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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.

In recent years, a multiplicative hybrid (MH) route choice model was proposed to overcome the drawbacks of the multinomial logit (MNL) model and the multinomial weibit (MNW) model. This paper compa...

The chi-squared test for independence in two-way categorical tables depends on the assumptions that the data follow the multinomial distribution. Thus, we suggest alternatives when the assumptions of multi- nomial distribution do not hold. First, we consider the Bayes factor which is used for hypothesis testing in Bayesian statistics. Unfortunately, this has the problem that it is sensitive to the choice of prior distributions. We note here that the intrinsic Bayes factor is not appropriate because the prior distribu- tions under consideration are all proper. Thus, we propose using Bayesian estimation which is generally not as sensitive to prior specifications as the Bayes factor. Our approach is to construct a 95% simultaneous credible re- gion (i.e., a hyper-rectangle) for the interactions. A test that all interactions are zero is equivalent to a test of independence in two-way categorical tables. Thus, a 95% simultaneous credible region of the interactions provides a test of independence by inversion.

Although commuting is often viewed as a burden, transportation research has recently investigated satisfaction with commuting or commute travel times, with a goal to understand intrinsic utilities of travel time: when and for whom travel is productive or beneficial, beyond reaching a destination. However, few studies have examined perceived satisfaction with a range of travel times, and those that have only report aggregate trends. Thus, there is a need to illuminate and explain heterogeneity in travel time satisfaction profiles. By exploring individual-level responses to questions about satisfaction with hypothetical commute travel times among 588 commuters in Portland, Oregon, this study makes three contributions. First, through clustering, we identify eight different satisfaction with travel time profiles. Only one (the smallest group) has the same non-monotonic shape found in past research. Others are distinguished by different tolerable commute times: when (compared to an average/threshold commute time of 30 min) satisfaction levels drop. On this basis, we further categorize profiles into three groups: Monotonic low-tolerance (ML), Monotonic high-tolerance (MH), and Non-monotonic (NM) commuters. Second, through multinomial and ordered logit models, we determine factors associated with having a specific satisfaction profile or tolerable commute time. Significant differences are found for commute travel times (actual or ideal), mode choice (cycling), measures of intrinsic utility (satisfaction with actual commute times and the teleportation test), and a few personal characteristics (self-employment). Third, through visual comparisons, we find within-person consistency in responses to all of these questions about the intrinsic utility of travel time, supporting their use in past and future research.

A study based on discrete choice experiments is conducted to investigate how bioecological attributes of birding sites enter the utility functions of specialized birders and affect their travel intentions. Estimates are based on generalized multinomial and scales-adjusted latent class models. We find that the probability of observing a rare or a new bird species, and the numerosity of species significantly affect birders’ choice destination. We also find that individual preferences among attributes are correlated and affected by scale and taste heterogeneity. We identify two latent classes of birders. In the first class fall birders attaching a strong interest in qualitative aspects of sites and low importance on distance from home. Class 2 groups birders addicted both on all qualitative and quantitative bioecological attributes of sites as well as on the distance. In general, we assess that the majority of birders prefer to travel short distances, also when the goal is viewing rare or new birds. Finally, we estimate marginal welfare changes in biological attributes of sites in terms of willingness to travel.

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 dis...

This article considers hypothesis testing using Bayes factor in the context of categorical data models represented in two- dimensional contingency tables. The study includes multinomial model for a general I × J table data. Other data characteristics such as low as well as polarized cell counts and size of the tables are also considered. The objective is to investigate the sensitivity of Bayes factor taking these features into account so as to understand the performance of non-informative priors itself. Consistency has been studied based on different types of data and using Dirichlet prior with eight different choices for multinomial model followed by a bootstrap simulation. Study has emphasized the reasonable choice of values for the parameters that normally represents the underlying physical phenomena, though partially vague in nature.

