Multinomial Choice Model Research Articles

An Optimal Greedy Heuristic with Minimal Learning Regret for the Markov Chain Choice Model

We study the assortment optimization problem and show that local optima are global optima for all discrete choice models that can be represented by the Markov Chain model. We develop a forward greedy heuristic that finds an optimal assortment for the Markov Chain model and runs in $O(n^2)$ iterations. The heuristic has performance bound $1/n$ for any regular choice model which is best possible among polynomial heuristics. We also propose a backward greedy heuristic that is optimal for Markov chain model and requires fewer iterations. Numerical results show that our heuristics performs significantly better than the estimate then optimize method and the revenue-ordered assortment heuristic when the ground truth is a latent class multinomial logit choice model. Based on the greedy heuristics, we develop a learning algorithm that enjoys asymptotic optimal regret for the Markov chain choice model and avoids parameter estimations, focusing instead on binary comparisons of revenues.

Semi-parametric estimation of multinomial choice model with unobserved heterogeneity

We propose a semi-parametric method for estimating the multinomial choice model using cyclical monotonicity moment inequalities. In our semiparametric approach, we do not specify the parametric distribution for the utility shocks, thus accommodating a wide variety of substitution patterns among alternatives. Compared with the conditional likelihood estimation method proposed by Chamberlain and the method proposed by Shi, Shum, and Song, simulations show that our method has some advantages in terms of mean bias, standard deviation and root mean squared error.

Preference heterogeneity, neighbourhood effects and basic services: logit kernel models for farmers’ climate adaptation in Ethiopia

Climate change adaptations by farmers are usually analysed with multinomial choice models, which ignore heterogeneity and ‘mixing’ across alternatives and individuals. Moreover, not enough attention is devoted to basic utilities other than extension services. Aimed at a reassessment that accounts for these issues, this paper formulates conditional and mixed logit (logit kernel) models with/without neighbourhood effects. In particular, a spatial logit kernel allows capturing behavioural differences and interdependence between neighbours. The analysis was based on a survey covering 162 villages of the Ethiopian Nile basin, with 50 farm households—multistage stratified randomly sampled—in each of 20 districts (woredas). Supplementary information concerned linear programming solutions on adaptation choice attributes in smallholder farming areas, under two scenarios. Lastly, cross-district aid emergency allocation priorities for food security and agriculture, among others, served as yardsticks for comparison with prevailing adjustment decisions and location characteristics. Closeness to farms with more educated farmers and larger plot sizes turned out to increase the likelihood of a household opting to sell livestock and land along with combined measures of farmland enhancement. Logit kernel outperformed conditional logit in explanatory power, and random parameters highlighted individual and group heterogeneity in preferences. Access to electricity, healthcare, and reliable and safe water supply strengthen farmers’ ability to respond to climate change. Specific adaptation measures can contribute in turn to improve the capacity of rural communities to mitigate the severity of health and nutrition crises. By contrast, in woredas hit by recurrent epidemics and droughts, many farmers appear to be unable to resort even to basic adaptation measures, such as planting of new trees. This prompts an additional need for institutional support and infrastructure development.

Evolution of fishing capacity in a Mediterranean fishery in the first two decades of the 21st c.

The viability of Mediterranean marine fisheries is increasingly under threat due to the low biological productivity of overexploited stocks, low economic performance of the fishing units, and offer of unattractive jobs, among other. This has resulted in a decrease of 30% in the number of fishing units active in European Union Mediterranean fisheries over the period 1995–2016. The detailed causes for this decline are investigated here based on an analysis of the entry/exit dynamics of the entire fleet having operated in Catalonia (NW Mediterranean) as a case study. The decision made by owner-operators, in terms of entering, remaining or exiting the fishery, of 1195 fishing units in the period 2000–2018 was analysed. The results show that fishing vessels have a high probability (95%) of remaining in the fishery and very low probability of entering (<1%). The exit rate was estimated at 4.5% annually, resulting in a reduction of 42% of the fleet size over the study period, from 894 active vessels at the beginning of 2000 to 518 at the end of 2018. A statistical analysis of the factors conditioning the entry/exit dynamics by means of a multinomial choice model showed that the age of the vessel, the value of landings, the amount of decommission aid offered by the local fisheries management administration and a proxy variable for fuel costs were significant explanatory variables. The study concludes that the fleet is likely to continue to shrink, without immediate stock or ecosystem conservation benefits, unless bold steps to reformulate fisheries management in the Mediterranean are taken.

