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Spatial Choice Models
Spatial Autocorrelation Dacey M 1965 A review of measures of contiguity for two and kcolor maps. In: Berry B, Marble D (eds.) Spatial Analysis: A Reader in Statistical Geography. Englewood Cliffs, NJ, pp. 479–95 Dunn R, Harrison A 1993 Two dimensional systematic sampling of land use. Applied Statistics 42: 585–601 Foster B 1980 Urban residential ground cover using Landsat digital data. Photogrammetric Engineering and Remote Sensing 46: 547–58 Geary R 1954 The contiguity ratio and statistical mapping. The Incorporated Statistician 5: 115–45 Green P 1996 MCMC in image analysis. In: Gilks G, Richardson S, Spiegelhalter D (eds.) Marko Chain Monte Carlo in Practice. Chapman & Hall, London, pp. 381–99 Haining R 1983 Anatomy of a price war. Nature 304: 679–80 Haining R 1984 Testing a spatial interacting-markets hypothesis. Reiew of Economics and Statistics 66: 576–83 Haining R 1987 Small area aggregate income models: theory and methods with an application to urban and rural income data for Pennsylvania. Regional Studies 21: 519–30 Haining R 1990 Spatial Data Analysis in the Social and Enironmental Sciences. Cambridge University Press, Cambridge, UK Haining R, Wise S, Ma J 1998 Exploratory spatial data analysis in a GIS environment. The Statistician 47: 457–69 Isaaks E, Srivastava R 1989 An Introduction to Applied Geostatistics. Oxford University Press, Oxford, UK Krishna Iyer P 1949 The first and second moments of some probability distributions arising from points on a lattice, and their application. Biometrika 36: 135–41 Marshall R 1991 A review of methods for the statistical analysis of spatial patterns of disease. Journal of the Royal Statistical Society, Series A 154: 421–41 Milne A 1959 The centric systematic area sample treated as a random sample. Biometrics 15: 270–97 Mollie A 1996 Bayesian mapping of disease. In: Gilks G, Richardson S, Spiegelhalter D (eds.) Marko Chain Monte Carlo in Practice. Chapman & Hall, London, pp. 359–79 Moran P 1948 The interpretation of statistical maps. Journal of the Royal Statistical Society, Series B 10: 243–51 Ord J 1975 Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70: 120–6 Richardson, S 1992 Statistical methods for geographical correlation studies. In: Elliott P, Cuzick J, English D, Stern R (eds.) Geographical and Enironmental Epidemiology: Methods for Small Area Studies. Oxford University Press, Oxford, UK pp. 181–204 Ripley B 1981 Spatial Statistics. Wiley, New York Whittle P 1954 On stationary processes in the plane. Biometrika 41: 434–49 Waldhor T 1996 The spatial autocorrelation coefficient Moran’s I under heteroscedasticity. Statistics in Medicine 15: 887–92
R. P. Haining
constitutes the basis for the evolution of spatial structures. In turn, the supply of facilities across space provides opportunities for individuals and households to conduct their activities, but at the same time also sets the space-time constraints that restrict behavior. Over the years, many different attempts at modeling spatial choice behavior have been reported in the literature. These models predict the probability that an individual will choose a choice alternative as a function of its locational and non-locational attributes. In this article, the background, theoretical underpinnings, and basic methodology of these modeling approaches are examined. From the outset, it should be clear that limited available space prevents us from discussing modeling approaches in considerable detail.
