On the Logit Approach to Competitive Facility Location

The random utility model in competitive facility location is one approach for estimating the market share captured by a retail facility in a competitive environment. However, it requires extensive computational effort for finding the optimal location for a new facility because its objective function is based on a k -dimensional integral. In this paper we show that the random utility model can be approximated by a logit model. The proportion of the buying power at a demand point that is attracted to the new facility can be approximated by a logit function of the distance to it. This approximation demonstrates that using the logit function of the distance for estimating the market share is theoretically founded in the random utility model. A simplified random utility model is defined and approximated by a logit function. An iterative Weiszfeld-type algorithm is designed to find the best location for a new facility using the logit model. Computational experiments show that the logit approximation yields a good location solution to the random utility model.     

Estimating a Destination-Choice Model from a Choice-based Sample with Limited Information

In most applications of multinomial logit and other probabilistic discrete-choice models, the estimation data set is either a simple random sample of the population of interest or an exogenously stratified sample. Often, however, it is cheaper and easier to sample individuals while they are carrying out the chosen activity of concern. This produces a choice-based sample, which presents important problems of estimation and inference. This paper is concerned with estimation of destination-choice models from choice-based samples when neither the aggregate market shares of alternatives nor the probability distribution of explanatory variables in the population is known. The method of Cosslett (1981) for estimating multinomial logit models from such data is summarized, and the limitations on information about choice behavior that can be recovered from the sample are explained. An empirical model of pharmacy choice in the Namur, Belgium, area is presented. It is shown that useful and important information about destination-choice behavior can be obtained from a choice-based sample, even without knowledge of aggregate market shares and the probability distribution of explanatory variables.     

Studying Rules Changes in the U.S. House: Evidence from an Alternative Empirical Model

Binder (1996) and Schickler (2000) define the current debate as to why the U.S. House has changed its standing rules regarding the majority rule and the minority rights. I revisit their empirical models—binary logit and ordered logit—and theoretically and statistically test the appropriateness of these models. I find that both of them are actually choosing inappropriate models. Their theoretical claims cannot be properly examined by utilizing their choices of models. In addition, the data do not satisfy the “parallel regression” assumption but do satisfy the “independence of irrelevant alternatives” assumption, which supports using an alternative multinomial logit model. I further extend the model, and find the dynamic nature of rules changes in the U.S. House. It appears there is no symmetry between the rules changes that promote the majority rule and the rules changes that enhance the minority rights.     

Modeling Micro-Spatial Employment Location Patterns: A Comparison of Count and Choice Approaches

This article studies employment location patterns in the Puget Sound Region of Washington State at a micro level of geography. Traditional discrete choice modeling using multinomial logit (MNL) models may be problematic at a micro level of geography due to the high dimensionality of the set of alternative locations and the likely violations of the independence from irrelevant alternatives (IIA) assumption. Count models are free from the IIA assumption and, unlike logit models, actually benefit from large numbers of alternatives by adding degrees of freedom. This study identifies the best-fitting count model as the zero-inflated negative binomial (ZINB) model, because this model more effectively addresses the large number of cells with no jobs and reflects a dual process that facilitates the identification of threshold clustering effects such as those found in specialized employment centers. The estimation and prediction results of ZINB are compared with those of MNL with a random sampling of alternatives estimated on an equivalent data set. The ZINB and MNL models largely agree on major trends, with the ZINB model providing more insightful details, but with less capacity to predict large count situations.     

Exogenous Workplace Choice in Residential Location Models: Is the Assumption Valid?

This paper examines the assumption implicit in most models of residential location that the choice of workplace is exogenously determined. Monocentric models have generally made this assumption, but it has come under increasing scrutiny. A nested logit model of workers' choices of workplace, residence, and housing tenure within the Dallas-Fort Worth metropolitan area is developed to provide a test. A unique dataset that includes the workplace and residence census tracts of workers in Dallas-Fort Worth, and their demographic and socioeconomic characteristics, is used to estimate the model. The results confirm that a joint choice specification better represents actual choice behavior in a multinodal metropolis.     

A Selection Bias Approach to Destination Choice

Research on consumer search behavior commonly envisages destination choice as a two-step process: (1) delineate the search set, and (2) evaluate choices therein. However, much of the empirical work in destination choice—including logit and nested logit formulations—models only the latter, and not the set delineation itself. In the presence of correlation between error terms in set delineation and choice selection, statistical estimators are biased, a problem that Heckman and others have called selection bias. In this paper, an alternative two-stage method is proposed to estimate the parameters of models of set delineation and choice selection. Monte Carlo simulation is used to explore the properties of these two-stage estimators, and to show the magnitude of bias inherent in traditional methods of estimation.     