This paper computes semiparametric efficiency bounds for finite-dimensional parameters in discrete choice models with nonparametric regressors in the form of conditional expectations. These can include expectations about exogenous events as well as expectations about the choices of other agents. Thus, the models studied here include incomplete-information games, social-interactions models as well as single-agent discrete choice models with uncertainty as special cases. Our bounds rely on the assumption of rational expectations and on regularity conditions of equilibrium beliefs. The paper focuses on binary-choice models but the derivation of the bounds illustrates how our approach can be extended to multinomial choice cases. Explicit efficiency bound expressions for the models examined here had not been derived before. Furthermore, since we also characterize the efficient influence functions, our results can also potentially be used to construct semiparametrically efficient estimators for these models.

The global market for life insurance products has been stable over the years. However, equity-linked products which form about �fifteen percent of the total life insurance market has experienced a decline in premiums written. The impact of model risk when hedging these investment guarantees has been found to be significant�. We propose a framework to determine the worst case value of an equity-linked product through partial hedging using quantile and conditional value-at-risk measures. The model integrates both the mortality and the financial risk associated with these products to estimate the value as well as the hedging strategy. We rely on robust optimization techniques for the worst case hedging strategy. To demonstrate the versatility of the framework, we present numerical examples of point-to-point equity-indexed annuities in multinomial lattice dynamics.

Transport models inherit uncertainties due to a variety of assumptions, inputs and their structural properties. With the increase in complexity of modern travel demand models, the uncertainty analysis becomes more important and it becomes a non-trivial procedure that requires a careful consideration for its investigation. This paper analyses the model uncertainty of the activity-based microsimulation (ABM) travel demand model including specification and parameter uncertainty. The ABM model predicts the entire day activity-travel schedule and was developed and calibrated using a variety of datasets from Singapore. The model is computationally heavy as it includes 22 sub-models, which follows multinomial and nested logit structure for different activity-travel decisions and in overall includes 817 parameters. The model specification uncertainty addressed in the study include simulation error and sample uncertainty, both measured by means of simulation techniques under various scenarios with running the entire model. The parameter uncertainty is estimated based on the simulation with sampling from a parametric multivariate distribution preserving the correlations between the sampled variables. The parameter uncertainty includes a sensitivity-based screening of the sub-models to identify the major contributors, followed by simulation runs of the entire model for the most influential parameters. The results showed that the order of magnitude of all considered kinds of uncertainty strongly depends on how frequently the alternative is predicted in the choice process. The parameter uncertainty is higher than the sampling uncertainty, and the sampling uncertainty is comparable with the simulation uncertainty. Moreover, this is the first study to compare the order of magnitude of the simulation, sampling and parameter uncertainties of an ABM model. The suggested method can be used to analyse both input and parameter uncertainties in computationally heavy models that have a hierarchical structure consisting of smaller sub-models. The uncertainty calculated for the model outcomes in this study will allow practitioners to choose a strategy for dealing with it.

This study investigates the potential market demand of shared-ride taxi and shuttle services designed to serve members of organizations in dense urbanized areas. It develops and compares two different multivariate count data modeling approaches, the multinomial distribution and the full enumeration of count alternatives, under an integrated choice and latent variable framework. The study accounts for day-to-day variability in commuting behavior, also known as multimodality, by modeling the weekly frequency of commuting by different travel modes instead of modeling choices for a single trip/day. Using stated preference data collected in the Spring of Academic Year 2016–2017, the models are applied to a case study of students who are highly dependent on private cars at the American University of Beirut (AUB), Lebanon. Policy analysis is conducted to investigate the impact of different price levels and modal attributes on the students’ mode choice behavior. Under practical scenarios, results show that more than 55% of students would adopt a multimodal travel behavior in a given week and that 9–20% of trips are expected to be made by shared-taxi and 12–25% by shuttle. Thus, modeling single trip/day choices instead of weekly decisions would lead to limitations in model forecasts related to the full impact of the proposed policies over longer periods. Results also show that the full enumeration model guarantees higher prediction accuracy and results in an estimate of value of time that is closer to other local estimates for the study area.