1. Graity Models The modeling of spatial choice behavior gained considerable momentum when Wilson (1971) introduced a family of spatial interaction models, based on the principle of gravity, to describe and predict social phenomena. This principle states that the interaction between two bodies is proportional to their masses, and inversely proportional to the square of distance. Wilson elaborated this principle in a number of ways. First, he suggested that any distance decay function that reflects the notion that, ceteris paribus, the intensity of interaction decreases with increasing distance may be used to replace straight distance. Secondly, he argued that in spatial problems often the number of departures from particular origins and\or the number of arrivals at particular destinations is known, implying that so-called balancing factors have to be introduced in the model to satisfy these constraints. Wilson distinguished an unconstrained spatial interaction model (departures and arrivals are not known), a production-constrained spatial interaction model (number of departures per zone is known), an attractions-constrained spatial interaction model (number of arrivals per zone is known), and the doubly constrained spatial interaction model (both number of departures and number of arrivals per zone are known). In the context of spatial choice behavior, the production constrained spatial interaction model is most interesting as it predicts which destination will be chosen. It can be expressed as: pij l AiOiWj f (dij)
Spatial Choice Models The interrelationship between spatial structure and individual choice behavior has traditionally been at the forefront of geographic research. Geographers have realized that spatially varying consumer demand 14768
(1)
where, pij is the probability that an individual in zone i will choose destination j; Ai is a balancing factor, guaranteeing that the number of predicted interactions from zone i is equal to its number of observed interactions; Oi is the number of observed interactions from zone i; Wj is a vector of variables, representing
Spatial Choice Models the attractiveness of destination j; f (dij) is some function of the distance between origin i and destination j. Although much empirical work has been conducted on spatial interaction models since this seminal work, most of the relevant literature has been concerned with operational problems. Theoretical progress has been limited. For example, different measures of distance (straight-line distance, Euclidean distance, cityblock metric, and travel time) and attractiveness have been suggested. Likewise, different functions for representing the distance decay effect have been proposed (power, exponential, and more complex functions). Finally, an exponent has been added to the specification of attractiveness term to allow for the fact that the larger destinations tend to have extra attraction beyond their size because of the benefits of economies of scale. The estimation of spatial interaction models is typically based upon aggregate, zonal data of interaction flows (shopping, recreation, migration, traffic, etc). To that effect, the study area is delineated carefully to avoid large external flows, and divided into a number of smaller homogeneous zones. The spatial interaction model is calibrated using observations about interactions between these zones as input. As a result, the parameters of the spatial interaction model are highly influenced by the geometry of the study area. This caused a search for improvements of the model, and for alternative modeling approaches. In this context, some authors suggested the development of models that estimate the effects of attraction variables endogenously. Another way of dealing with this problem was to incorporate some measure of spatial structure into a spatial interaction model (Fotheringham 1983). The simplest approach to the specification of this additional term is the use of a Hansen-type accessibility measure. This so-called competing destinations model may be expressed as: pij l AiOiWjC δj d −ijβ
(2)
where Ai l
A B
WjC δj d −ijβ j
C
−"
(3)
D
and Cj l Wjd −jkγ
(4)
kj
2. The Reealed Preference Model The fact that the spatial interaction model is heavily influenced by the geometry of the study led Rushton (1969) to develop a preference-scaling model. The
purpose of the model was to derive rules of spatial choice behavior. To that effect, choice alternatives were classified into so-called locational types, which are a combination of an attractiveness category and a distance category. Spatial choice behavior is assumed to reflect a trade-off between attractiveness and distance separation. Pairwise choice data are then used to calculate the proportion of times a particular locational type is chosen, given that both are present. Based on this data, the locational types are positioned on a unidimensional preference scale using a nonmetric multidimensional scaling algorithm. Over the years, this basic model has been elaborated in a number of important ways. First, Rushton (1974) showed how graphical methods, trend surface analysis, or conjoint analysis might be used to decompose the preference scale into the contributions of the two basic variables. Second, Girt (1976) suggested linking the preference function to overt behavior by relating distances on the preference scale to choice probabilities. Third, Timmermans (1979) suggested deriving the choice sets of individuals from data on information fields and consumer attitudes, and using these to scale the alternatives. Although Rushton’s preference scaling model does have considerable appeal, it never received any major following. One of the reasons might be that the model is based on two explanatory variables only, while heterogeneity in preferences is not accounted for. The model has also been criticized because of its conceptual basis. It has been suggested that the model may not represent preferences at all, but rather inconsistencies in individual choice behavior.