Impacts of Multiple-Period Lags in Dynamic Logit Models

This paper will provide an introduction to a new field of research, viz. the sensitivity of the solution trajectory of a dynamic logit model (belonging to the class of discrete choice models) in the light of a multiperiod lag structure. It is well known from recent advances in the area of chaos and turbulence theory that the stability of a dynamic system is critically dependent on various factors, such as threshold values of parameters, initial conditions, and also the lag structure. This paper aims to identify the consequences of different lag structures in dynamic logit models (including also dynamic spatial interaction models). Various simulation experiments will be used to show that the onset of instability of the solution trajectory tends to decrease as the number of time lags increases (depending also on the growth rate of the system).     

Modeling Strategies for Categorical Data: Examples from Housing and Tenure Choice

Models to investigate categorical data can be divided into preprocessing, limited parameterization, and formal logit models. To illustrate the advantages of preprocessing and limited parameterization models they are applied to a data set of tenure and type of housing choice before the data are examined with hierarchical logit and nested logit models. The preprocessing approaches are useful in selecting optimal subsets of independent variables with respect to the dependent variable. The ease of application and interpretation of a limited parameterization approach extends the clarity of the results from the preprocessing approaches. Because some variables are only relevant at specific levels of other independent variables, nonstandard (nested) logit models are necessary to understand the nested relationships.     

DISCRETE SPATIAL CHOICE MODELS FOR AGGREGATE DESTINATIONS*

ABSTRACT. In problems of spatial choice, the choice set is typically more aggregated than the one considered by decision-makers, often because choice data are available only at the aggregate level. These aggregate choice units will exhibit heterogeneity in utility and in size. To be consistent with utility maximization, a choice model must estimate choice probabilities on the basis of the maximum utility within heterogeneous aggregates. The ordinary multinomial logit model applied to aggregate choice units fails this criterion as it is estimated on the basis of average utility. In this paper, we derive and discuss a model which utilizes the theory underlying the nested logit model to estimate the appropriate maximum utilities of aggregates. We also demonstrate that the aggregate alternative error terms are asymptotically Gumbel, thereby relaxing the assumption of extreme value distributed error terms. This is accomplished with help from the asymptotic theory of extremes.     

Exposing Unobserved Spatial Similarity: Evidence from German School Choice Data

In a spatial context, flexible substitution patterns play an important role when modeling individual choice behavior. Issues of correlation may arise if two or more alternatives of a selected choice set share characteristics that cannot be observed by a modeler. Multivariate extreme value (MEV) models provide the possibility to relax the property of constant substitution imposed by the multinomial logit (MNL) model through its independence of irrelevant alternatives (IIA) property. Existing approaches in school network planning often do not account for substitution patterns, nor do they take free school choice into consideration. In this article, we briefly operationalize a closed‐form discrete choice model (generalized nested logit [GNL] model) from utility maximization to account for spatial correlation. Moreover, we show that very simple and restrictive models are usually not adequate in a spatial choice context. In contrast, the GNL is still computationally convenient and obtains a very flexible structure of substitution patterns among choice alternatives. Roughly speaking, this flexibility is achieved by allocating alternatives that are located close to each other into nests. A given alternative may belong to several nests. Therefore, we specify a more general discrete choice model. Furthermore, the data and the model specification for the school choice problem are presented. The analysis of free school choice in the city of Dresden, Germany, confirms the influence of most of the exogenous variables reported in the literature. The estimation results generally indicate the applicability of MEV models in a spatial context and the importance of spatial correlation in school choice modeling. Therefore, we suggest the use of more flexible and complex models than standard logit models in particular. En un contexto espacial, los patrones sustitución flexible juegan un papel importante en el modelamiento del comportamiento de las decisiones individuales. Varios problemas de correlación pueden presentarse si dos o más alternativas de elección comparten características no observables por el modelador. Los modelos de valor extremo (multivariate extreme value‐MEV) ofrecen la posibilidad de relajar la propiedad de sustitución constante (constant substitution) presente en los modelos logit multinomiales (multinomial logit‐MNL), a través de su propiedad de independencia de alternativas irrelevantes (Independence of irrelevant alternatives property ‐IIA). A menudo, los enfoques existentes en la planificación de redes escolares no toman en consideración los patrones de sustitución y de libre elección de escuela. En este artículo, los autores presentan brevemente el funcionamiento de un modelo de elección discreta (discrete choice model) para la maximización de utilidad o modelo logit anidado generalizado (generalized nested logit model‐GNL) para dar cuenta de la autocorrelación espacial. Los autores sostienen que modelos demasiado simples y restrictivos no suelen ser adecuados en un contexto de elección espacial. En contraste el modelo GNL es conveniente en términos de su computación y obtiene una estructura muy flexible de los patrones de sustitución entre las alternativas de elección. En términos generales, esta flexibilidad se logra mediante la asignación (o anidación) de las alternativas cercanas en el espacio (una alternativa puede pertenecer a varios nidos). Por lo tanto, los autores presentan un modelo de elección discreta más general. El estudio presenta además datos y la especificación del modelo para un caso de elección de escuela concreto: el análisis de libre elección de escuela en la ciudad de Dresden, Alemania. El análisis confirma la influencia de la mayoría de las variables exógenas presentes en la literatura. Los resultados de la estimación demuestran en términos generales la aplicabilidad de los modelos MEV en un contexto espacial y la importancia de la autocorrelación espacial en el modelado de elección de escuela. Los autores concluyen sugiriendo el uso de modelos más flexibles y complejos que los modelos utilizados habitualmente, en particular los modelos logit estándar. 从空间视角看,灵活的替代模式在个人行为选择建模中发挥着重要作用。当存在两个或两个以上备选方案集具有共性且无法被建模者观察到时,就可能出现相关性问题。多元极值模型（MEV）通过不相关的替代属性（IIA）实现了对多元logit模型（MNL）中常数限制的松弛替代。现有校园网络规划方法通常无法解释替代模式,而且没有考虑到自由择校因素。本文简要地建立一个封闭离散选择模型（广义嵌套（GNL）模型）,从效用最大化角度来解释空间相关性。此外分析还表明,非常简单的约束模型通常不具有足够的空间选择情境。相比之下,GNL模型计算便捷,且可以在各选择方案中获得非常灵活的替代模式。大致而言,这种灵活性大体是通过与住处位置距离上彼此靠近的替代选择分配而获得,一个给定的选择可能属于不同的住处。因此,我们给出了一个更一般的离散选择模型。此外,还给出了针对择校问题的数据和模型设定。基于德国德累斯顿市自由择校分析,证实了已有研究中多数外生变量的影响。估计结果证实了MEV模型在空间分析中的适用性以及择校模型中空间相关的重要性,并建议使用更加灵活和复杂的模型而不是标准的logit模型。     