Life expectancy is increasing in many countries and this may lead to a higher frequency of adverse health outcomes. Therefore, there is a growing demand for predicting the risk of a sequence of events based on specified factors from repeated outcomes. We proposed regressive models and a framework to predict the joint probabilities of a sequence of events for multinomial outcomes from longitudinal studies. The Markov chain is used to link marginal and sequence of conditional probabilities to predict the joint probability. Marginal and sequence of conditional probabilities are estimated using marginal and regressive models. An application is shown using the Health and Retirement Study data. The bias of parameter estimates for all models from all bootstrap simulation is less than 1% in most of the cases. The estimated mean squared error is also very low. Results from the simulation study show negligible bias and the usefulness of the proposed model. The proposed model and framework would be useful to solve real-life problems from various fields and big data analysis.

To quantify travel demand, it is necessary to understand the travelers’ mode choice behavior. The Logit model is widely used in travel mode choice because of its closed form. Nevertheless, the variance of the utility function is unchanged in Logit-based models, indicating that the perceived error of the traveler on the option is fixed as the utility changes, which is inconsistent with the actual situation. While in Weibit-based models, travelers’ perception error of options grows with the increase of the utility. Moreover, the relative difference is captured, and the asymmetric property exists, which is different from Logit-based models. This paper contributes to the literature by comparing the performances of the Logit-based and Weibit-based models. In this article, six discrete choice models for travel mode choice are discussed based on data of Swiss metro, which includes multinomial Logit model, multinomial Weibit model, and derived models. The Weibit-based models outperform the Logit-based models, considering with the adjusted likelihood ratio index of all models in this paper.

This paper investigates the lead–lag relationships in high-frequency data. We propose multinomial dynamic time warping (MDTW) that deals with non-synchronous observation, vast data, and time-varying lead–lag. MDTW directly estimates the lead–lags without lag candidates. Its computational complexity is linear with respect to the number of observation and it does not depend on the number of lag candidates. The experiments adopting artificial data and market data illustrate the effectiveness of our method compared to the existing methods.

It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.

Purpose: Cotton is the backbone of Pakistan economy, as country is the 4th largest producer of cotton in the world. Despite this importance there is steep decline in cotton production over time due to climate change. The need to evaluate the potential of adaptation in improving cotton yield has necessitated this study. Design/Methodology/Approach: This study is based on the farm household survey of four cotton producing districts, two from each Punjab and Sindh that were purposively selected from heat stress regions of Pakistan. Data were analyzed through multinomial endogenous switching regression model and treatment effect framework. Findings: Farm management practices were evaluated for their significance in reducing adverse impacts of climatic extremes on cotton yield. Adaptation in the combination of first three strategies observed to be the most successful strategies in increasing yield. Implications/Originality/Value: For effective adaptation access to credit and extension, education, farming experience, and sources of information revealed to be important predictors

This study aims to investigate earnings management during the fourth quarter and explains why there is a large kink in the distribution of annual earnings around zero. We use multinomial logistic r...

This study aims at determining the use of Multinomial Logistic Regression (MLR) model which is one of the important methods for categorical data analysis. This model particularly deals with one nominal or ordinal response variable that has more than two categories. Despite the fact that many researchers have applied this model in data analysis in many areas, for instance behavioral, social, health, and educational, a study on spending habits of University students have never been done. To identify the model by practical way, we conducted a survey research among students from University of Embu. Segment of the population of students in undergraduate level, a sample of 376 was selected. We employed the use stratified random sampling and simple random sampling without replacement in each stratum. The response variable consisted of five categories. Four of explanatory variables were used for building the primary (MLR) model. The model was tested through a set of statistical tests to ensure its appropriateness for the data. From the results, the study reveals that year of study, family financial level, gender and school are significant factors in explaining spending habits of students. Despite the fact that gender is one of the deterministic factors of financial behavior of student, this model identified family level of income as a major deterministic factor. Conclusively, using MLR model accurately defines the relationship between the group of explanatory variables and the response variable. It also identifies the effect of each of the variables, and we can predict the classification of any individual case. The researchers recommend that, the Universities peer counselling department, should hold trainings on the basis of major determinant of financial spending behavior i.e. family financial level.