3. Discrete Choice Models The spatial interaction model has been criticized for its reliance on aggregate, zonal interaction flows. This criticism has led to the development of disaggregate discrete choice models that are based on individual choice behavior. Discrete choice models may be derived from at least two formal theories: Luce’s strict utility theory and Thurstone’s random utility theory. In particular, Luce assumed that the probability of choosing a choice alternative is equal to the ratio of the utility associated with that alternative to the sum of the utilities for all the alternatives in the choice set. Luce thus assumed deterministic preference structures and postulated a constant-ratio decision rule. In contrast, random utility theory is based on stochastic preferences in that an individual is assumed to draw a utility function at random on each choice occasion. An individual’s utility for a choice alternative is assumed to consist of a deterministic component and a random utility component. Given the principle of utility maximizing behavior, the probability of choosing a choice alternative is then equal to the 14769
Spatial Choice Models probability that its utility exceeds that of all other choice alternatives in the choice set. The specification of the model depends on the assumptions regarding the distributions of the random utility components. The best-known model is the multinomial logit (MNL) model. It can be derived by assuming that the random utility components are independently, identically Type I extreme value distributed. It can be expressed as: pik l
exp [U(Xk, Si)] exp [U(Xj, Si)]
(5)
j
where U(Xk, Si) is the deterministic part of the utility of choice alternative k of individual i with socioeconomic characteristics Si. One of the most important criticisms that have been expressed against the multinomial logit model concerned the fact that the utility of a choice alternative is independent of the existence and the attributes of other alternatives in the choice set (the Independence from Irrelevant Alternatives or IIA property). It predicts that the introduction of a new, similar choice alternative will reduce market shares in direct proportion to the utility of the existing alternatives, which is counterintuitive in the case of a high degree of similarity between particular alternatives. Therefore, various alternative models have been developed to relax the IIA assumption (Timmermans and Golledge 1990). Similar work in this regard has been conducted by Williams (1977). The best-known model that circumvents the IIA-property is the nested logit model. Choice alternatives that are assumed to be correlated are grouped into the same nest. Each nest is represented by an aggregate alternative with a composite utility, consisting of the so-called inclusive value, and a parameter to be estimated. To be consistent with utility-maximizing behavior, the inclusive values should lie in the range between 0 and 1, and the values of the parameters should change consistently from lower levels to higher levels of the hierarchy.
4. Conjoint Preference and Choice Models Unlike discrete choice models, the parameters of the conjoint preference and choice models are not derived from real-world data, but from experimental design data. Conjoint models involve the following steps when applied to spatial choice problems (e.g., Timmermans 1984). First, each choice alternative is described by its position in a set of attributes, considered relevant for the problem at hand. Next, a series of levels for each attribute is chosen. Having defined the attributes and 14770
their levels, the next step involves creating an experimental design to generate a set of hypothetical choice alternatives. This design should be created such that the necessary and sufficient conditions to estimate the model of interest are satisfied. Respondents are then required to evaluate the resulting attribute profiles. Their responses are decomposed into the utility contribution of the attribute levels. Once partworth utilities have been estimated, choice behavior can be predicted by assuming that an individual will choose the alternative with the highest overall evaluation. Alternatively, different probabilistic rules can be postulated. To avoid such ad hoc rules, Louviere and Woodworth (1983) suggested estimating the preference function and choice model simultaneously. To that end, the attribute profiles should be placed into choice sets. Again, the composition of the choice sets depends on the properties of the choice model. Over the years, the basic conjoint preference and choice models have been elaborated in many different ways. To avoid the problem of information overload and reduce respondent demand, Louviere (1984) suggested the Hierarchical Information Integration method. It assumed that individuals first group the attributes into higher-order decision constructs. Separate designs are constructed for each decision construct, and a bridging experiment is designed for measuring the tradeoff between the evaluations of the decision constructs. Oppewal et al. (1994) suggested an improved methodology by using multiple-choice experiments to test the implied hierarchical decision structure. Other recent advances include the development of group preference models, the development of models of portfolio choice, the inclusion of contextual effects and constraints, and the combined use of experimental design and revealed preference data, to name a few.
