A class of RUM choice models that includes the model in which the utility has logistic distributed errors

Robust maximum capture facility location under random utility maximization models

The objective of this study is to understand how senders choose shipping services for different products, given the availability of both emerging crowd-shipping ( CS) and traditional carriers in a logistics market. Using data collected from a United States (U.S.) survey, Random Utility Maximization (RUM) and Random Regret Minimization (RRM) models have been employed to reveal factors that influence the diversity of decisions made by senders. Shipping costs, along with additional real-time services such as courier reputations, tracking info, e-notifications, and customized delivery time and location, have been found to have remarkable impacts on senders’ choices. Interestingly, potential senders were willing to pay more to ship grocery items such as food, beverages, and medicines by CS services. Moreover, the real-time services have low elasticities, meaning that only a slight change in those services will lead to a change in sender behavior. Finally, data-science techniques were used to assess the performance of the RUM and RRM models and found to have similar accuracies. The findings from this research will help logistics firms address potential market segments, prepare service configurations to fulfill senders’ expectations, and develop effective business operations strategies.

On the robustness of efficient experimental designs towards the underlying decision rule

BackgroundDual eligibles, persons who qualify for both Medicare and Medicaid coverage, often receive poorer quality care relative to other Medicare beneficiaries.ObjectivesTo determine whether dual-eligibles are discharged to lower quality post-acute skilled nursing facilities (SNFs) compared to Medicare-only beneficiaries.Research DesignFollowing the random utility maximization (RUM) model, we specified a discharge function using a conditional logit model and tested how this discharge rule varied by dual-eligibility status.Subjects692,875 Medicare fee-for-service patients (22% duals) who were discharged for Medicare paid SNF care between July 2004 and June 2005.MeasuresMedicare enrollment and the Medicaid Analytic Extract files were used to determine dual-eligibility. The proportion of Medicaid patients and nursing staff characteristics provided measures of SNF quality.ResultsDuals are more likely to be discharged to SNFs with a higher share of Medicaid patients and fewer nurses. These results are robust to estimation with an alternative sub-sample of patients based on primary diagnoses, propensity of being dual-eligible, and likelihood of remaining in the nursing home.ConclusionsDisparities exist in access to quality SNF care for duals. Strategies to improve discharge planning processes are required to redirect patients to higher quality providers, regardless of Medicaid eligibility.

Consumer preferences for alternative fuel vehicles: Comparing a utility maximization and a regret minimization model

This research aims to understand the park-and-ride (PNR) lot choice behaviour of users i.e., why PNR user choose one PNR lot versus another. Multinomial logit models are developed, the first based on the random utility maximization (RUM) concept where users are assumed to choose alternatives that have maximum utility, and the second based on the random regret minimization (RRM) concept where users are assumed to make decisions such that they minimize the regret in comparison to other foregone alternatives. A PNR trip is completed in two networks, the auto network and the transit network. The travel time of users for both the auto network and the transit network are used to create variables in the model. For the auto network, travel time is obtained using information from the strategic transport network using EMME/4 software, whereas travel time for the transit network is calculated using Google’s general transit feed specification data using a backward time-dependent shortest path algorithm. The involvement of two different networks in a PNR trip causes a trade-off relation within the PNR lot choice mechanism, and it is anticipated that an RRM model that captures this compromise effect may outperform typical RUM models. We use two forms of RRM models; the classical RRM and µRRM. Our results not only confirm a decade-old understanding that the RRM model may be an alternative concept to model transport choices, but also strengthen this understanding by exploring differences between two models in terms of model fit and out-of-sample predictive abilities. Further, our work is one of the few that estimates an RRM model on revealed preference data.

This chapter provides an overview of the random utility maximisation (RUM) model, reviewing its assumptions and delving into its theoretical foundations. We explore the multinomial logit (MNL) model, which is widely used in DCE literature due to its many advantages. These include its robustness, ease of estimation, and straightforward interpretation, with closed-form choice probabilities that simplify calculations. We also review advanced specifications of the mixed logit model, including the random parameters logit (RP-MXL) and latent class (LC-MXL) models, and walk you through the most common goodness of fit models used in DCE research.

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright © 2000 John Wiley & Sons, Ltd.

This chapter introduces probability theory as a system of models, based on measure theory, of some real-world phenomena. The models are measure spaces of total measure 1 and usually have certain distinguished measurable functions defined on them. Section 1 begins by establishing the measure-theoretic framework and a short dictionary for passing back and forth between terminology in measure theory and terminology in probability theory. The latter terminology includes events, random variables, mean, probability distribution of a random variable, and joint probability distribution of several random variables. An important feature of probability is that it is possible to work with random variables without any explicit knowledge of the underlying measure space, the joint probability distributions of random variables being the objects of importance. Section 2 introduces conditional probability and uses that to motivate the mathematical definition of independence of events. In turn, independence of events leads naturally to a definition of independent random variables. Independent random variables are of great importance in the subject and play a much larger role than their counterparts in abstract measure theory. Examples at the end of the section indicate the extent to which functions of independent random variables can remain independent. The techniques in the examples are of use in the subject of statistical inference, which is introduced in Section 10. Section 3 states and proves the Kolmogorov Extension Theorem, a foundational result allowing one to create stochastic processes involving infinite sets of times out of data corresponding to finite subsets of those times. A special case of the theorem provides the existence of infinite sets of independent random variables with specified probability distributions. Section 4 establishes the celebrated Strong Law of Large Numbers, which says that the Cesaro sums of a sequence of identically distributed independent random variables with finite mean converge almost everywhere to a constant random variable, the constant being the mean. This is a theorem that is vaguely known to the general public and is widely misunderstood. The proof is based on Kolmogorov’s inequality. Sections 5–8 provide background for the Central Limit Theorem, whose statement and proof are in Section 9. Section 5 discusses three successively weaker kinds of convergence for random variables—almost sure convergence, convergence in probability, and convergence in distribution. Convergence in distribution will be the appropriate kind for the Central Limit Theorem. Section 6 contains the Portmanteau Lemma, which gives some equivalent formulations of convergence in distribution, Section 7 introduces characteristic functions as Fourier transforms of probability distributions, and Section 8 proves the Levy Continuity Theorem, which formulates convergence in distribution in terms of characteristic functions. Section 9 contains the statement and proof of the Central Limit Theorem, followed by some simple examples. This theorem is the most celebrated result in probability theory and has many applications in mathematics and other fields. Section 10 is a brief introduction to the subject of statistical inference, showing how the Central Limit theorem plays a role in practice through the $t$ test of W. S. Gosset.