Simultaneous-Equation Systems Involving Binary Choice Variables

Simultaneous-equation systems of continuous variables are well known in the social sciences. Unfortunately, these methods cannot be used when dealing with discrete endogenous variables. Although for discrete types of data a broad range of methods and techniques have been developed, their applicability is restricted to single-equation systems (for example, logit or probit formulations) or to association-type models (log-linear models), mainly because of the lack of suitable estimation methods and computer programs. The basic problem is the multivariate error structure of the endogenous variables. This paper presents a simultaneous-equation system of binary endogenous variables. The model is applied empirically to longitudinal data on mode choice and is compared with the well-known log-linear model.     

A Spatial Logit Association Model for Cluster Detection

In this paper, I propose to set out a logit spatial association model for binary spatial events and develop a scan algorithm to search for spatial associations. I extend the traditional logit model with a spatial autocorrelated component so that the model includes not only known risk factors, but also spatially autocorrelated regions as control or explanatory factors. The case study of West Virginia lung cancer shows that the model effectively captures cool and hot spots in lung cancer mortality.     

Preferences for Housing, Jobs, and Commuting: A Mixed Logit Analysis

This paper reports stated preferences of Dutch workers for combinations of housing, employment, and commuting. The analysis uses standard logit models as well as mixed logit models. Estimation results offer insights into the relative importance of various aspects of housing, employment, and commuting. Households dislike commuting and the value of commuting time implied by the model is high in comparison to the wage rate. Nevertheless, preferences for some housing attributes are strong enough to make substantially longer commuting acceptable to most workers. Of special interest is the strong preference for living in small-or medium-size cities, especially among two income households. Using a mixed logit model instead of a standard logit model results in a substantial improvement of the loglikelihood, reflecting the importance of heterogeneity among respondents. If no individual characteristics are incorporated into the model, the mixed logit implies substantially lower average monetary evaluations of most attributes. These differences are much smaller if some individual characteristics are incorporated into the model.     

Building Spatial Choice Models from Aggregate Data

Abstract Choice model construction is usually based on information about a number of separate choice situations, for which all relevant quantities are known. This paper concerns the case where only higher level, aggregate information is available about the choice results and the prevailing conditions. We demonstrate the applicability of a generic inverse parameter estimation method in estimating a model for grocery store choice. We also propose some enhancements to standard spatial choice models and demonstrate their applicability.     

THE JOINT CHOICE OF AN INDIVIDUAL'S OCCUPATION AND DESTINATION*

ABSTRACT This study examines the relationship between an individual's occupation choice and destination choice. It portrays the relationship as an interaction between the supply of occupational skills by individuals and demand by different labor‐market regions. The unusual merger of a multinomial logit model of occupational choice and the conditional logit model of destination choice in a simultaneous equation framework requires derivation of a unique variance–covariance matrix. Results indicate strong association between supply of (migration) and demand for (industry mix) an individual's occupational skills. These effects are especially strong for destinations experiencing slow economic growth, while relatively unimportant for high‐growth locations.     