5. Complex Spatial Choice Behaior The previous models are all typically based on singlepurpose, single-stop behavior. Over the years, however, it became clear that an increasing proportion of trips involved multistop behavior. Moreover, Ha$ gerstrand’s time geography had convincingly argued that behavior does not reflect preferences only, but also constraints. Thus, various attempts have been made to develop models of trip chaining and activity-travel patterns. Originally, most models relied on semi-Markov process models or Monte Carlo simulations. More recently, utility-maximizing models have dominated the field. An important contribution in this regard was made by Kitamura (1984), who introduced the concept of prospective utility. It states that the utility of a destination is not only a function of its inherent attributes and the distance to that destination, but also
Spatial Cognition of the utility of continuing the trip from that destination. Dellaert et al. (1998) generalized Kitamura’s approach to account for multipurpose aspects of the trip chain. Trip chaining is only one aspect of multiday activity\travel patterns. Several models have recently been suggested to predict more comprehensive activity patterns. These models can be differentiated into the older constraints-based models (e.g., Lenntorp 1976), utility-maximizing models (e.g., Recker et al. 1986), rule-based or computational process models (e.g., Golledge et al. 1994, ALBATROSS – Arentze and Timmermans 2000).
6. Conclusions This article has given a very brief overview of spatial choice modeling. Due to the limited available space, we have focused on some of the key modeling approaches, disregarding alternatives (e.g., dynamic models) altogether. If we examine the accomplishments, one cannot escape the conclusion that the models developed over the years have been increasing in complexity. The theoretical underpinnings of the recent activity-based models are much richer than the Markov or gravity models of the 1960s. Moreover, the brief overview indicates that geographers have been using alternative data, such as experimental design data and activity diaries, in addition to the more conventional survey data. See also: Spatial Analysis in Geography; Spatial Decision Support Systems; Spatial Interaction; Spatial Interaction Models; Spatial Optimization Models; Spatial Pattern, Analysis of; Spatial Statistical Methods; Spatial Thinking in the Social Sciences, History of
Bibliography Arentze T A, Timmermans H J P 2000 ALBATROSS: a Learning-based Transportation-oriented Simulation System. EIRASS, Eindhoven University of Technology, The Netherlands Dellaert B, Arentze T A, Borgers A W J, Timmermans H J P, Bierlaire M 1998 A conjoint based multi-purpose multi-stop model of consumer shopping centre choice. Journal of Marketing Research 35: 177–88 Ettema D F, Timmermans H J P 1997 Actiity-based Approaches to Trael Analysis. Elsevier Science, Oxford, UK Fotheringham A S 1983 A new set of spatial interaction models: The theory of competing destinations. Enironment and Planning, A 15: 1121–32 Girt J L 1976 Some extensions to Rushton’s spatial preference scaling model. Geographical Analysis 8: 137–56 Golledge R G, Kwan M P, Ga$ rling T 1994 Computational process modeling of travel decisions using a geographical information system. Papers in Regional Science 73: 99–117
Kitamura R 1984 Incorporating trip chaining into analysis of destination choice. Transportation Research 18B: 67–81 Lenntorp B 1976 Paths in space-time environments. Lund Studies in Geography, Series B, no. 44 Louviere J J 1984 Hierarchical information integration: a new method for the design and analysis of complex multiattribute judgment problems. In: Kinnear T C (ed.) Adances in Consumer Research 11, ACRA, Provo, UT, pp. 148–55 Louviere J J, Woodworth G 1983 Design and analysis of simulated consumer choice or allocation experiments: An approach based on aggregate data. Journal of Marketing Research 20: 350–67 Oppewal H, Louviere J J, Timmermans H J P 1994 Modeling hierarchical information integration processes with integrated conjoint choice experiments. Journal of Marketing Research 31: 92–105 Recker W W, McNally M G, Root G S 1986 A model of complex travel behavior: part I – theoretical development. Transportation Research, A 20A: 307–318 Rushton G 1969 Analysis of spatial behavior by revealed space preference. Annals of the Association of American Geographers 59: 391–400 Rushton G 1974 Decomposition of space preference structures. In: Golledge R G, Rushton G (eds.) Spatial Choice and Spatial Behaior. Ohio State University Press, Columbus, OH, pp. 119–33 Timmermans H J P 1979 A spatial preference model of regional shopping behaviour. Tijdschrift oor Economische en Sociale Geografie 70: 45–8 Timmermans H J P 1984 Decompositional multiattribute preference models in spatial choice analysis: a review of some recent developments. Progress in Human Geography 8: 189– 221 Timmermans H J P, Golledge R G 1990 Applications of behavioural research on spatial choice problems II: preference and choice. Progress in Human Geography 14: 311–54 Williams H C W L 1977 On the formation of travel demand models and economic evaluation measures of user benefit. Enironment and Planning, A 9: 285–34 Wilson A G 1971 A family of spatial interaction models and associated developments. Enironment and Planning, A 3: 1–32
