Irrelevant Alternatives Property Research Articles

Minimax decision rules for planning under uncertainty: Drawbacks and remedies

It is common to use minimax rules to make planning decisions when there is great uncertainty about what may happen in the future. Using minimax rules avoids the need to determine probabilities for each future scenario, which is an attractive feature in many public sector settings. However there are potential problems in the application of a minimax approach. In this paper our aim is to give guidance for planners considering a minimax approach, including minimax regret which is one popular version of this. We give an analysis of the behaviour of minimax rules in the case with a finite set of possible future scenarios. Minimax rules will have sensitivity to the choice of a small number of scenarios. When regret-based rules are used there are also problems arising since the independence of irrelevant alternatives property fails, which can lead to opportunities to game the process. We analyse these phenomena considering cases where the decision variables are chosen from a convex set in Rn, as well as cases with a finite set of decision choices. We show that the drawbacks of minimax regret hold even when restrictions are placed on the problem setup, and we show how working with a structured set of scenarios can ameliorate the difficulty of having a final decision depend on the characteristics of just a handful of extreme scenarios.

Disaggregated approach to urban trip distribution: a comparative analysis between artificial neural networks and discrete choice models

Discrete choice models have been used over the years in disaggregated approaches to forecast destination choices. However, there are important constraints in some of these models that pose obstacles to using them, such as the Independence of Irrelevant Alternatives (IIA) property in the Multinomial Logit model, the need to assume specific structures and high calibration times, depending on the complexity of the case being evaluated. However, some of these mentioned constraints could be mitigated using Mixed Models or Nested Logit. Therefore, this paper proposes a comparative analysis between the Artificial Neural Network (ANNs), the Multinomial and Nested Logit models for disaggregated forecasting of urban trip distribution. A case study was conducted in a medium-sized Brazilian city, Santa Maria (RS), Brazil. The data used come from a household survey, prepared for the Urban Mobility Master Plan. For the sake of comparison, hit rates and frequency of trip distribution distances were analyzed, showing that ANNs can be as efficient as the Discrete Choice models for disaggregated forecasting of urban trip destination without, however, assuming some constraints. Finally, based on the results obtained, the efficiency of ANNs is observed for predicting alternatives with a low number of observations. They are important tools for obtaining Origin-Destination matrices from incomplete sample matrices or with a low number of observations. However, it is important to mention that discrete choice models can provide important information for the analyst, such as statistical significance of parameters, elasticities, subjective value of attributes, etc.

Cross-Category Retailing Management: Substitution and Complementarity

Problem definition: This paper studies pricing and assortment management for cross-category products, a common practice in brick-and-mortar retailing and e-tailing. Academic/practical relevance: We investigate the complementarity effects between the main products and the secondary products, in addition to the substitution effects for products in the same category. Methodology: In this paper, we develop a multistage sequential choice model, under which a consumer first chooses a main product and then selects a secondary product. The new model can alleviate the restriction of the independence of irrelevant alternatives property and allows more flexible substitution patterns and also takes into account complementarity effects. Results: We characterize the impact of the magnitude of complementarity effects on pricing and assortment management. For the problems that are hard to solve optimally, we propose simple heuristics and establish performance guarantee. In addition, we develop easy-to-implement estimation algorithms to calibrate the proposed sequential choice model by using sales data. Managerial implications: We show that ignoring or mis-specifying complementarity effects may lead to substantial losses. The methodologies on modeling, optimization, and estimation have potential to make an impact on cross-category retailing management.

A P-Hub Location Problem for Determining Park-and-Ride Facility Locations with the Weibit-Based Choice Model

Park and ride (P&R) facilities provide intermodal transfer between private vehicles and public transportation systems to alleviate urban congestion. This study developed a mathematical programming formulation for determining P&R facility locations. A recently developed Weibit-based model was adopted to represent the traveler choice behavior with heterogeneity. The model’s independence of irrelevant alternatives (IIA) property was explored and used to linearize its nonlinear probability. Some numerical examples are provided to demonstrate a feature of the proposed mixed integer linear programing (MILP). The results indicate a significant impact of route-specific perception variance on the optimal P&R facility locations in a real-size transportation network.

Optimal bundle composition in competition for continuous attributes

We propose a model to design bundles’ composition under competition, quantifying its effect in terms of profit and market share in a game among competing firms. According to our literature review, no previous models on optimal bundle composition can handle the competition as we do in this paper. Besides, we explain how a firm designing multiple bundles with equal price obtains a replication of identical bundles and an artificially increased estimation of the firm’s profit and market share, which is a consequence of the well-known Independence of Irrelevant Alternatives Property. To mitigate this effect, we use the Constrained Multinomial Logit Model, which induces differentiation in composition through soft constraints that represent the minimum quantity of the attributes offered in bundles. Although this methodology helps, its use implies more effort to estimate its parameters; nevertheless, these are feasible to be assessed. Firms can use our model to identify the bundles in which they should focus their commercial efforts, given the characteristics of their consumers.