Price Discounts and Customized Product Assortment under Multinomial Logit Choice Model: A Robust Approach

With increasing availability of consumer data and rapid advancement and applications of technologies, online retailers are gaining better knowledge of shopping behavior and preferences of their customers. Thus more and more retailers are providing customized product assortment to better match the needs of customers and generate more sales. In this paper, we study a two-stage revenue management model where a retailer decides non-customized price discounts at stage one due to fairness consideration and customized product assortment at stage two (upon the arrival of customers) under the multinomial logit choice model. We employ a robust approach for the joint discounts and customized assortment optimization problem to handle data uncertainty for estimating customer preferences and distribution of different customer segments. We analyze the structural properties of the problems and propose efficient computational methods to solve the problems with/without cardinality constraint on the assortment. In certain cases, our algorithm converges at a superlinear rate. When there is a cardinality constraint on the assortment, we find the retailer should offer deeper discounts as the constraint becomes more restrictive. We also provide some discussion on the value of our robust solution and the extension when the customer discount sensitivity function is also uncertain. Finally, our extensive numerical study shows that the solutions under the robust approach perform very well compared to the one assuming accurate information and has robustness when there is uncertainty.

Bus headway optimization with consumer surplus as a measure of societal benefit

ABSTRACT This paper derives the square root bus dispatch optimization developed by Newell from consumer surplus rather than the original cost minimization function. We then extend the model to consider dispatch-variant demand and outline its property relative to the original model by Newell. Demand elasticity is introduced via a multinomial logit mode choice model. Results are tested for City of Edmonton mode choice and ridership. The sensitivity of the function to wait time cost and passenger demand is tested. For the observed passenger demand and value of travel time, our analysis suggests there is a portion of riders who are captive and will suffer increasing wait time costs, but many passengers will make the choice to utilize other modes of travel when faced with increasing bus headways.

Social–ecological feedbacks drive spatial exploitation in a northern freshwater fishery: A halo of depletion

Abstract Freshwater fisheries are complex social–ecological systems spatially structured by coupled feedbacks between people and nature. Spatial exploitation dynamics depend on angler preferences for multiple attributes that influence their site choices. Anglers then reciprocally impact local fish populations through size‐selective catch and harvest. Thus, feedbacks among angler site choices, their capture efficiency (i.e. catchability) and fish population dynamics permeate through whole landscapes. We studied the coupled feedbacks and effects of spatial exploitation in an iconic northern freshwater fishery of conservation concern. Specifically, we evaluated several coupled feedbacks in the spatially structured Yukon lake trout fishery using a Bayesian multinomial choice model fitted to onsite interviews and fishery‐independent population assessments to identify whether: (a) trip context (day vs. multi‐day trips) shaped angler preferences and site choices, (b) catch‐based quality was influenced by a size–numbers trade‐off and density‐dependent catchability and (c) fish population structure was associated with the gravity of resource usage resulting from spatial exploitation. Overall, we found that angler site choices were shaped by preferences for multiple characteristics including travel time and catch‐based quality. Angler preferences also varied with trip contexts—for example, anglers on day trips were less willing to travel than anglers on multi‐day trips. We detected strong density‐dependent catchability, which led to hyperstable catches and relatively few anglers dominated most of the catch. There was a strong demographic trade‐off between lake trout body size and abundance that appeared to dynamically interact with anglers' size‐selective preferences for larger lake trout. Coupled feedbacks among angler site choices, size‐selective and hyperstable catches, and density‐dependent growth and survival appeared to structure spatial exploitation patterns leading to a halo of depletion in fish body sizes and fishing quality near urban centres. Synthesis and applications. Feedbacks between fish and anglers affected spatial exploitation patterns leading to a halo of depletion in Yukon lake trout. We recommend fisheries' managers consider the size, distance and behaviours of nearby angler communities using measures of gravity to craft policies aligning expected resource usage with spatial conservation risks. Such approaches may help managers balance stakeholder needs with conservation targets across whole ecosystems.