H. Timmermans Copyright # 2001 Elsevier Science Ltd. All rights reserved.
Spatial Cognition Spatial cognition concerns the study of knowledge and beliefs about spatial properties of objects and events in the world. Cognition is about knowledge: its acquisition, storage and retrieval, manipulation, and use by humans, nonhuman animals, and intelligent machines. Broadly construed, cognitive systems include sensation and perception, thinking, imagery, memory, learning, language, reasoning, and problemsolving. In humans, cognitive structures and processes are part of the mind, which emerges from a brain and nervous system inside of a body that exists in a social and physical world. Spatial properties include location, size, distance, direction, separation and connection, shape, pattern, and movement. 14771
International Encyclopedia of the Social & Behavioral Sciences
ISBN: 0-08-043076-7
R. P. Haining
constitutes the basis for the evolution of spatial structures. In turn, the supply of facilities across space provides opportunities for individuals and households to conduct their activities, but at the same time also sets the space-time constraints that restrict behavior. Over the years, many different attempts at modeling spatial choice behavior have been reported in the literature. These models predict the probability that an individual will choose a choice alternative as a function of its locational and non-locational attributes. In this article, the background, theoretical underpinnings, and basic methodology of these modeling approaches are examined. From the outset, it should be clear that limited available space prevents us from discussing modeling approaches in considerable detail.
1. Graity Models The modeling of spatial choice behavior gained considerable momentum when Wilson (1971) introduced a family of spatial interaction models, based on the principle of gravity, to describe and predict social phenomena. This principle states that the interaction between two bodies is proportional to their masses, and inversely proportional to the square of distance. Wilson elaborated this principle in a number of ways. First, he suggested that any distance decay function that reflects the notion that, ceteris paribus, the intensity of interaction decreases with increasing distance may be used to replace straight distance. Secondly, he argued that in spatial problems often the number of departures from particular origins and\or the number of arrivals at particular destinations is known, implying that so-called balancing factors have to be introduced in the model to satisfy these constraints. Wilson distinguished an unconstrained spatial interaction model (departures and arrivals are not known), a production-constrained spatial interaction model (number of departures per zone is known), an attractions-constrained spatial interaction model (number of arrivals per zone is known), and the doubly constrained spatial interaction model (both number of departures and number of arrivals per zone are known). In the context of spatial choice behavior, the production constrained spatial interaction model is most interesting as it predicts which destination will be chosen. It can be expressed as: pij l AiOiWj f (dij)
Spatial Choice Models The interrelationship between spatial structure and individual choice behavior has traditionally been at the forefront of geographic research. Geographers have realized that spatially varying consumer demand 14768
(1)
where, pij is the probability that an individual in zone i will choose destination j; Ai is a balancing factor, guaranteeing that the number of predicted interactions from zone i is equal to its number of observed interactions; Oi is the number of observed interactions from zone i; Wj is a vector of variables, representing
Spatial Choice Models the attractiveness of destination j; f (dij) is some function of the distance between origin i and destination j. Although much empirical work has been conducted on spatial interaction models since this seminal work, most of the relevant literature has been concerned with operational problems. Theoretical progress has been limited. For example, different measures of distance (straight-line distance, Euclidean distance, cityblock metric, and travel time) and attractiveness have been suggested. Likewise, different functions for representing the distance decay effect have been proposed (power, exponential, and more complex functions). Finally, an exponent has been added to the specification of attractiveness term to allow for the fact that the larger destinations tend to have extra attraction beyond their size because of the benefits of economies of scale. The estimation of spatial interaction models is typically based upon aggregate, zonal data of interaction flows (shopping, recreation, migration, traffic, etc). To that effect, the study area is delineated carefully to avoid large external flows, and divided into a number of smaller homogeneous zones. The spatial interaction model is calibrated using observations about interactions between these zones as input. As a result, the parameters of the spatial interaction model are highly influenced by the geometry of the study area. This caused a search for improvements of the model, and for alternative modeling approaches. In this context, some authors suggested the development of models that estimate the effects of attraction variables endogenously. Another way of dealing with this problem was to incorporate some measure of spatial structure into a spatial interaction model (Fotheringham 1983). The simplest approach to the specification of this additional term is the use of a Hansen-type accessibility measure. This so-called competing destinations model may be expressed as: pij l AiOiWjC δj d −ijβ
