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.     

Local Spatial Autocorrelation in a Biological Model

We review the recently developed local spatial autocorrelation statistics I_i, c_i, G_i, and G_i*. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for I_i and c_i, as well as under total randomization for c_i. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 × 21 lattice of stepping stones (sixty-four individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random surfaces. We find that spatially random designs give reliable test results by permutational methods of testing significance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing significance failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets.     

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.     

Loglinear Residual Tests of Moran's I Autocorrelation and their Applications to Kentucky Breast Cancer Data

This article bridges the permutation test of Moran's I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran's I based on Pearson residuals ( I _PR) and deviance residuals ( I _DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both I _PR and I _DR are effective to account for heterogeneous population sizes. The tests based on I _PR and I _DR are applied to a set of log-rate models for early-stage and late-stage breast cancer with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables can sufficiently explain spatial clustering of early-stage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four late-stage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of early-stage disease, which in turn would reduce late-stage incidence rates.     

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.     

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.     

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).     

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.     

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.     

BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

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.     

THE IMPACT OF REMITTANCES ON REGIONAL CONSUMPTION AND INVESTMENT

This paper examines the effects of international remittances on regional economic development using spatial data from an original household survey carried out in the Republic of Moldova. I analyze remittance flows with a model that estimates regional (urban and rural) budget shares of consumption and investment expenditure categories for rural and urban households. An important contribution of the paper is that it analyzes the effect of remittances in the regions where spending takes place, which is not necessarily the same as the region where the households originating this spending reside. Using the multinomial logit approach, I control for potential selectivity and endogeneity biases of remittances. The results show that remittances lead to significantly increasing marginal productive investments in urban regions at the expense of rural regions. The fundamental finding of the study is that remittances influence the flight of productive capital out of rural areas into urban regions (a pattern similar to the crowding‐out effect of the Dutch Disease). The analysis carried out in this paper can be applied to other temporary income transfers and exogenous spending injected in the region that affect households' regional expenditure patterns.     

The contribution of Sir Alan Wilson to spatial interaction and transport modelling

ABSTRACT

In a series of papers in the mid-1960s and early 70s, building on his key 1967 paper, Alan Wilson made a series of fundamental contributions to the specification and application of land-use transport models. In this paper the basis of his entropy-maximizing approach to spatial distribution models is outlined with a demonstration that the methods have applications very much beyond its transport roots. The entropy maximization method laid the foundations for the development of a range of multinomial logit share models. He expanded the core transport ideas to the whole range of comprehensive models, initially building on, and extending, Lowry's iconic Pittsburgh model. The factors that have sustained the longevity of Wilson's models are explored and articulated.     

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.     

中国外资银行空间网络演化的结构特征及其影响因素

本文基于外资银行网点数据,借鉴连锁型网络模型,构建了1990年、2001年和2015年中国外资银行空间网络并分析演化结构特征,最后借助条件Logit模型探讨了外资银行空间分布的影响因素。研究表明：①中国外资银行空间网络小世界网络特征明显,具有较大的集聚系数和较小的平均路径长度,网络中局域小集团网络化特征和核心-边缘结构明显。②随着网络规模的平稳增长,网络的有序性呈现出增强趋势,网络中金融连接度和金融可达性增加,金融传输效率和组织效率进一步提高,核心-边缘结构现象有所加剧。③外资银行空间分布的主导因素在不同时期不一样,1990年主导因素是市场机会和区位效应,2001年和2015年的主导因素是金融集聚,但指标的具体影响概率有所降低。     

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."     

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.     

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.     

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。