Multiple Contexts as Cross-classified Models: The Labor Vote in the British General Election of 1992

Voters make their decisions in social and geographical contexts that can be seen as different levels in an overall data structure. Increasingly these structures are being analyzed by multilevel models, but this approach has so far been limited to structures that are strictly hierarchical. This paper outlines the approach of cross-classified multilevel models in which units at lower levels in the structure can be nested in more than one higher-level unit simultaneously. An appropriate modeling framework is outlined, models are specified, and particular attention is paid to efficient computation. The approach is illustrated through a cross-classified logit analysis of Labor versus Conservative support for a nationally representative sample of voting behavior for the 1992 British General Election. The data is structured so that individual voters at level 1 are nested within constituencies at level 2 which are cross-classified by geographical and functional regionalizations at level 3. A conclusion discusses the general utility of a cross-classified approach to geographically based contextual research, while two technical appendices provide details on model estimation.     

Joint Effects of Personal Factors and Ecological Variables on the Interprovincial Migration Pattern of Young Adults in Canada: A Nested Logit Analysis

This paper applies a nested logit model to the 1981 census micro data to study the joint effects of personal factors (sex, mother tongue, nativity, education, and marital status) and ecological variables on the 1976–1981 interprovincial migration pattern of young adults in Canada. In multivariate contexts, personal factors not only are of paramount importance in explaining the departure process but also have significant interactions with ecological variables in determining the destination choice pattern.     

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.     

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.     

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.     

Milieux innovateurs: Determinants and policy implications

National and regional differences are more and more frequently explained by differences in milieux. This type of explanation raises three questions: Can we identify milieux? What are the determinants of milieux? Are there differences between industries in the matter of determinants of milieux? Most studies on milieux innovateurs are based on case studies and qualitative data. This paper is quantitative and comparative in nature. It attempts to identify milieux and their determinants by using data from the 1999 Statistics Canada Innovation Survey. Based on two synthetic indicators of interactions (weak/strong) and learning (weak/strong), four categories of milieux innovateurs are differentiated which become the dependent variables. In order to see what the determinants of the various milieux innovateurs are and to see in what ways the most favorable milieux innovateurs compare to the others, binomial logit models have been estimated for four industries using the following independent variables: competitive pressures, barriers to knowledge exchange, use of government support, number of employees, collaborative arrangements, R&D activities, regions.     

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。     

Alternative Nested Logit Model Structures and the Special Case of Partial Degeneracy

Partially degenerate nested logit (NL) models have broad applicability in regional science. However, the literature on them is relatively sparse and confusion exists on some aspects of identification and related matters. This paper addresses a number of conceptual and econometric aspects of partially degenerate NL models. These include identification, scaling, invariance, and consistency with the utility-maximizing postulate that underlies discrete choiceanalysis. This is accomplished within the larger, encompassing framework of nondegenerate NL models of which the partially degenerate model is a special case.     

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.     

Return and Onward Interprovincial Migration through Economic Boom and Bust in Canada,from 1976–81 to 1981–86

This paper applies a three-level nested logit model to the micro data of the 1981 and 1986 Canadian census to study the effects of personal factors and provincial attributes on the interprovincial migration patterns of the non-native young adults (aged 20–44) through the economic boom of 1976–81 and the economic bust of 1981–86. We found strong evidence that through both boom and bust periods, both return and onward migrations were in the “right” direction, in that they responded to economic variables in a rational way. However, the large proportion of migrants choosing to make a return migration indicates the importance of the province of birth in the mental map of the potential migrants. We also found that the selectivities in the migration behaviors with respect to certain personal factors (especially education) remained basically the same through both boom and bust periods.     