(2)
where Ai l
A B
WjC δj d −ijβ j
C
−"
(3)
D
and Cj l Wjd −jkγ
(4)
kj
2. The Reealed Preference Model The fact that the spatial interaction model is heavily influenced by the geometry of the study led Rushton (1969) to develop a preference-scaling model. The
purpose of the model was to derive rules of spatial choice behavior. To that effect, choice alternatives were classified into so-called locational types, which are a combination of an attractiveness category and a distance category. Spatial choice behavior is assumed to reflect a trade-off between attractiveness and distance separation. Pairwise choice data are then used to calculate the proportion of times a particular locational type is chosen, given that both are present. Based on this data, the locational types are positioned on a unidimensional preference scale using a nonmetric multidimensional scaling algorithm. Over the years, this basic model has been elaborated in a number of important ways. First, Rushton (1974) showed how graphical methods, trend surface analysis, or conjoint analysis might be used to decompose the preference scale into the contributions of the two basic variables. Second, Girt (1976) suggested linking the preference function to overt behavior by relating distances on the preference scale to choice probabilities. Third, Timmermans (1979) suggested deriving the choice sets of individuals from data on information fields and consumer attitudes, and using these to scale the alternatives. Although Rushton’s preference scaling model does have considerable appeal, it never received any major following. One of the reasons might be that the model is based on two explanatory variables only, while heterogeneity in preferences is not accounted for. The model has also been criticized because of its conceptual basis. It has been suggested that the model may not represent preferences at all, but rather inconsistencies in individual choice behavior.
3. Discrete Choice Models The spatial interaction model has been criticized for its reliance on aggregate, zonal interaction flows. This criticism has led to the development of disaggregate discrete choice models that are based on individual choice behavior. Discrete choice models may be derived from at least two formal theories: Luce’s strict utility theory and Thurstone’s random utility theory. In particular, Luce assumed that the probability of choosing a choice alternative is equal to the ratio of the utility associated with that alternative to the sum of the utilities for all the alternatives in the choice set. Luce thus assumed deterministic preference structures and postulated a constant-ratio decision rule. In contrast, random utility theory is based on stochastic preferences in that an individual is assumed to draw a utility function at random on each choice occasion. An individual’s utility for a choice alternative is assumed to consist of a deterministic component and a random utility component. Given the principle of utility maximizing behavior, the probability of choosing a choice alternative is then equal to the 14769
Spatial Choice Models probability that its utility exceeds that of all other choice alternatives in the choice set. The specification of the model depends on the assumptions regarding the distributions of the random utility components. The best-known model is the multinomial logit (MNL) model. It can be derived by assuming that the random utility components are independently, identically Type I extreme value distributed. It can be expressed as: pik l
exp [U(Xk, Si)] exp [U(Xj, Si)]
(5)
j
where U(Xk, Si) is the deterministic part of the utility of choice alternative k of individual i with socioeconomic characteristics Si. One of the most important criticisms that have been expressed against the multinomial logit model concerned the fact that the utility of a choice alternative is independent of the existence and the attributes of other alternatives in the choice set (the Independence from Irrelevant Alternatives or IIA property). It predicts that the introduction of a new, similar choice alternative will reduce market shares in direct proportion to the utility of the existing alternatives, which is counterintuitive in the case of a high degree of similarity between particular alternatives. Therefore, various alternative models have been developed to relax the IIA assumption (Timmermans and Golledge 1990). Similar work in this regard has been conducted by Williams (1977). The best-known model that circumvents the IIA-property is the nested logit model. Choice alternatives that are assumed to be correlated are grouped into the same nest. Each nest is represented by an aggregate alternative with a composite utility, consisting of the so-called inclusive value, and a parameter to be estimated. To be consistent with utility-maximizing behavior, the inclusive values should lie in the range between 0 and 1, and the values of the parameters should change consistently from lower levels to higher levels of the hierarchy.