A computationally fast estimator for semiparametric multinomial choice model

In this article, based on cyclical monotonicity moment inequalities implied by the random utility choice model, we propose a computationally fast estimator for semiparametric multinomial choice models. The term semiparametric refers to the fact that we do not specify a particular functional form for the error term in the random utility function. The proposed estimators are consistent. Comparing with the estimators developed by the cyclic monotonicity method, simulations show the estimators we proposed have great advantages on the running time.

Whether, when and which: Modelling advanced seat reservations by airline passengers

Motivated by the growing importance of ancillary revenues in the airline industry, we propose a statistical model for Advanced Seat Reservation (ASR). We focus on the questions of whether, when and which seats are selected by passengers. To answer these questions, we employ a discrete time duration model, combined with a multinomial choice model with varying consideration set. Unknown smooth covariate effects are used, along with seat-specific random effect terms for seat selection. The model is applied to a rich dataset of 485,279 bookings on five intercontinental routes, extracted from the complete booking database of a major European airline. We find strong evidence of ‘middle seat avoiding’ and ‘front seat preferring’ effects, along with substantial additional seat-specific heterogeneity. We also show that the probability of making an ASR depends on its price in relation to the ticket price, the distribution channel, the number of days to departure and seasonal effects. These and other insights allow for product differentiation and variable pricing in ASR for each and every seat. In addition, simple variations of the statistical model can also be used for other ancillary products—such as on-board dining and preferential baggage checking—that are purchased in the same way as ASR.

Whether, When and Which: Modelling Advanced Seat Reservations by Airline Passengers

Motivated by the growing importance of ancillary revenues in the airline industry, we propose a statistical model for Advanced Seat Reservation (ASR). We focus on the questions of whether, when and which seats are selected by passengers. To answer these questions, we employ a discrete time duration model, combined with a multinomial choice model with varying consideration set. Unknown smooth covariate effects are used, along with seat-specific random effect terms for seat selection. The model is applied to a rich dataset of 485,279 bookings on five intercontinental routes, extracted from the complete booking database of a major European airline. We find strong evidence of ‘middle seat avoiding’ and ‘front seat preferring’ effects, along with substantial additional seat-specific heterogeneity. We also show that the probability of making an ASR depends on its price in relation to the ticket price, the distribution channel, the number of days to departure and seasonal effects. These and other insights allow for product differentiation and variable pricing in ASR for each and every seat. In addition, simple variations of the statistical model can also be used for other ancillary products—such as on-board dining and preferential baggage checking—that are purchased in the same way as ASR.

Incorporating Product Choice into Transit Fare Policy Scenario Models

Customer fare product choices can affect both ridership and revenue, so they are strategically important for transit agencies. Nearly all major agencies offer choices between pay-per-use and pass products, and with each potential fare change, agencies face decisions about whether to modify pass “multiples”—the number of rides needed to “break even” on a pass purchase. However, the simple elasticity spreadsheet models often used to analyze the potential ridership and revenue impacts of fare changes make little or no adjustment for shifts in fare product choices. This paper reviews different options for incorporating product choice into fare policy scenario models, and it presents a ridership and revenue prediction procedure that combines a multinomial logit fare product choice model with the logic of an elasticity spreadsheet model. This combination facilitates evaluation of complex fare changes that are likely to alter fare product market shares while maintaining much of the flexibility and simplicity of a traditional spreadsheet model. Additionally, the proposed model uses only preexisting, revealed-preference automated fare collection data rather than requiring customer surveys. The proposed model is demonstrated using examples at the Chicago Transit Authority (CTA). The CTA experienced a large shift from passes to pay-per-use following a fare change in 2013, illustrating the potential value of accounting for fare product choices in fare scenario evaluation.

Estimating Multinomial Choice Models with Unobserved Choice Sets

This paper proposes a new approach to estimating multinomial choice models when each consumer’s actual choice set is unobservable but could be bounded by two known sets, i.e., the largest and smallest possible choice sets. The bounds on choice set, combined with a monotonicity property derived from utility maximization, imply a system of inequality restrictions on observed choice probabilities that could be used to identify and estimate the model. A key insight is that the identification of random utility model can be achieved without exact information on consumers’ choice sets, which generalizes the identification result of the standard multinomial choice model. The effectiveness of the proposed approach is demonstrated via a range of Monte Carlo experiments as well as an empirical application to consumer demand for potato chips using household scanner data.