Regression models for multinomial responses with time dependent covariates have been studied recently both in longitudinal and time series setup. For practical importance, in this paper, we focus on a longitudinal multinomial response model with two categorical covariates to study their main and interaction effects after accommodating a lag 1 dynamic relationship between past and present multinomial responses. The proposed model could be generalized easily to accommodate multiple (more than two) categorical covariates and their interactions. As far as the estimation of the regression and the dynamic dependence parameters is concerned, we follow a recent parameter dimension-split based approach suggested by Sutradhar (Sankhya A80, 301–329 2018) but unlike the conditional method of moments (CMM) used in this study, we use a more efficient estimation approach, namely the so-called conditional generalized quasi-likelihood (CGQL) method for the estimation of the dynamic dependence parameters. The regression parameters are also estimated by using the same CGQL approach where responses become independent conditional on the past responses which is similar in principle to the likelihood estimation where the likelihood function is formed as a product of transitional probabilities conditional on the past responses. The asymptotic properties of the CGQL estimators are provided in details. The higher efficiency performance of the CGQL approach over the CMM approach is also demonstrated, for example, for the estimation of the dynamic dependence parameters.

We introduce a Bayesian approach for analyzing high‐dimensional multinomial data that are referenced over space and time. In particular, the proportions associated with multinomial data are assumed to have a logit link to a latent spatio‐temporal mixed effects model. This strategy allows for covariances that are nonstationarity in both space and time, asymmetric, and parsimonious. We also introduce the use of the conditional multivariate logit‐beta distribution into the dependent multinomial data setting, which leads to conjugate full‐conditional distributions for use in a collapsed Gibbs sampler. We refer to this model as the multinomial spatio‐temporal mixed effects model (MN‐STM). Additionally, we provide methodological developments including: the derivation of the associated full‐conditional distributions, a relationship with a latent Gaussian process model, and the stability of the non‐stationary vector autoregressive model. We illustrate the MN‐STM through simulations and through a demonstration with public‐use quarterly workforce indicators data from the longitudinal employer household dynamics program of the US Census Bureau.

In a recent study, Zhao et al. (2017) presented a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model; it provided an efficient way of calculating the fair value of the strike for variance swaps. In this article, the authors expand the methodology to price nonlinear derivatives written on realized variance. They introduce a new option contract, a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework they also show how to value forward-start variance swaps, VIX futures, and VIX options. Numerical tests show that the methodology is efficient and accurate.

Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics.

In this paper, we consider the valuation of vulnerable options under a Markov-modulated jump-diffusion model, where the option writer's asset value is subject to price pressure from other financial institutions due to distressed selling. A change of numeraire technique, proposed by Geman et al. [ 14 ], is employed to obtain a semi-analytical pricing formula for an vulnerable European option in the presence of regime switching effect. The method is numerically implemented using the multinomial approach in Costabile et al. [ 6 ]. We study the impacts of distressed selling and regime switching on the European option prices via numerical experiments.

Spatial dependence plays a key role in all phenomena involving the geographic space, such as the social processes associated with transport and land use. Nevertheless, spatial dependence in multinomial discrete models has not received the same level of attention as have the other kinds of correlations in the discrete modeling literature, mainly due to the complexity of its treatment. This paper aims at offering a brief discussion on the different kinds of spatial correlation affecting multinomial discrete models and the different ways in which spatial correlation has been addressed in the discrete modeling literature. Furthermore, the paper offers a discussion on the advantages and limitations of the different approaches to treat spatial correlation and it also proposes a compromise solution among complexity, computational costs, and realism that can be useful in some specific situations.

