| 书目名称 | Gravity Models of Spatial Interaction Behavior | | 编辑 | Ashish Sen,Tony E. Smith | | 视频video | | | 丛书名称 | Advances in Spatial and Network Economics | | 图书封面 |  | | 出版日期 | Book 1995 | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-79880-1 | | isbn_softcover | 978-3-642-79882-5 | | isbn_ebook | 978-3-642-79880-1Series ISSN 1430-9599 | | issn_series | 1430-9599 |
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Front Matter |
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Abstract
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Introduction |
Ashish Sen,Tony E. Smith |
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Abstract
Since the early 1940’s, efforts to model the spatial interaction behavior of human populations have been largely dominated by .. The appeal of these models can be attributed both in the simplicity of their mathematical form and the intuitive nature of their underlying assumptions. For, as observed by Isard and Bramhall (1960, p. 515), these models amount to the simplest possible representation of the basic . that, all else being equal, ‘the interaction between any two populations can be expected to be directly related to their size; and… inversely related to distance’. Thus, to the extent that interaction behavior is consistent with this hypothesis, one may expect gravity models to perform reasonably well empirically.
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Spatial Interaction Processes: An Overview |
Ashish Sen,Tony E. Smith |
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Abstract
In this chapter we introduce the basic theoretical framework to be employed throughout the rest of the book. The formal details of the framework will be developed in a more abstract theoretical setting in Chapter 3 below. Hence the objectives here are to introduce the main concepts in an informal manner, and to illustrate their meaning in terms of simple examples. To do so, we begin in Section 1.2 below with a consideration of the basic theoretical perspectives embodied in the present approach to spatial interaction behavior.
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Gravity Models: An Overview |
Ashish Sen,Tony E. Smith |
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Abstract
Given the general class of spatial interaction processes outlined in Chapter 1, we are now ready to develop the specific class of behavioral models which form the central focus of this book — namely . of spatial interaction behavior. To do so, we begin by recalling from the discussion following the Poisson Characterization Theorem in Chapter 1 that each independent interaction process, . = {.:. ∈ .}, is completely characterized by its associated ., E.(.), . ∈ ., for each separation configuration, . ∈ .. Hence each explicit model of mean interaction frequencies yields a complete specification of probabilistic interaction behavior in this context. With this observation in mind, recall from the Introduction that gravity models are precisely of this type. In particular, if the ‘interaction levels’, ., in expressions (2) through (4) in the Introduction are now interpreted as mean interaction frequencies for the separation configuration defined by distances, . then each of these expressions is seen to constitute an explicit (finite parameter) model of mean interaction frequencies. More generally, even for spatial interaction processes in which the axioms of frequency independence and/or
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Spatial Interaction Processes: Formal Development |
Ashish Sen,Tony E. Smith |
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Abstract
In this chapter, the basic notations of interaction processes and their associated frequency processes are developed in a formal way. We begin in Section 3.2 below with a development of certain mathematical concepts which will be employed throughout the analysis. This is followed in Section 3.3 by a development of a general probability model of interactions which focuses on the locational and frequency attributes of interaction patterns. In Section 3.4, the class of . discussed in Section 1.4.2 is then formalized, and the important subclass of . discussed in Section 1.4.3 is developed in detail. In Section 3.5, the corresponding concepts of . and . are developed, and the fundamental . discussed in Section 3.6.2 is established in terms of these concepts. Finally, the application of this general result to the classes of threshold interaction processes and search processes discussed in Examples 2 and 4 of Chapter 2 are developed formally in Sections 3.7 and 3.8, respectively.
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Gravity Models: Formal Development |
Ashish Sen,Tony E. Smith |
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Abstract
In this chapter, the classes of gravity models developed in Chapter 2 are formalized, and are shown to be characterized by the axioms in Chapter 2. We begin in Section 4.2 below by developing a formal specification of the various gravity model classes within the probabilistic framework of Chapter 3. In Section 4.3, we examine in more detail certain of the illustrations of these model classes developed in Chapter 2. In Section 4.4, the general behavioral axioms of Chapter 2 are then formalized within the framework of Chapter 3. The central results of the chapter are developed in Section 4.5. First, the aggregate characterizations of general gravity representations presented in Section 2.2.3(A) of Chapter 2 are formally established in Theorem 4.1. Next, the local characterizations of general gravity representations in Section 2.2.3(B) of Chapter 2 are established in Theorem 4.2. The characterizations of exponential gravity representations in Section 2.4.3 of Chapter 2 are then established in Theorem 4.3. Finally in Section 4.6, the generalizations of gravity models discussed in Sections 2.5.2 and 2.5.3 of Chapter 2 are formally developed within the framework of Chapter 3.
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Maximum Likelihood |
Ashish Sen,Tony E. Smith |
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Abstract
As mentioned in the introduction to the book, the key use for the gravity model is forecasting and for forecasting, it is important to know which aspects of the base period remain unchanged into the forecast period. Therefore, in the context of the gravity model, we would usually need to know which aspects of the model are configuration-free. In Part I of this book, we saw the conditions under which one or more of the functions .(.), .(j) and .(.) are configuration-free and therefore can be assumed to remain invariant from base to forecast period. However, we still need to get numerical estimates of the parameters in these functions. This chapter and the next are devoted to this topic.
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Least Squares |
Ashish Sen,Tony E. Smith |
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Abstract
Maximum likelihood procedures are very much in favor among those interested in parameter estimation, and as mentioned in Chapter 5 for good reason. However, ML methods are not the only estimation methods. Very frequently used alternatives to maximum likelihood are various methods using linear and non-linear least squares. In this chapter we examine the use of these procedures for estimation of gravity model parameters.
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Back Matter |
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Abstract
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发表于 2025-3-21 19:59:31
