Accommodating spatial correlation in local-interaction formation model under a heavy rain disaster

Transcription

1 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 28 th, 2014

2 Research Background 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. 2

3 Review Classification of Interaction model Existence of Interaction Decision Making Influence of Interaction Collective model Chiappori(1988) Given In household Household Weight Utility Global Interaction Model Brock and Durlauf(2000) Given Whole to one Individual Probability (whole to one) Local Interaction Model Brock and Durlauf(2000) Given one to one Individual Probability (one to one) Network Formation Barabasi and Albert(1999) Not given (formate) one to one No (group) Number of interaction One to one relationship 3

4 What is group influence? 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. 4

5 Capturing correlations of interactions? 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 river High risk Low risk - The similarity of the difference is caused by spatial risk. - The correlation of observation errors of the difference is also caused by spatial risk. 5

6 Capturing correlations of interactions? 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 6

7 Introduction of spatial division A B 1. All nodes are divided by spatial characteristics 2. The interactions are distinguished by their divisions which two nodes belonged to. - Intra interaction set - Inter interaction set (A-A, B-B) (A-B) interaction set s A-A A-B B-B 3. The interactions which belong to the same set have a correlation. interaction l legend interaction intra interaction set inter interaction set 7

8 Formulation Discrete choice model for interaction choice root make or not: m make Not make interaction set: s A-A B-B A-B Interaction: l Choice probability Conditional probability of l Conditional probability of s Logsum variables of s Marginal probability of m Logsum variables of m P( m, s, l) = P( l s) P( s m) P( m) (1) P( l s) = P( s m) = V s = µ ln P( m) = V m l = µ m ln s ( vl µ l ) exp( v ) s l µ l exp( Vs µ s ) exp( V ) s m s µ s exp( v ) l s l µ l (( Vm + vm ) µ m ) (( Vm + vm ) µ m ) exp( ( V + v ) µ ) exp l exp exp s m s s s (2) (3) (4) (5) (6) Specific Utility Scale parameter v, v l m µ µ l s µ m Error terms are given as the i.i.d extreme value (TypeI) =1 8

9 The 2004 mudslide disasters in Niihama 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 10

10 The Survey in Niihama Survey( ) 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

11 Number of interactions and rainfalls 13

12 Setting utility Making Interaction Utility Altruistic Utility (inequality) Making Utility v A v v, t = βdisdij + βhouhij + βroadrij + ( 1 σ ) A l= ij ij, t ij ij, t k t { D D W W man man one one } ij, β + β + β + β ij, t = dam i, t j, t weak i j man i j one i j σ (8) m= make, t m= no, t = 0 = β rain Whole pairs exp ( rt ) Dataset: Each group choice every 15 minutes Timeline (9) ij A ij, t (10) i, j : d h r ij : : : : σ : β : : i, t : : A mani : Dummy: one man in household i one : Dummy: Number of household is one k r t ij t ij ij D W i i (7) Household Path distance ij Density of house on the path ij Main road proportion of the path ij Risk of household i Number of children and elderly Number of making interaction ij Hourly amount of rainfall Parameter of unequal breaking Estimation parameter 14

13 Spatial division 100m to shelters N to shelters Damaged Group has 36 interactions sets Spatial division Near Pond Group has 15 interaction sets road railway river 4 tank pond 6 having pair household 15

14 Estimation Result N-GEV NL 推定値 t 値 推定値 t 値 Path Distance β dis ** ** Density of house β hou * ** Main road β road Dif of risk (intra) β dam.s ** ** Dif of risk (inter) β dam.d ** ** Dif of weak (intra) β weak.s Dif of weak (inter) β weak.d Dif of one man (intra) β man.s Dif of one man (inter) β man.d Dif of one person (intra) β one.s Dif of one person (inter) β one.d *-- Rainfall β rain ** ** Altruistic σ Scale parameter (interaction) μ l ** ** Scale parameter (set) μ s ** Number of choices Log likelihood(0) Log likelihood(conv) Likelihood ratio ρ Adjusted likelihood ratio ρ Note: --- = not applicable ** = significant at.05 * = significant at.10 16

15 Conclusion and future works 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

16 References Baker, EJ. (1979) Predicting response to hurricane warnings: a reanalysis of data from four studies, Mass Emergencies, Vol. 4, pp Urata, J. and Hato, E. (2012) Modeling the Cooperation Network Formation Process for Evacuation Systems Design in Disaster Areas with a Focus on Japanese Megadisasters, Leadership Manage. Eng., Vol.12, pp Pamela, M-T., Wolshon, B. (2013) Evacuation transportation modeling: An overview of research, development, and practice, Transportation research Part C, Vol. 27, pp Chiappori, PA. (1988) Rational household labor supply, Econometrica: Journal of the Econometric Society, Vol. 56(1), pp Brock, WA., Durlauf, SN. (2000) Interactions-based models, National Bureau of Economic Research, Technical working paper No Barabasi, A.-L., Albert, R. (1999) Emergence of Scaling in Random Networks, Science, Vol. 286, pp