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.     

FUNCTION AND COMPETITION AMONG URBAN CENTERS*

ABSTRACT This paper uses a logit model of consumer choice to examine how changes in the spatial behavior of rural consumers will affect the commercial base of smaller urban places. Various socio-economic changes in a region can be expected to cause a number of behavioral changes, including changes in where people work and shop. The analysis presented in the paper emphasizes the importance of location to the commercial prospects of small trade centers as consumers become more spatially mobile and engage in more multipurpose shopping. Places that are centrally located have the best prospects for ensuring that functions are either maintained or suffer the least decline as a result of competition from higher-order centers. Remoter locations will be adversely affected by these competitive pressures.     

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.     

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.     

A Spatial Mixture Model of Innovation Diffusion

The diffusion of new product or technical innovation over space is here modeled as an event‐based process in which the likelihood of the next adopter being in region r is influenced by two factors: (i) the potential interactions of individuals in r with current adopters in neighboring regions, and (ii) all other attributes of individuals in r that may influence their adoption propensity. The first factor is characterized by a logit model reflecting the likelihood of adoption due to spatial contacts with previous adopters, and the second by a logit model reflecting the likelihood of adoption due to other intrinsic effects. The resulting spatial diffusion process is then assumed to be driven by a probabilistic mixture of the two. A number of formal properties of this model are analyzed, including its asymptotic behavior. But the main analytical focus is on statistical estimation of parameters. Here it is shown that standard maximum‐likelihood estimates require large sample sizes to achieve reasonable results. Two estimation approaches are developed which yield more sensible results for small sample sizes. These results are applied to a small data set involving the adoption of a new Internet grocery‐shopping service by consumers in the Philadelphia metropolitan area.     

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).     

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.     

A Conditional Logit Approach to U.S. State-to-State Migration

This paper uses a conditional logit approach to study interstate migration in the United States for each of eleven years, from 1986–1987 to 1996–1997. We test substantive hypotheses regarding migration in the United States and demonstrate the richness of the conditional logit approach in studies of place-to-place migration. We investigate migration responses to relative economic opportunities (unemployment rate, per capita income) and the associated costs of moving (distance between origin and destination and its square). We also investigate how noneconomic factors, such as amenities, affect migration between states through a state fixed effect. Finally, we study the magnitude of unmeasured costs associated with a particular migration. The conditional logit model also allows us to compute various trade-off and other values that are of interest in migration analysis.     

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.     

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.     

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。     

Incorporating the effects of spatial structure in discrete choice models of migration

Discrete-choice theory and logit models are evaluated for their usefulness in analyzing migration patterns in a zonal system. The authors "argue that spatial effects and more specifically the relative location of zones are not taken into account in such analyses. We, therefore, introduce a measure of spatial structure and advocate its usage as a predictor of migration in such models. In an example of intrametropolitan migration in Toronto [Canada], we demonstrate that this variable is not only significant but also it improves the performance of all the other variables with the greatest impact on the distance between zones. In addition, inclusion of this variable improves the overall performance of the model in terms of residuals."     

Does Policy Diffusion Need Space? Spatializing the Dynamics of Policy Diffusion

For decades, scholars in multiple disciplines have examined spatial diffusion, or the spatiotemporal properties associated with the diffusion of innovations. These properties include contagious, hierarchical, and relocation diffusion. Each of these refers to a spatial model that epitomizes how innovations spread among geographic locations. Policy diffusion, a separate but homologous research tradition, had its theoretical underpinnings in spatial diffusion. However, contemporary policy diffusion has focused largely on mechanism‐based diffusion. This article demonstrates how exploratory spatial data analysis can be used to uncover spatial policy diffusion properties. In this study, municipal smoking regulation adoptions, religious‐based initiatives, and bag ban and bag fees are examined. This study finds evidence that for each policy more than one property is occurring; therefore, this study proposes that a hybrid model best explains diffusion. This article demonstrates how examining spatial diffusion properties, in addition to diffusion mechanisms, can improve the conceptualization of diffusion theories, enhance mechanism or theory‐based specification of diffusion models, and unravel the specific regional or neighboring causal pathways linking policies between adopting jurisdictions.     