An Economist and a Psychologist Form a Line: What Can Imperfect Perception of Length Tell Us About Stochastic Choice?

Standard choice experiments are hampered by the fact that utility is either unknown or imperfectly measured by experimenters. As a consequence, the inferences available to researchers are limited. By contrast, we design a choice experiment where the objects are valued according to only a single attribute with a continuous measure and we can observe the true preferences of subjects. Subjects have an imperfect perception of the choice objects but can improve the precision of their perception with cognitive effort. Subjects are given a choice set involving several lines of various lengths and are told to select one of them. They strive to select the longest line because they are paid an amount that increases with the length of their choice. Our design allows us to observe the search history, the response times, and make unambiguous conclusions about the optimality of choices. We find a negative relationship between the demanding nature of the choice problems and the likelihood that subjects select the optimal lines. We also find a positive relationship between the demanding nature of the choice problems and the response times. However, we find evidence that sub-optimal choices are associated with longer response times than are optimal choices. This result appears to be consistent with Fudenberg, Strack, and Strzalecki (2018). Additionally, our experimental design permits a multi-nomial discrete choice analysis. Our results suggest that the errors in our data are better described as having a Gumbel distribution rather than a normal distribution. We also observe effects consistent with memory decay and attention. Finally, we find evidence that choices in our experiment exhibit the independence from irrelevant alternatives (IIA) property.

Consumer Choice with Consideration Set: Threshold Luce Model

This paper investigates the threshold Luce model, a recently proposed choice model with a threshold for the consideration-set formation. Under the threshold Luce model, consumers first form their consideration set: If an alternative with significantly low utility is dominated by another one, it will not be included in the consideration set. The threshold Luce model can alleviate the independence of irrelevant alternatives (IIA) property and allow more flexible substitution patterns. We characterize the optimal strategy and develop efficient solutions for price and assortment optimization problems. Under the threshold Luce model, the price competition may have zero, one, two, or infinite Nash equilibria, depending on the magnitude of the threshold effect. Moreover, we also develop an efficient estimation method to calibrate the threshold Luce model. Our numerical study on synthetic and real data sets shows that the new model can improve the goodness of fit and prediction accuracy of consumer choice behavior, which suggests the threshold effect should be taken into account in decision making.

Cross-Category Retailing Management: Substitution and Complementarity

This paper studies pricing and assortment management for cross-category products, a common practice in brick-and-mortar retailing and e-tailing. We investigate the complementarity effects between the main products and the secondary products, in addition to the substitution effects for products in the same category. In this paper, we develop a multi-stage sequential choice model, under which a consumer first chooses a main product and then selects a secondary product. The new model can alleviate the restriction of the independence of irrelevant alternatives (IIA) property, and allows more flexible substitution patterns and also takes into account complementarity effects. We characterize the impact of the magnitude of complementarity effects on pricing and assortment management. For the problems that are hard to solve optimally, we propose simple heuristics and establish performance guarantee. In addition, we develop easy-to-implement estimation algorithms to calibrate the proposed sequential choice model by using sales data. We show that ignoring or mis-specifying complementarity effects may lead to substantial losses. The methodologies on modeling, optimization and estimation have potential to make impact on cross-category retailing management.

Capturing correlation with a mixed recursive logit model for activity-travel scheduling

Representing activity-travel scheduling decisions as path choices in a time–space network is an emerging approach in the literature. In this paper, we model choices of activity, location, timing and transport mode using such an approach and seek to estimate utility parameters of recursive logit models. Relaxing the independence from irrelevant alternatives (IIA) property of the logit model in this setting raises a number of challenges. First, overlap in the network may not fully characterize perceptual correlation between paths, due to their interpretation as activity schedules. Second, the large number of states that are needed to represent all possible locations, times and activity combinations imposes major computational challenges to estimate the model. We combine recent methodological developments to build on previous work by Blom Västberg et al. (2016) and allow to model complex and realistic correlation patterns in this type of network. We use sampled choices sets in order to estimate a mixed recursive logit model in reasonable time for large-scale, dense time-space networks. Importantly, the model retains the advantage of fast predictions without sampling choice sets. In addition to estimation results, we present an extensive empirical analysis which highlights the different substitution patterns when the IIA property is relaxed, and a cross-validation study which confirms improved out-of-sample fit.

