, generalized extreme value (GEV) model and multinomial probit model have been found to be very promising and much better than other models.

Probabilistic choice and stochastic dominance

This paper presents an axiomatic model of probabilistic choice under risk. In this model, when it comes to choosing one lottery over another, each alternative has a chance of being selected, unless one lottery stochastically dominates the other. An individual behaves as if he or she compares lotteries to a reference lottery—the least upper bound or the greatest lower bound in terms of stochastic dominance. The proposed model is compatible with several well-known violations of expected utility theory such as the common ratio effect and the violations of betweenness. Necessary and sufficient conditions for the proposed model are completeness, weak stochastic transitivity, continuity, common consequence independence, outcome monotonicity, and odds ratio independence.