4. Conjoint Preference and Choice Models Unlike discrete choice models, the parameters of the conjoint preference and choice models are not derived from real-world data, but from experimental design data. Conjoint models involve the following steps when applied to spatial choice problems (e.g., Timmermans 1984). First, each choice alternative is described by its position in a set of attributes, considered relevant for the problem at hand. Next, a series of levels for each attribute is chosen. Having defined the attributes and 14770
their levels, the next step involves creating an experimental design to generate a set of hypothetical choice alternatives. This design should be created such that the necessary and sufficient conditions to estimate the model of interest are satisfied. Respondents are then required to evaluate the resulting attribute profiles. Their responses are decomposed into the utility contribution of the attribute levels. Once partworth utilities have been estimated, choice behavior can be predicted by assuming that an individual will choose the alternative with the highest overall evaluation. Alternatively, different probabilistic rules can be postulated. To avoid such ad hoc rules, Louviere and Woodworth (1983) suggested estimating the preference function and choice model simultaneously. To that end, the attribute profiles should be placed into choice sets. Again, the composition of the choice sets depends on the properties of the choice model. Over the years, the basic conjoint preference and choice models have been elaborated in many different ways. To avoid the problem of information overload and reduce respondent demand, Louviere (1984) suggested the Hierarchical Information Integration method. It assumed that individuals first group the attributes into higher-order decision constructs. Separate designs are constructed for each decision construct, and a bridging experiment is designed for measuring the tradeoff between the evaluations of the decision constructs. Oppewal et al. (1994) suggested an improved methodology by using multiple-choice experiments to test the implied hierarchical decision structure. Other recent advances include the development of group preference models, the development of models of portfolio choice, the inclusion of contextual effects and constraints, and the combined use of experimental design and revealed preference data, to name a few.
5. Complex Spatial Choice Behaior The previous models are all typically based on singlepurpose, single-stop behavior. Over the years, however, it became clear that an increasing proportion of trips involved multistop behavior. Moreover, Ha$ gerstrand’s time geography had convincingly argued that behavior does not reflect preferences only, but also constraints. Thus, various attempts have been made to develop models of trip chaining and activity-travel patterns. Originally, most models relied on semi-Markov process models or Monte Carlo simulations. More recently, utility-maximizing models have dominated the field. An important contribution in this regard was made by Kitamura (1984), who introduced the concept of prospective utility. It states that the utility of a destination is not only a function of its inherent attributes and the distance to that destination, but also
Spatial Cognition of the utility of continuing the trip from that destination. Dellaert et al. (1998) generalized Kitamura’s approach to account for multipurpose aspects of the trip chain. Trip chaining is only one aspect of multiday activity\travel patterns. Several models have recently been suggested to predict more comprehensive activity patterns. These models can be differentiated into the older constraints-based models (e.g., Lenntorp 1976), utility-maximizing models (e.g., Recker et al. 1986), rule-based or computational process models (e.g., Golledge et al. 1994, ALBATROSS – Arentze and Timmermans 2000).