In this paper we develop a general class of dynamic brand choice models, called Lightning Bolt (LB) models, which are consistent with the theory of random utility maximization of consumer choice behavior. The underlying random utility process is Markov, and the inter-temporal evolution of the (utility-maximizing) brand choice process is also Markov. The models permit parsimonious parameterizations of the random utility process in brand choices with the resulting switching probabilities being functionally related to explanatory variables. The model allows for structural state dependence (feedback), habit persistence (inertia), and unobserved heterogeneity. The theoretical development shows that several well known stochastic brand choice models can be deduced from random utility maximization theory. From a managerial perspective, the usefulness of the proposed model stems from its ability to separate out the effects of habits, state dependence and heterogeneity. Strong state dependence effects imply incentives for inducing trial of a brand (e.g., product sampling). In contrast with state dependence, a strong habit persistence effect may be indicative of buyer behavior where inducement of trial of a different brand may not be sufficient to maintain a (sustained) defection of the consumer from the habitually purchased brand to the trial brand. Failure to distinguish between these two effects has important implications. For example, a model that only accounts for state dependence effects would, in the presence of only habit persistence, incorrectly attribute it to state dependence. Based on this the manager could decide to embark on an expensive sampling program that might prove ineffective due to the absence of state dependence. It is also important to distinguish between the effects of unobserved heterogeneity and state dependence. In the absence of true state dependence, failing to account for unobservable variations across households (such as differences in price sensitivities), results in the temporally persistent unobservable elements showing up as state dependence in the model. Hence, a manager may incorrectly opt for sampling as the appropriate marketing action, whereas, a couponing or price promotion strategy should have been preferred. We estimate the model parameters using the AC Nielsen household scanner panel data set on catsup purchases. Further, we investigate empirical techniques for overcoming the “initial conditions” problem that affects many dynamic models of brand choice. Through simulation analysis using the estimated parameters, we show that the calculated profitability of a promotion must take into account the multi-period impact due to state dependence. Further, we demonstrate how ignoring heterogeneity can result in spurious state dependence, thereby making marketing tactics such as product sampling appear far more attractive than they actually are. Specifically, the model that accounts only for habit persistence and state dependence effects predicts a share increase of 2.4% points through sampling for one of the brands in the empirical analysis. Once the effects of unobserved heterogeneity are accounted for, however, this number drops precipitously to 0.3%. While even this low number might fulfill the objectives of the brand manager, it ensures that expectations are not eight times that number. It is important to note that this paper is a first attempt at analyzing the three fundamental dimensions of dynamic brand choice behavior. Our formulation represents a “reduced form” approach as opposed to a “structural” approach. Other limitations of the model include our focus on time-invariant choice sets. Extensions of the model to situations where choice sets vary over time are possible, but are difficult. Another limitation is the dependence on multivariate extreme value distributions. An alternative would be to use multivariate normal distributions, i.e., a probit-like structure which has certain useful properties. A comparison of the two approaches would be useful. Empirical extensions of the model to allow for higher-order processes and nested logit type model structures could also be fruitful. Explicitly incorporating variety-seeking behavior in the model would further enrich the theoretical framework proposed in this paper.

Decision field theory: Improvements to current methodology and comparisons with standard choice modelling techniques

Generalized Extreme Value models for count data: Application to worker telecommuting frequency choices

IG-OU processes are a subclass of the non-Gaussian processes of Ornstein–Uhlenbeck type, which are important models appearing in financial mathematics and elsewhere. The simulation of these processes is of interest for its applications in statistical inference. In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables—one has an inverse Gaussian distribution and the other has a compound Poisson distribution. And in distribution, the compound Poisson random variable is equal to a sum of Poisson-distributed number positive random variables, which are independent identically distributed and have a common specified density function. The exact simulation of the IG-OU processes, proceeding from time 0 and going in steps of time interval Δ, is achieved via the representation of the stochastic integral. Comparing to the approximate method, which is based on Rosinski’s infinite series representation of the same stochastic integral, by the quantile–quantile plots, the advantage of the exact simulation method is obvious. In addition, as an application, we provide an estimator of the intensity parameter of the IG-OU processes and validate its superiority to another estimator by our exact simulation method.

On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables

The prophet inequality for a sequence of independent nonnegative random variables shows that the ratio of the mean of the maximum of the sequence to the optimal expected return using stopping times is always bounded by 2; i.e., on average, the proportional advantage of a prophet with complete foresight over a gambler using nonanticipating stopping rules is at most 2. Here, an inequality linking the mean of the sum of the $k$ largest order statistics of the sequence and the optimal expected return is derived. This implies that if the $k$ largest order statistics are close to the maximum in mean then the proportional advantage of the prophet is at most of order $(k + 1)/k$. An extension of the additive prophet inequality for uniformly bounded independent random variables is also given.