Discrete Choice Models for Commuting Interactions

An emerging quantitative spatial economics literature models commuting interactions by a gravity equation that is mathematically equivalent to a multinomial logit model. This model is widely viewed as restrictive because of the independence of irrelevant alternatives (IIA) property that links substitution behavior in response to changes in the attractiveness of choice alternatives to choice probabilities in a mechanistic way. This is relevant for counterfactual analysis. In this paper we examine the appropriateness of the commuting model from a theoretical as well as an empirical point of view. We show that conventional specification tests of the multinomial logit model are of limited use when alternative specific constants are used, as is common in the recent literature, and offer no information with respect to the validity of IIA. In particular, we show that maximum likelihood estimation of relevant nested logit model is impossible because the crucial parameters are not identified. We discuss cross-nested and mixed logit as alternatives. We argue that a comparison between predicted and actual changes in commuting flows in response to a change in the attractiveness of choice alternatives provides a more informative test for the validity of the multinomial logit model for commuting interaction and report the results of such a test – as well as others – for data referring to Copenhagen.

Utility independence versus IIA property in independent probit models

In the field of conjoint choice analysis consumer preferences are commonly estimated via multinomial logit (MNL) or multinomial probit (MNP/IP) models. The basic assumption of both the MNL model and the independent probit (IP) model is independence of utilities between alternatives, also referred to as IID assumption. Since the MNL model in addition exhibits the Independence of Irrelevant Alternatives (IIA) property, it is often directly concluded that the IP model likewise exhibits the IIA property, thereby relating IID to IIA. However, this is not true considering Luce’s definition of the IIA property. The objective of this paper is twofold: First, we clarify that IID does not imply IIA in the specific context of the IP model. Second, we work out the sources for the non-proportional shifting of the ratio of choice shares that distinguishes the IP model from the MNL model. Accordingly, we first theoretically review the true property of the IP model and subsequently illustrate with a conjoint example that the IP model does not exhibit the IIA property. In addition, we provide a case-by-case analysis to explain the non-proportional shifting of choice shares in the substitution pattern of the IP model and work out the principles for that non-proportional shifting mechanism.

On the similarities between random regret minimization and mother logit: The case of recursive route choice models

This paper focuses on the comparison of the random regret minimization (RRM) and mother logit models for analyzing the choice between alternatives having deterministic attributes. The mother logit model allows utilities of a given alternative to depend on attributes of other alternatives. It was designed to relax the independence from irrelevant alternatives (IIA) property while keeping the random terms independently and identically distributed extreme value distributed (McFadden et al., 1978).We adapt and extend the RRM model proposed by Chorus (2014) to the case of recursive logit (RL) route choice models (Fosgerau et al., 2013). We argue that these RRM models can be cast as mother logit models and we define such models that are equivalent to the RRM ones considered in this paper. The results show that one of the RRM models and its mother logit equivalent has the best out-of-sample fit indicating that utility functions based on attribute differences best explains the choices in our application.

Presenting the Independence of Irrelevant Alternatives property in a first course on logit modeling

The brief treatment of IIA offered in most introductory courses and textbooks leaves a number of important points unsaid, and may paint an incomplete and misleading picture of its nature. This note supplements such treatments with additional detail. Specifically, we first present three causes or types of IIA violations, and describe some common ways in which they occur. We then present some typical tests/remedies for IIA violations, indicating which types of violation they are best suited to identify, and how they “work” in terms of remedying a violation. We close with some additional pertinent observations.

Multinomial choice models based on Archimedean copulas

Multinomial choice models are used for the analysis of unordered, mutually exclusive choice alternatives. Conventionally used multinomial choice models are the multinomial logit, nested logit, multinomial probit and random parameters logit models. This paper develops multinomial choice models based on Archimedean copulas. In contrast to the multinomial logit and nested logit models, no independence of irrelevant alternatives property is implied. Moreover, copula-based multinomial choice models are more parsimonious than the multinomial probit and random parameters logit models, which makes them attractive from a computational point of view and makes them particularly suitable for prediction purposes. When the number of alternatives becomes large, additional complexity can be introduced using nested Archimedean copulas. Nested structures can often be motivated from individual behavior. The paper also considers an empirical application to travel mode choice. It is found that copula-based multinomial choice models provide a good compromise between fit and parsimony.

A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction.

Public preference for the attributes of the marina port in Korea: a choice experiment study

As of late, the Korean government needs quantitative information on economic feasibility analysis for marina port development projects. This study applies a choice experiment to measure public preference for the attributes of marina port in Korea. We consider the trade-offs between price and four attributes of marina port (capacity, access, waterfront, and program) for selecting a preferred alternative and elicit the marginal willingness to pay (MWTP) estimates for each attribute. We also test whether irrelevant alternatives property for the estimation model holds and compare the estimation results of the multinomial logit (MNL) and the nested logit (NL) models. The results show that the NL model outperforms the MNL model. In the NL model, MWTPs for increasing the level of a waterfront from promenade to both promenade and rest area and for the provision of marine leisure experience program are KRW13 384 (USD11.8) and KRW17 937 (USD15.8), respectively. This study is expected to provide policymakers with quantitative information for evaluating marina port construction projects in Korea.