In Sect. 5.1 we considered binary regression models, that is, regression situations where the response is observed in two categories. In many applications, from social science to medicine, response variables often have more than two categories. For example, consumers may choose between different brands of a product or they may express their opinion about some product in ordered categories ranging from “very satisfied” to “not satisfied at all.” Similarly, voters choose between several parties or they assess the quality of candidates in ordered categories. In medicine, we may, for example, not only distinguish between “infection” and “no infection” but also between several types of infection, as in Example 6.1 below.

In this chapter, we consider the problem of the elicitation and specification of an uncertainty distribution based on expert judgements, which may be a subjective prior distribution in a Bayesian analysis, for a set of probabilities which are constrained to sum to one. A typical context for this is as a prior distribution for the probabilities in a multinomial model. The Dirichlet distribution has long been advocated as a natural way to represent the uncertainty distribution over the probabilities in this context. The relatively small number of parameters allows for specification based on relatively few elicited quantities but at the expense of a very restrictive structure. We detail recent advances in elicitation for the Dirichlet distribution and recently proposed alternative approaches, which offer greater flexibility at the expense of added complexity. In order of increasing flexibility, they are the generalised Dirichlet distribution, multivariate copulas and vines. An extension of multinomial models containing covariates is discussed.

This study conducts a comprehensive comparative analysis of regression-based multinomial models and artificial neural network models in intercity travel mode choices. The four intercity travel modes of airplane, high-speed rail (HSR), train, and express bus were used for analysis. Passengers’ activity data over the process of intercity travel were collected to develop the models. The standard multinomial logit (MNL) regression and Bayesian multinomial logit (BMNL) regression were compared with the radial basis function (RBF) and multilayer perceptron (MLP). The results show that MLP performs best in terms of predictive accuracy, followed by BMNL and MNL, and RBF is the least accurate. The performances of all models were examined against changes in data balance, and it was found that rebalancing can improve fitting performance while slightly reducing the predictive performance. This comparative study and its parameter estimation shed new light on the comparison of traditional and emerging models in travel behavior studies, and the findings can be used as heuristic guidance for all stakeholders.

We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross‐sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models coupled with variation in regressors: with cross‐section data, we match across individuals while with panel data, we match within individuals over time. Across models, we relax the Indpendence of Irrelevant Alternatives (or IIA assumption, see McFadden (1974)) and allow for arbitrary correlation in the unobservables that determine utility of various alternatives. For the cross‐sectional model, estimation is based on a localized rank objective function, analogous to that used in Abrevaya, Hausman, and Khan (2010), and presents a generalization of existing approaches. In panel data settings, rates of convergence are shown to exhibit a curse of dimensionality in the number of alternatives. The results for the dynamic panel data model generalize the work of Honore and Kyriazidou (2000) to cover the semiparametric multinomial case. A simulation study establishes adequate finite sample properties of our new procedures. We apply our estimators to a scanner panel data set. Multinomial response rank estimation dynamic panel data C14 C23 C35

In this study we seek to study the implications of ignoring intra-household heterogeneity in choice models estimated using scanner data. Using a unique data set that identifies choices made by individual customers within a household, we estimate multinomial choice models at the household level with and without incorporating intra-household heterogeneity using the Markov Chain Monte Carlo (MCMC) procedures. We find that the estimates obtained at the customer level are significantly different from those obtained at the household level. We use the estimates obtained at the household and customer level to conduct a policy simulation to target households with a promotion. We find that using customer level estimates to target households with a promotion results in significantly higher profits relative to targeting based on household level estimates which ignores intra-household heterogeneity.

In a multinomial set-up with k possible outcomes, we develop estimation under a “middle censoring” paradigm, which is as defined in Jammalamadaka and Mangalam (2003). This problem has many special features because of the inter-dependent probabilities, which we explore here.