The Impact of Zoning and Built Environment Characteristics on Transit, Biking, and Walking

This study furthers existing research on the link between the built environment and travel behavior, particularly mode choice (auto, transit, biking, walking). While researchers have studied built environment characteristics and their impact on mode choice, none have attempted to measure the impact of zoning on travel behavior. By testing the impact of land use regulation in the form of zoning restrictions on travel behavior, this study expands the literature by incorporating an additional variable that can be changed through public policy action and may help cities promote sustainable real estate development goals. Using a unique, high-resolution travel survey dataset from Denver, Colorado, we develop a multinomial discrete choice model that addresses unobserved travel preferences by incorporating sociodemographic, built environment, and land use restriction variables. The results suggest that zoning can be tailored by cities to encourage reductions in auto usage, furthering sustainability goals in transportation.

Nonseparable multinomial choice models in cross-section and panel data

Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identification of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimensional unobserved heterogeneity with cross-section and panel data. We show that derivatives of choice probabilities with respect to continuous attributes are weighted averages of utility derivatives in cross-section models with exogenous heterogeneity. In the special case of random coefficient models with an independent additive effect, we further characterize that the probability derivative at zero is proportional to the population mean of the coefficients. We extend the identification results to models with endogenous heterogeneity using either a control function or panel data. In time stationary panel models with two periods, we find that differences over time of derivatives of choice probabilities identify utility derivatives “on the diagonal,” i.e. when the observed attributes take the same values in the two periods. We also show that time stationarity does not identify structural derivatives “off the diagonal” both in continuous and multinomial choice panel models.

시나리오기법 및 선택실험법 기반 한국 전기차 시장 수요예측 연구

This study presents a scenario-based, long-term forecasting model of electric vehicle (EV) sales. A simulated choice experiment using the multinomial hybrid choice model was estimated, where consumer utility was dependent on vehicle type, total cost of ownership (TCO), and personal variables. Results show that lower TCO, lower range-anxiety, and greater environmental concern lead to greater choice probability for EVs. Using the parameters of the TCO variable and the intercept, an initial probability of choosing an EV over an internal combustion engine car was derived. To this initial estimate, macro factors were incorporated, including charging infrastructure, oil prices, battery technology, and government incentives. Charging infrastructure was modeled as the convenience factor; battery technology and government incentives were modeled as affecting vehicle costs; and oil prices as affecting the operating cost. Based on long-term changes in the macro factors, three scenarios were selected: the reference scenario, the low-battery cost scenario, and the high oil price scenario. The forecasting model shows that long-term changes in oil prices are much more important than long-term changes in battery cost in terms of determining the adoption of electric vehicles. This is because fuel cost, over time, has a bigger impact on TCO, whereas the importance of battery prices on TCO decreases. Results also indicate that convenience is the main inhibitor of EV adoption, implying that the government’s policy should transition from providing cash-back incentives to building better charging infrastructure.

Estimating Elasticities for Freight Transport Using a Network Model: An Applied Methodological Framework

This paper presents a general framework that can be used to estimate direct and cross elasticities for freight transport using a network model. This methodology combines operational research (network assignments in a geographical information system) with more classical econometrics (multinomial logit choice models). The application of the method to a real-world case is illustrated by a simple model that relies on the generalized cost of transport as the only explanatory variable in the utility function. The methodological framework allows, however, for the implementation of more complex functions. Beside the generalized cost functions for road, rail and inland waterways transport, the network model needs origin-destination matrixes and digitized networks. They are imported from ETIS Plus, a European transport policy information system. A set of direct and cross elasticities is presented. The estimated values are obtained using two methods: the first computes standard elasticities, while the second estimates arc elasticities. Figures are presented for Europe and for a large region around the Benelux countries, where more competition exists between the three modes of interest.

Finland: Venator – TiO2

Many strategic decisions made by firms involve a choice among several discrete alternatives. International Business (IB) scholars are often interested in modelling the factors that potentially influence these (multinomial) choices: these factors might include not only characteristics of the firms making the choices but also attributes of the alternative choices. This paper provides a succinct and intuitive introduction to the possible applications of multinomial choice models in IB research. We briefly outline the theory behind discrete choice modelling, and then explain how multinomial choice models may be estimated (including how the datasets need to be formatted) and how the significance of the coefficient estimates as well as the diagnostic statistics may be tested and interpreted.