Representing the Shape and Orientation of Destinations in Spatial Choice Models

This paper illustrates the importance of spatial unit shape and orientation in spatial choice analysis. It also examines the implications of assuming spatial units to be dimensionless points in this context. Through theory and simulation experiments, it is shown how these aspects cannot be ignored and how the ordinary multinomial logit model applied at the spatially aggregate level is particularly vulnerable to such oversights. The aggregated spatial logit model in the end is recommended as a general formulation which addresses many of these fundamental issues of interest to geographers and regional scientists.     

Strategic voting and constituency context: Modelling party preference and vote in multiparty elections

We examine the role of strategic motivations in mediating the relationship between underlying political preferences and vote choice, in a multiparty, single member, simple plurality system, and examine the role of constituency context in determining the scope for strategic voting. Political preference data from the British Election Panel Survey, 1997–2001, were modelled with mixed multinomial logit models. Latent variables were used to model the stable party political traits underlying observed preferences, allowing correlation between choices and so avoiding the restrictive assumption of independence from irrelevant alternatives. Ranked approval ratings were used to characterize the underlying political preferences in the presence of insincere voting. From these models we estimate that approximately 9% of votes cast may have been affected by strategic factors. In keeping with ‘Duvergers law’, the smallest of the three main parties, the Liberal Democrats, were found to be most affected by strategic voting.     

Testing Competing Explanations of Black Opinions on Affirmative Action

Using the 1996 National Black Election Study, I estimate black opinions of affirmative action by developing models that capture the effects of self‐interest, group consciousness, reference groups, and social justice. The method I used is ordered logit. An examination of the data show that, unlike many studies that examine the effects of self‐interest on public opinion, I find that self‐interest matters. I also find that black individuals also support affirmative action from a sense of group consciousness. The results also suggest that some support affirmative action consistent with the reference group theory and the pursuit of social justice.     

METROPOLITAN OUTMIGRATION PATTERN OF CANADIAN LABOUR FORCE ENTRANTS, 1971–76

This paper analyses the 1971 -76 metropolitan out-migration pattern of Canadian males in the labour force entrance age group. Migration is conceptualized within a three-level choice framework, and statistical inference is based on a multinomial logit model. It was found (1) that the propensity to outmigrate and the destination choice pattern vary substantially among the 23 metropolitan areas; (2) that 83 per cent of the variation in the destination choice probabilities of metropolitanward migrants can be explained by only five variables (log of distance, cultural dissimilarity, temperature, employment growth, and population size); and (3) that housing conditions are essentially the results (rather than the causes) of intermetropolitan migration .     

THE AGGREGATED SPATIAL CHOICE MODEL VS. THE MULTINOMIAL LOGIT: AN EMPIRICAL COMPARISON USING MIGRATION MICRODATA

Frequently, in spatial interaction analysis, researchers are forced to use destinations that are zonal aggregates of the ‘real’ destinations perceived by the participants in the interaction process. Previous simulation studies demonstrated that, under certain circumstances, the aggregated spatial choice model can outperform the popular ordinary multinomial logit model, both in explanatory power and predictive ability. In this paper, the two models are compared with interprovincial migration microdata for the time period 1990-91, obtained from the 1991 Canadian census. Since this is not meant to be a migration study, the analysis is limited to out-migrants from Ontario. The results indicate that, at least with the data used, the multinomial logit model performed reasonably well. The paper, however, highlights some practical advantages that can accrue from the use of the aggregated model. Dans l'analyse de l'interaction à référence spatiale, il arrive fréquemment que les chercheurs soient contraints de se servir de destinations qui regroupent les?vraies?destinations perçues par les participants dans le processus d'interaction. Les études en simulations antérieures ont démontré que, dans certaines circonstances, le modèle groupé des choix à référence spatiale peut donner de meilleurs résultats que le modèle ordinaire commun du logit multinomial, sur le plan de la capacité d'explication comma sur celui de la valeur de prévision. Dans la présente étude, on fait la comparaison entre les deux modèles en utilisant les microdonnées sur l'émigration interprovinciale en 1990-91 obtenues par le recensement de 1991. L'analyse ne porte que sur les émigrants de l'Ontario puisqu'elle ne vise pas particulièrement l'étude de l'émigration. D'après les résultats, le modèle employant le logit multinomial fonctionne relativement bien, au moins avec les données utilisées. Toutefois, l'étude souligne certains avantages pratiques pouvant inciter à se servir davantage du modèle groupé.