Multivariate meta-analysis may be appropriate when some or all studies in a meta-analysis report more than one outcome. This chapter describes the multivariate meta-analysis model and compares various methods for its estimation, focusing on two-stage methods. The standard model requires the within-study correlations between estimates for different outcomes to be known; various approaches when they are not known are discussed. Advantages and disadvantages of the multivariate approach compared with multiple univariate meta-analyses are then described. Advantages are that multivariate meta-analysis can yield more precise and/or less biased estimates for single outcomes through “borrowing of strength” and that it enables inferences to be drawn across multiple outcomes. Disadvantages are its greater complexity, with potential borrowing of strength often not being achieved, possible estimation problems, and extra modeling assumptions. Applications are discussed to confounder adjustment in observational studies, diagnostic test accuracy (where a one-stage approach is preferred), longitudinal data, and multinomial data.

The Student distribution has already been used to obtain robust maximum likelihood estimator (MLE) in the framework of binary choice models. But, until recently, only the logit and probit binary models were extended to the case of multinomial choices, resulting in the multinomial logit (MNL) and the multinomial probit (MNP). The recently introduced family of reference models, well defines a multivariate extension of any binary choice model, i.e. for any link function. In particular, this is the first extension of the binary robit to the case of multinomial choices. These models define the choice probability for category j relative to an (interchangeable) reference category. This paper highlights the robustness of reference models with Student link function, by showing that the influence function is bounded. Inference of the MLE is detailed through the Fisher's scoring algorithm, which is appropriated since reference models belong to the family of generalized linear models (GLMs). These models are compared to the MNL on the benchmark dataset of travel mode choice between Sydney and Melbourne. The results obtained on this dataset with reference models are completely different compared with those usually obtained with MNL, nested logit (NL) or MNP that failed to select relevant attributes. It will be shown that the travel mode choice is totally deterministic according to the transfer time. In fact, the use of Student link function allow us to detect the total artificial aspect of this famous dataset.

Hypotheses concerning the distribution of multinomial proportions typically entail exact equality constraints that can be evaluated using standard tests. Whenever researchers formulate inequality constrained hypotheses, however, they must rely on sampling-based methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of multinomial inequality constraints. An empirical application showcases that bridge sampling outperforms current Bayesian methods, especially when relatively little posterior mass falls in the restricted parameter space. The method is extended to mixtures between equality and inequality constrained hypotheses. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

This paper focuses on studying the relationships among a set of categorical (ordinal) variables collected in a contingency table. Besides the marginal and conditional (in)dependencies, thoroughly analyzed in the literature, we consider the context-specific independencies holding only in a subspace of the outcome space of the conditioning variables. To this purpose we consider the hierarchical multinomial marginal models and we provide several original results about the representation of context-specific independencies through these models. The theoretical results are supported by an application concerning the innovation degree of Italian enterprises.

The heteroscedastic logit model is useful to describe choices of individuals when the randomness in the choice-making varies over time. For example, during surveys individuals may become fatigued and start responding more randomly to questions as the survey proceeds. Or when completing a ranking amongst multiple alternatives, individuals may be unable to accurately assign middle and bottom ranks. The standard heteroscedastic logit model accommodates such behavior by allowing for changes in the signal-to-noise ratio via a time-varying scale parameter. In the current literature, this time-variation is assumed equal across individuals. Hence, each individual is assumed to become fatigued at the same time, or assumed to be able to accurately assign exactly the same ranks. In most cases, this assumption is too stringent. In this paper, we generalize the heteroscedastic logit model by allowing for differences across individuals. We develop a multinomial and a rank-ordered logit model in which the time-variation in an individual-specific scale parameter follows a Markov process. In case individual differences exist, our models alleviate biases and make more efficient use of data. We validate the models using a Monte Carlo study and illustrate them using data on discrete choice experiments and political preferences. These examples document that inter- and intra-individual heteroscedasticity both exist.