INTERPRETING SPATIAL ECONOMETRIC ORIGIN‐DESTINATION FLOW MODELS

Spatial interaction or gravity models have been used to model flows that take many forms, for example population migration, commodity flows, traffic flows, all of which reflect movements between origin and destination regions. We focus on how to interpret estimates from spatial autoregressive extensions to the conventional regression‐based gravity models that relax the assumption of independence between flows. These models proposed by LeSage and Pace ( 2008 , 2009 ) define spatial dependence involving flows between regions. We show how to calculate partial derivative expressions for these models that can be used to quantify these various types of effect that arise from changes in the characteristics/explanatory variables of the model.     

Markovian Models of Movement Within Urban Spatial Structures

Much work has assumed that movement within urban spatial structures is an “adaptive” process. Nonetheless, mathematical models have not yet been specified and tested which formulate both how different individuals “adapt” over time in destination or route selection, and how predictions about aggregate movement can be derived from postulates about different persons. Two adaptive first-order Markov models for heterogeneous individuals are suggested by the literature. When formulated and tested, however, these models are inadequate to describe travel within urban spatial structures. This implies that the use of Markovian processes to model movement may be overrated. More confidence may be placed in other formulations such as linear learning models of route and destination choice.     

SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS*

ABSTRACT. We determine the location equilibria in a duopoly model under a novel solution concept. Typically, spatial equilibrium is described as either a simultaneous price and location game, or else as a two-stage location-then-price game. We introduce a new alternative, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the two standard solution concepts when products are homogeneous. We show this is also true for the new concept. We then provide numerical results for a specific functional form (the logit model) which introduces product heterogeneity into the standard framework, restoring equilibrium when the degree of substitutability between products is not too small.     

Designs for Detecting Spatial Dependence

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such structure. The starting point of this analysis involves two different linear regression models: (1) an ordinary linear regression model with i.i.d. error terms—the nonspatial case and (2) a regression model with a spatially autocorrelated error term, a so-called simultaneous spatial autoregressive error model. The procedure can be divided into two main parts: The first is use of an exchange algorithm to find the optimal design for the respective data collection process; for its evaluation an artificial data set was generated and used. The second is estimation of the parameters of the regression model and calculation of Moran's I , which is used as an indicator for spatial dependence in the data set. The method is illustrated by applying it to a well-known case study in spatial analysis.     

ON FRONTIER SPECIFICATIONS FOR DISCRETE BINARY CHOICE ANALYSIS

ABSTRACT. In estimating a discrete choice model one is actually estimating the parameters of a conditional indirect utility function. I explore the consequences of recognizing that this function is a maximum-value (frontier) function. I formulate several frontier choice models and, using a pilot empirical study of transportation mode choice, compare the resulting estimates with those of the conventional logit specification. Most strikingly, it appears that the values of time implied by the frontier models are substantially below those of the logit model. This implies that policies designed to improve travel times may be of less value to consumers than is conventionally believed.     

DIAGNOSTICS FOR REGRESSION MODELING IN SPATIAL ECONOMETRICS*

ABSTRACT. This paper describes statistics for model criticism in spatial econometrics. The purpose of these statistics is to evaluate how well a chosen model fits the data and to identify influential cases and how they affect the aggregate picture. The paper reviews results in Martin (1992) for the regression model with correlated errors where the coefficients of the variance matrix are assumed either known or fixed. The problems of applying the statistics in spatial econometric modeling are discussed. An application is reported which considers diagnostics for the mean function and highlights cases that might influence estimates of the parameter of the error model. Different ways of assessing the influence of cases are also described.     

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.