6. Conclusions This article has given a very brief overview of spatial choice modeling. Due to the limited available space, we have focused on some of the key modeling approaches, disregarding alternatives (e.g., dynamic models) altogether. If we examine the accomplishments, one cannot escape the conclusion that the models developed over the years have been increasing in complexity. The theoretical underpinnings of the recent activity-based models are much richer than the Markov or gravity models of the 1960s. Moreover, the brief overview indicates that geographers have been using alternative data, such as experimental design data and activity diaries, in addition to the more conventional survey data. See also: Spatial Analysis in Geography; Spatial Decision Support Systems; Spatial Interaction; Spatial Interaction Models; Spatial Optimization Models; Spatial Pattern, Analysis of; Spatial Statistical Methods; Spatial Thinking in the Social Sciences, History of
Bibliography Arentze T A, Timmermans H J P 2000 ALBATROSS: a Learning-based Transportation-oriented Simulation System. EIRASS, Eindhoven University of Technology, The Netherlands Dellaert B, Arentze T A, Borgers A W J, Timmermans H J P, Bierlaire M 1998 A conjoint based multi-purpose multi-stop model of consumer shopping centre choice. Journal of Marketing Research 35: 177–88 Ettema D F, Timmermans H J P 1997 Actiity-based Approaches to Trael Analysis. Elsevier Science, Oxford, UK Fotheringham A S 1983 A new set of spatial interaction models: The theory of competing destinations. Enironment and Planning, A 15: 1121–32 Girt J L 1976 Some extensions to Rushton’s spatial preference scaling model. Geographical Analysis 8: 137–56 Golledge R G, Kwan M P, Ga$ rling T 1994 Computational process modeling of travel decisions using a geographical information system. Papers in Regional Science 73: 99–117
Kitamura R 1984 Incorporating trip chaining into analysis of destination choice. Transportation Research 18B: 67–81 Lenntorp B 1976 Paths in space-time environments. Lund Studies in Geography, Series B, no. 44 Louviere J J 1984 Hierarchical information integration: a new method for the design and analysis of complex multiattribute judgment problems. In: Kinnear T C (ed.) Adances in Consumer Research 11, ACRA, Provo, UT, pp. 148–55 Louviere J J, Woodworth G 1983 Design and analysis of simulated consumer choice or allocation experiments: An approach based on aggregate data. Journal of Marketing Research 20: 350–67 Oppewal H, Louviere J J, Timmermans H J P 1994 Modeling hierarchical information integration processes with integrated conjoint choice experiments. Journal of Marketing Research 31: 92–105 Recker W W, McNally M G, Root G S 1986 A model of complex travel behavior: part I – theoretical development. Transportation Research, A 20A: 307–318 Rushton G 1969 Analysis of spatial behavior by revealed space preference. Annals of the Association of American Geographers 59: 391–400 Rushton G 1974 Decomposition of space preference structures. In: Golledge R G, Rushton G (eds.) Spatial Choice and Spatial Behaior. Ohio State University Press, Columbus, OH, pp. 119–33 Timmermans H J P 1979 A spatial preference model of regional shopping behaviour. Tijdschrift oor Economische en Sociale Geografie 70: 45–8 Timmermans H J P 1984 Decompositional multiattribute preference models in spatial choice analysis: a review of some recent developments. Progress in Human Geography 8: 189– 221 Timmermans H J P, Golledge R G 1990 Applications of behavioural research on spatial choice problems II: preference and choice. Progress in Human Geography 14: 311–54 Williams H C W L 1977 On the formation of travel demand models and economic evaluation measures of user benefit. Enironment and Planning, A 9: 285–34 Wilson A G 1971 A family of spatial interaction models and associated developments. Enironment and Planning, A 3: 1–32
H. Timmermans Copyright # 2001 Elsevier Science Ltd. All rights reserved.
Spatial Cognition Spatial cognition concerns the study of knowledge and beliefs about spatial properties of objects and events in the world. Cognition is about knowledge: its acquisition, storage and retrieval, manipulation, and use by humans, nonhuman animals, and intelligent machines. Broadly construed, cognitive systems include sensation and perception, thinking, imagery, memory, learning, language, reasoning, and problemsolving. In humans, cognitive structures and processes are part of the mind, which emerges from a brain and nervous system inside of a body that exists in a social and physical world. Spatial properties include location, size, distance, direction, separation and connection, shape, pattern, and movement. 14771
International Encyclopedia of the Social & Behavioral Sciences
ISBN: 0-08-043076-7