Choice Based Revenue Management for Parallel Flights

This paper describes a revenue management problem of a major airline that operates in a very competitive market involving two major hubs and having more than 30 parallel daily flights. We consider choice based stochastic assortment optimization problems to maximize the expected revenue for the airline. The inputs include models of booking arrival rates, competitor assortment selection probabilities, customers' booking choices among the airline's own flights as well as competitors' flights, booking-to-ticketing conversion probabilities, and go-show and no-show probabilities. We build a variety of booking choice models to incorporate unobserved heterogeneous customer preferences for different departure times. The way departure time preferences are modeled dramatically affects price sensitivity estimates, and therefore the modeling of heterogeneous departure time preferences matters. We also show that customer choice behavior exhibits discontinuities, with much greater demand for the cheapest alternative than for the second cheapest alternative even when the price difference is small, and much greater demand for fully refundable tickets than almost fully refundable tickets. We formulate a deterministic (fluid) optimization problem corresponding to each of the booking choice models, and we show that in some cases these problems can be solved efficiently even when the discontinuities cause violation of the independence from irrelevant alternatives property. The resulting solutions are used to determine assortment selection policies for the stochastic problem. Simulation studies show that several of these policies generate significantly more revenue than the airline's existing policy, and that the improved performance of these policies is robust with respect to misspecification errors as well as with respect to errors in parameter estimates.

Characterizing Household Vehicle Fleet Composition and Count by Type in Integrated Modeling Framework

There has been considerable interest, and consequent progress, in the modeling of household vehicle fleet composition and utilization in the travel behavior research domain. The multiple discrete-continuous extreme value (MDCEV) model is a modeling approach that has been applied frequently to characterize this choice behavior. One key drawback of the MDCEV modeling methodology is that it does not provide an estimate of the count of vehicles in each vehicle type alternative represented in the MDCEV model. Moreover, the classic limitations of the multinomial logit model, such as violations of the independence of irrelevant alternatives property in the presence of correlated alternatives and the inability to account for random taste variations, apply to the MDCEV model as well. A new methodological approach, developed to overcome these limitations, is applied in this paper to model vehicle fleet composition and count in each body type. The modeling methodology involves tying together a multiple discrete-continuous probit (MDCP) model and a multivariate count (MC) model capable of estimating vehicle counts in vehicle type categories considered by the MDCP model. The joint MDCP-MC model system was estimated by using a Greater Phoenix, Arizona, travel survey data set. The joint model system was found to offer behaviorally intuitive results and to provide superior goodness of fit in comparison with an independent model system that ignores the jointness between the MDCP component and the MC component.

A latent class generalised nested logit model and its application to modelling carrier choice with market segmentation

This article develops a new latent class (LC) model with a generalised nested logit (GNL) formulation to enhance the methodology of market segmentation analysis. The standard generalised nested logit (or the cross-nested logit model) is a special case of the latent class generalised nested logit model (LCGNL) that accounts for heterogeneity in individuals’ preferences by a number of segments and simultaneously identifies segment sizes and individual profiles. In addition, the LCGNL model allows flexible substitution patterns among alternatives. This extends the standard LC model with the multinomial logit formulation, such that the independence from irrelevant alternatives property does not hold within segments. The proposed model was used to identify potential segments of travellers’ preferences towards air and bus carriers. The estimation results of the LCGNL models indicate that degrees of competition vary across carriers and that differential sensitivity in preference parameters exists between segments. The LCGNL model outperforms the other models; therefore, it is a better approach for analysing carrier choice behaviour.

Analysis of driver injury severity in rural single-vehicle crashes

Rural roads carry less than fifty percent of the traffic in the United States. However, more than half of the traffic accident fatalities occurred on rural roads. This research focuses on analyzing injury severities involving single-vehicle crashes on rural roads, utilizing a latent class logit (LCL) model. Similar to multinomial logit (MNL) models, the LCL model has the advantage of not restricting the coefficients of each explanatory variable in different severity functions to be the same, making it possible to identify the impacts of the same explanatory variable on different injury outcomes. In addition, its unique model structure allows the LCL model to better address issues pertinent to the independence from irrelevant alternatives (IIA) property. A MNL model is also included as the benchmark simply because of its popularity in injury severity modeling. The model fitting results of the MNL and LCL models are presented and discussed. Key injury severity impact factors are identified for rural single-vehicle crashes. Also, a comparison of the model fitting, analysis marginal effects, and prediction performance of the MNL and LCL models are conducted, suggesting that the LCL model may be another viable modeling alternative for crash-severity analysis.