This paper, using the dynamic multinomial choice random effect panel Logit model, and focusing on the intermediate exchange rate regimes, tries to provide new empirical explanations to the special polarization phenomenon. The main findings are as follows: Firstly, the state dependence can influence the choice of exchange rate regimes greatly, and the state dependence can explain the phenomenon of the special polarization. Secondly, the non-state dependence factors influence exchange rate regimes choice of different development stage economies in different manner. The non-state dependence factors can also explain the special polarization. Thirdly, the policy makers will choose the less-flexible exchange rate regimes with the increasing of capital account openness. The intermediate exchange rate regimes can survive and stabilize the economy under certain conditions. Lastly, this paper draws a series of important conclusions and policy implications.

This paper analyzes the GPS traces recorded by cyclists in the framework of the Mobile Mobility Panel throughout the Netherlands. The objective of this paper is to analyze bicycle route choice via network attributes and trip length over a sequence of trips by approximately 280 bicycle users, who were asked to register their trips by means of a specific smartphone application. Approximately 3,500 bike trips were recorded throughout the Netherlands over a four-week period in 2014. The bike trips have been matched to a specific bicycle network built and updated by a Dutch cyclists’ union. Route choice models were estimated, using both the binomial logit model and the mixed multinomial logit model with Path-size logit model formulation. The chosen alternatives were part of the choice set for the mixed multinomial logit model. Also, the shortest route was generated for each origin-destination pair. The results show that trip lengths and trip distribution over time reveal a population sample much used to cycling, frequently and over long distances. Furthermore, when considering the composition of chosen routes in terms of link type, the usage of cycleway links is frequent. For repeated trips, the shortest route option tends to be chosen more; frequent cyclists, on systematic trips, tend to optimize their trip and prefer the shortest routes. This is even truer for males and for non-leisure trips. The estimated probabilities for both multinomial and binomial models show that the binomial model tends to overestimate the probabilities of choosing the shortest route. This result is stronger in non-leisure trips, where people tend to choose a more personalized route, instead of the shortest. This research contributes to the generation of a more efficient distribution of bicycle trips over the network. Future research can more specifically address the intrapersonal variation in route—destination choice given the availability of longitudinal data.

This paper creates a multinomial framework for ideal point estimation (mIRT) using recent developments in Bayesian statistics. The core model relies on a flexible multinomial specification that includes most common models in political science as “special cases.” I show that popular extensions (e.g., dynamic smoothing, inclusion of covariates, and network models) can be easily incorporated whilst maintaining the ability to estimate a model using a Gibbs Sampler or exact EM algorithm. By showing that these models can be written and estimated using a shared framework, the paper aims to reduce the proliferation of bespoke ideal point models as well as extend the ability of applied researchers to estimate models quickly using the EM algorithm. I apply this framework to a thorny question in scaling survey responses—the treatment of nonresponse. Focusing on the American National Election Study (ANES), I suggest that a simple but principled solution is to treat questions as multinomial where nonresponse is a distinct (modeled) category. The exploratory results suggest that certain questions tend to attract many more invalid answers and that many of these questions (particularly when signaling out particular social groups for evaluation) are masking noncentrist (typically conservative) beliefs.

Regression mixture models are becoming more widely used in applied research. It has been recognized that these models are quite sensitive to underlying assumptions, yet many of these assumptions are not directly testable. We discuss a diagnostic tool based on reconstructed residuals that can help uncover violations of model assumptions. These residuals are found by using the posterior probability of class membership to assign, based on a multinomial distribution, a class to each observation. Standard residual checks can be applied to these posterior draw residuals to explore violations of the model assumptions. We present several illustrations of the diagnostic tool.