Disaggregate Migration Behavior and the Volume of Interregional Migration

Nested multinomial logit models are used to investigate migration behavior during the 1971–74 period for a large sample of the population of Ecuador. The nested form of the model makes it possible to test hypotheses about the importance of destination characteristics in conditioning the odds for out-migration. Our empirical results indicate that the odds for migration from each origin are conditioned by the expected utilities of the available set of destinations, as well as characteristics of the origins and the personal characteristics of potential migrants. The association between destination characteristics and the frequency of out-migration allows the total volumes of migration to be adjusted to interregional differences in place-specific utilities.     

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.     

ESTIMATION AND HYPOTHESIS TESTING FOR NONPARAMETRIC HEDONIC HOUSE PRICE FUNCTIONS

ABSTRACT In contrast to the rigid structure of standard parametric hedonic analysis, nonparametric estimators control for misspecified spatial effects while using highly flexible functional forms. Despite these advantages, nonparametric procedures are still not used extensively for spatial data analysis due to perceived difficulties associated with estimation and hypothesis testing. We demonstrate that nonparametric estimation is feasible for large datasets with many independent variables, offering statistical tests of individual covariates and tests of model specification. We show that fixed parameterization of distance to the nearest rapid transit line is a misspecification and that pricing of access to this amenity varies across neighborhoods within Chicago.     

Modeling Categorical Data with Chi Square Automatic Interaction Detection and Correspondence Analysis

For the past decade we have been concerned with the application of categorical data techniques to mobility and housing choice. In a previous issue of this journal we reviewed a number of these modeling techniques. We now extend that earlier work by introducing correspondence analysis as a geometric interpretative technique that fits in an intermediate position between CHAID and nested logit analysis. The method is illustrated on the same housing and tenure choice data as was used in the previous paper.     

Housing Choice in a Regulated Market: A Nested Multinomial Logit Analysis

The paper integrates several important elements of the institutionalized and regulated nature of the housing market and analyzes the relationship between household type and housing choice in Vienna within a nested multinomial logit framework. In particular, the concept of household specific choice sets is used to account for institutional, informational and income-based constraints of the choice process. Government subsidies (such as housing and rent allowances, non-interest-bearing state loans) are explicitly taken into account in the definition of variables. Housing choice is considered in three stages: the choice of a dwelling unit given dwelling type and residential zone, the choice of a dwelling type given residential zone, and the marginal choice of a residential zone. The coefficients are derived by means of a sequential ML-procedure. The empirical results clearly indicate that demographic variables have significant impacts on housing choice behavior. Income as a single explanatory variable as well as its interacting with size measures and the quality of the house are found to be important criteria for dwelling unit choice, as housing cost variables for dwelling type choice behavior. The dwelling unit and dwelling type choice submodels fit reasonably well, whereas the residential zone model is less successful.     

A Nested Logit Approach to Household Mobility

This study analyzes personal and site characteristics in a model of intraMSA and interMSA mobility. Households are assumed to choose a single type of move, intraMSA or interMSA, while simultaneously choosing a central city or suburban destination. We demonstrate that a nested logit model is appropriate on both theoretical and empirical grounds. The sample consists of intrametropolitan and intermetropolitan movers drawn from the 1990 U.S. Census PUMS. Personal characteristics drawn from the PUMS are matched to numerous site characteristics (climatic measures, other amenities, state and local fiscal characteristics, and other urban quality measures) drawn from a variety of sources. Nested logit direct and cross elasticities are presented for a number of site attributes.     

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.     

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.     

MODELING SPATIAL AUTOCORRELATION IN SPATIAL INTERACTION DATA: AN APPLICATION TO PATENT CITATION DATA IN THE EUROPEAN UNION*

ABSTRACT Spatial interaction models of the gravity type are widely used to model origin–destination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterize an origin region of a flow, variables that characterize a destination region of a flow, and finally variables that measure the separation between origin and destination regions. This paper outlines and compares two approaches, the spatial econometric and the eigenfunction‐based spatial filtering approach, to deal with the issue of spatial autocorrelation among flow residuals. An example using patent citation data that capture knowledge flows across 112 European regions serves to illustrate the application and the comparison of the two approaches.