Analysis of high-speed rail and airline transport cooperation in presence of non-purchase option

We study cooperation between the airline and high-speed rail (HSR) sectors by formulating their joint profit as a maximization problem using a multinomial logit choice model in a three-node setting. We allow the non-purchase option as an outside option available to consumers. The demand for each choice is not only a function of the price but also the service quality, such as the total trip time, frequency of service, and ease of connecting from the hub to a nearby HSR station. As a result, the following findings are presented. First, regardless of the service quality of either sector and the non-purchase option, cooperation decreases the total volume of the domestic market of a country. Second, when the attractiveness of the outside option is high, the HSR and air sectors can prevent a large reduction in the total volume by cooperation in the connecting market. However, this is not the case in the domestic market. Third, if the non-purchase quality in the domestic market is high, then cooperation increases the social welfare of the whole market. If the non-purchase quality is low, then cooperation increases the welfare of the whole market only in cases where the number of potential customers in the connecting market is relatively large. We also show the effect of improving air–rail service quality on each market share and on the total profit.

Reading between the Stars: Understanding the Effects of Online Customer Reviews on Product Demand

Problem definition: Many studies have examined quantitative customer reviews (i.e., star ratings) and found them to be a reliable source of information that has a positive effect on product demand. Yet the effect of qualitative customer reviews (i.e., text reviews) on demand has been less thoroughly studied, and it is not known whether (or how) the sentiment expressed in text reviews moderates the influence of star ratings on product demand. We are therefore led to examine how the interplay between review sentiment and star ratings affects product demand. Academic/practical relevance: Consumer perceptions of product quality—and how they are shared via customer reviews—are of extreme relevance to the firm, but we still do not understand how product demand is affected by the quantitative and qualitative aspects of customer reviews. Our paper seeks to fill this critical gap in the literature by analyzing star ratings, the sentiment of customer reviews, and their interaction. Methodology: Using 2002–2013 data for the US automobile market, we investigate empirically the impact of star ratings and review sentiment on product demand. Thus, we estimate an aggregated multinomial choice model after performing a machine learning–based sentiment analysis on the entire corpus of customer reviews included in our sample. We take advantage of a quasiexogenous shock to establish a causal link between online reviews and product demand. Results: We find robust empirical evidence that (i) review sentiment and star ratings both have a decreasingly positive effect on product demand and (ii) the effect (on demand) of their interaction suggests that the two components of reviews are complements. Positive sentiments in text reviews increase the positive effect of ratings when the effect of ratings is decidedly positive while they also compensate for the tendency of consumers to discount extremely high star ratings. Managerial implications: The firm should pay greater attention to quantitative and qualitative customer reviews so that it can better understand how consumers perceive the quality of its offerings.

Tracking the Impact of Media on Voter Choice in Real Time: A Bayesian Dynamic Joint Model

ABSTRACTCommonly used methods of evaluating the impact of marketing communications during political elections struggle to account for respondents’ exposures to these communications due to the problems associated with recall bias. In addition, they completely fail to account for the impact of mediated or earned communications, such as newspaper articles or television news, that are typically not within the control of the advertising party, nor are they effectively able to monitor consumers’ perceptual responses over time. This study based on a new data collection technique using cell-phone text messaging (called real-time experience tracking or RET) offers the potential to address these weaknesses. We propose an RET-based model of the impact of communications and apply it to a unique choice situation: voting behavior during the 2010 UK general election, which was dominated by three political parties. We develop a Bayesian zero-inflated dynamic multinomial choice model that enables the joint modeling of: the interplay and dynamics associated with the individual voter's choice intentions over time, actual vote, and the heterogeneity in the exposure to marketing communications over time. Results reveal the differential impact over time of paid and earned media, demonstrate a synergy between the two, and show the particular importance of exposure valence and not just frequency, contrary to the predominant practitioner emphasis on share-of-voice metrics. Results also suggest that while earned media have a reducing impact on voting intentions as the final choice approaches, their valence continues to influence the final vote: a difference between drivers of intentions and behavior that implies that exposure valence remains critically important close to the final brand choice. Supplementary materials for this article are available online.