Accommodating spatial correlation in local-interaction formation model under a heavy rain disaster The University of Tokyo Junji URATA Summer School for Advanced activity model and assignment theory BinN International Research Seminar #02 Sept 28th, 2014
● focusing on making interaction - interactions are important for evacuation and evacuees start earlier by interactions cf. Baker(1979), Pamela and Wolshon (2013), Urata and Hato(2012) ● focusing on making interaction in a group - A interaction between two people are influenced not only by two but also by others in group. Review Classification of Interaction model
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●   Personal decision-making model is too complex - This is many-bodied problem - Utilities are constructed by the relationships and differences of the two ●   Introduce group decision-making model - Comparing with whole interactions of the group and choosing one - A choice probability of a interaction is influenced by the relationships of the two and others' relationships.
●   Discrete choice model for interaction choice - The errors of these utilities have correlations between some interactions - The correlations arise from similarities of  the states of interactions What is similarities of interactions? - Focus on “spatial risk” - The difference of the risks of two nodes is bigger, interactions are easier to be formed because of altruistic preferences - The similarity of the difference is caused by spatial risk. - The correlation of observation errors of the difference is also caused by spatial risk.
●   Discrete choice model for interaction choice - The errors of these utilities have correlations between some interactions - The correlations arise from similarities of  the nodes of interactions What is similarities of interactions? - Travel costs for interactions are important factors - The costs are spatial factor and the error term is correlated by space. Give each interactions  the spatial correlations
1. All nodes are divided by spatial characteristics 2. The interactions are distinguished by their divisions which two nodes belonged to. (A-A, B-B) - Intra interaction set (A-B) - Inter interaction set legend 3. The interactions which belong to the same set have a correlation. intra interaction set inter interaction set 7
Discrete choice model for interaction choice make or not: m interaction set: s Interaction: l
(1) (2) (3) (4) Specific Utility V i , V m μ ≤ 1 Scale parameter μ, ≤ μ, = l (5) (6) Error terms are given as the i.i.d extreme value (TypeI) 8
Two disasters were caused by typhoons on August 18 and September 29 in 2004 The August typhoon ●a maximum rainfall of 55mm per hour •Mudslides left 3 people dead The September typhoon ●281mm of rainfall ●Mudslides left 5 people dead

Survey(2004.9-10)
•Surveyed residents’ behaviors during these disasters by interviews (Oral communication) •Interviewed them about their awareness of the danger, risk management behaviors, and collective behaviors •Collective behaviors include rescuing others, evacuating with others, accommodating evacuees, meeting and exchanging information.
Illustration of Collective Behaviors
•Nodes show households •Links show collective behaviors between the households 11
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Making Interaction Vl=ij,t
Utility Altruistic Utility (inequality) - D j,i + Bweak W i − W j + Bman man, − man j + Bone one,i
i,j: Household d ij Path distance ij h ij : Density of house on the path ij Main road proportion of the path ij D i , t： Risk of household i W, : Number of children and elderly man į : Dummy: one man in household i one i :  Dummy: Number of household is one Number of making interaction ij Hourly amount of rainfall b: β : Parameter of unequal breaking Estimation parameter
Dataset: Each group choice every 15 minutes Whole pairs ００１０００ .. 0 0 1 k¹ r, r ij imelin 14 Making Utility
Note: --- = not applicable ** = significant at .05 * = significant at .10 16
• • Modeling one to one interactions in group. The correlations of interactions are given by spatial characters and this method can give the correlations relatively easily. Applicate a real data and estimate the parameters • • Evaluate evacuation rate with interaction using this making interaction model and evacuation timing model. Making interaction model made interactions Evacuation timing model evacuation rate Route choice and necessary time for evacuation 17