Association indices have been a mainstay of social behaviour analysis for decades. However, researchers have long recognized that these indices can be biased under certain conditions. In this paper, I develop a process map of the steps necessary to transform social behaviour into estimates of association rates. This helps to distinguish the subject population's behaviour from the researcher's data collection protocol. By doing this, we can isolate the sources of bias. I also show that bias in association indices is often a function of the true association rate. This means that while bias does not affect the ordering of associations, it can impact analysis in unpredictable ways. Performing network analysis with biased association indices can lead researchers to arrive at different conclusions than if they had used unbiased estimators. To simplify the mathematical task of deriving unbiased estimators, I introduce three properties of maximum likelihood estimators that allow one to treat association data as output from a multinomial distribution, then use the functional invariance property of maximum likelihood estimators to solve for estimators. I apply these properties to a selection of common data collection protocols to show that there is no single association index that is appropriate for all cases. Instead, each of the commonly used indices is unbiased under appropriate conditions. Furthermore, when it is possible that some of the individuals are not identified, I introduce some new unbiased estimators. I close with a discussion of nontraditional techniques of collecting data that provide an opportunity to increase the number of outputs from the data collection process. These techniques may ultimately make it possible to specify association behaviour more carefully by allowing for more parameters in the data generation process.

When collecting panel data, we need to acknowledge that responses do not represent independent measurements. The known apparatus in transportation research offers several opportunities to estimate panel effects for well-known and widely applied models such as hazard and dynamic logit models. However, the transportation research community is not endowed with a rich set of methods to account for panel effects in dynamic probabilistic decision trees, which have been used as a formalism for the representation of decision heuristics. Building on scarce prior work in statistics, we elaborate an approach to estimate panel effects in dynamic probabilistic decision trees with multinomial action states. Given that panel data naturally have a hierarchical structure with repeated measures nested within individuals, we implement a mixed-effects model that simultaneously accounts for population-level effects (fixed effects), between-individual variances (random effects), and within-individual variances (autocorrelations). The approach uses an iterative estimation procedure between CHAID-based probabilistic tree induction and Bayesian generalized linear mixture modeling (GLMM). When extracting the dynamic probabilistic decision trees, it is assumed that the random effects are known, while it is assumed that the fixed effects are known when estimating the Bayesian GLMM. This iterative process continues until convergence is reached. A Monte Carlo technique is used to navigate between aggregate choice probabilities and individual level multinomial choices. We also test the significance of temporal autocorrelation within individuals. The suggested approach is illustrated using charging station choice of users of Plug-in Electric Vehicles (PEV). Results support the potential value of the suggested approach.

A well known result in probability is the Poisson limit for rare independent Bernoulli trials. The asymptotic result also holds for a multinomial setting where events are dependent. An interesting data type is a survival process in which one observes many individuals over time periods. The risk set is all those available at the beginning of each time period, thus the same individual can appear in successive risk sets. Individuals exit rarely. In our motivating example these are corporations who exit a public trading system by default or merger, so there are several exit types, hence the multinomial setting. There are also covariates available at the beginning of each period. We study the numbers of exits over time. Under rare multinomial conditions we show that the exits types converge to independent Poisson laws with respect to the exit types and also with respect to time. An immediate application is the construction of one step ahead predictions which may then be tabulated or plotted, giving a convenient tool to study themodel behaviour with respect to time. Thus one can obtain one step ahead prediction intervals for the number of exits of each type, in our case bankruptcy or merger. This is a tool that is useful for large institutional investors such as pension plans.

Economic problems that require micro-level analysis within a discrete-choice framework are often spatial processes, where standard models result in inconsistent parameter estimates. Existing methods for spatial discrete-choice models become infeasible in micro-level data applications due to large sample sizes. We propose an extension of Klier and McMillen’s (2008) generalized moments estimator to multinomial choice models with spatial lag dependence that is computationally simple. Simulations indicate that the proposed estimator captures accurately the degree of spatial dependence in the data, provided spatial dependence is not too high. The methodology is employed to analyze the conversion process to various land uses using parcel-level data from a rural-urban fringe county within a large metropolitan area. We find evidence of positive spatial dependence of about 0.36—a result consistent with the widely-accepted idea that land-use conversion is a spatial process. This suggests that uncoordinated local land-use policies designed at a small scale, while attempting to manage growth at a local level, may fragment urban development and result in suboptimal land-use patterns at a regional level.