Recent Advances in Modeling and Forecasting Kaiyu: Tools for Predicting and Verifying the Effects of Urban Revitalization Policy (New Frontiers in Regional Science: Asian Perspectives, 36)

Preface
Contents
Contributors
Part I: Retail Models
	Disaggregate Hierarchical Decision Huff Model Incorporating Consumer Kaiyu Choices Among Shopping Sites
		1 Introduction
			1.1 Aim of Constructing SCOPES (Saga Commercial Policy Evaluation System)
			1.2 Purpose
		2 Formulation and Estimation of Hierarchical Decision Huff Model
			2.1 Formulation of Multi-stage decision Behavior
			2.2 Estimation Method for Multi-stage Choice Model
				Huff model as a Multinomial Logit Model
				Relationship Between Log-Linear Model and Multinomial Logit Model
				The SCOPES Model as a Recursive Multi-stage Log-Linear Model: Formulation and Estimation
		3 Estimated Results of the SCOPES Model and the Policy Experiment of the Shop-Around Effect
			3.1 Estimated Results of the SCOPES Model
				Data Used
				Estimated Results
				Estimated Result of City Choice Model
				Estimated Result of Individual Large Store Choice
				Estimated Result of the Shop-Around Choice Model
			3.2 Aggregation of Disaggregate Consumer Behaviors
			3.3 A Policy Experiment of Shop-Around Effect
		4 Conclusion
		References
	A Dynamical Huff Model: Computing the Competitive Equilibrium Distribution of Shop Floor Areas over a City Center Commercial D...
		1 The Purpose of this Study
		2 Dynamical Huff Model
			2.1 Formulation of Dynamical Huff Model
			2.2 Properties of Equilibrium Points of Dynamical Huff Model
		3 Fixed-Point Algorithm
			3.1 Application of the Fixed-Point Algorithm to Computing the Equilibrium Point
			3.2 About the Merrill Method
		4 Competitive Equilibrium Shop Floor Distribution in Saga City
			4.1 Method of the Analysis
				Data Used
				Procedure of the Analysis
			4.2 Result of the Analysis
				Estimated Result of Multinomial Disaggregate Conditional Logit Huff Model
				Calculated Result of Equilibrium Shop Floor Distribution
		5 Conclusion and Future Challenges
		References
Part II: Kaiyu Markov Models
	Kaiyu Markov Model and Evaluation of Retail Spatial Structures
		1 Purpose of this Study
		2 Framework of the Analysis
			2.1 Formulation of the Shop-Around Effect
			2.2 Method for Measuring the Shop-around Effect
		3 Measurement Results of the Shop-Around Effect and Its Application
			3.1 Locations and Characteristics of Nobeoka City Commercial Districts
			3.2 Data Used
			3.3 Measurement of the Shop-Around Effect
				Measurement Results of Shop-Around Probabilities and Their Graphical Representation
				Measurement of the Average Shop-Around Effect
			3.4 Application to the Extraction of Planning Issues
		4 Conclusion and Future Challenges
		References
	Basics of Kaiyu Markov Models: Reproducibility Theorems-A Validation of the Infinite Kaiyu Representation
		1 Introduction
			1.1 Definition of Consumer´s Kaiyu (Shop-Around) Behavior
			1.2 Representations of Consumer´s Kaiyu Behavior
			1.3 Decision Tree
				Definition of Kaiyu (Shop-Around) Effect
				Kaiyu Effect Calculation by Decision Tree: Direct Method
				Recursive Method for Kaiyu Effect-Intuitive Approach
				Statistical Derivation of Recursive Equation for Kaiyu Effect: The Law of Iterated Expectation and Markov Property
			1.4 Phase Diagram
			1.5 Matrix Representation
		2 Stochastic Processes
			2.1 Discrete-Time Stochastic Process
			2.2 Markov Property
				Relationship Between Probability Expressed Based on Event Sets and that Based on Random Variables
				Relationship Between the Joint Event Expressed Based on Event Sets and that Based on Random Variables
				Conditional Probability and Chain Rule
			2.3 Transition Probability
			2.4 Stationary Markov Chain
			2.5 Higher-Order Transition Probability
		3 Kaiyu Markov Models
			3.1 Kaiyu Transition Probability Matrix
				Numerical Example
					Lattice Representation
					Equivalent Matrix Calculation
			3.2 Higher-Order Kaiyu Transition Probability Matrix
			3.3 Convergence of Positive Matrix Power Series
			3.4 Properties of the Kaiyu Markov Model
				Limit of Kaiyu Transition Matrix
				Kaiyu Effect Formula
				Total Visit Frequency
				Decomposition of the Kaiyu Effect
				Kaiyu Movement Formula
				Exit Distribution Formula
				Entrance-Exit Relationship Formula
		4 Matrix Record of Micro Kaiyu History Data
			4.1 Micro Kaiyu History Data
			4.2 Recording Micro Kaiyu Data as 0-1 Matrix
			4.3 Properties of Micro Kaiyu History Data Matrices
				Cycles and Permutation Matrices-Micro Kaiyu History 0-1 Data Matrices
				Line-Sum Symmetric Matrices-Aggregate Data Matrices from Micro Kaiyu History 0-1 Data
		5 Reproducibility Theorems: A Validation for the Infinite Kaiyu Representation
			5.1 Implication of Reproducibility Theorem
			5.2 Reproducibility Theorem for Kaiyu Effect
			5.3 Reproducibility Theorem for Kaiyu Movements
				Aggregate Reproducibility Theorem for Kaiyu Movements
				Disaggregate Reproducibility Theorem for Individual Micro Kaiyu Markov Model-The n-Length One-Cycles and their Kaiyu Markov Mo...
				Disaggregate Reproducibility Theorem and Aggregation
		6 Conclusion and Future Challenges
		7 Notes on Literature and Further Readings
		The Law of Iterated Expectations
			Definition
			Law of Iterated Expectations
		References
Part III: Estimation of Huff Model and Kaiyu Markov Models with Covariates
	Kaiyu Markov Model with Covariates to Forecast the Change of Consumer Kaiyu Behaviors Caused by a Large-Scale City Center Reta...
		1 Introduction
		2 A Review of Related Previous Studies with an Emphasis on the Literature in Japanese
		3 Kaiyu Markov Model with Covariates to Forecast Consumers´ Kaiyu Behaviors in a Commercial District
			3.1 An Absorbing Markov Chain Model for Consumer´s Shop-Around or Kaiyu Behavior in a Commercial District
				Definition of Consumer´s Shop-Around or Kaiyu Behavior
				Representing the Consumer´s Shop-Around or Kaiyu Behavior as a Stationary Absorbing Markov Chain
				The Definition of Shop-Around Effect on Each Shopping Node
			3.2 Incorporating Covariates into the Markov Chain Model of Consumer´s Shop-Around or Kaiyu Behavior
			3.3 A Theorem of the Observed Aggregate Stationarity: A Validation for Stationary Markovian Modeling
		4 An Application to the City Center of Fukuoka City, Japan
			4.1 Data
			4.2 Defining Nodes
			4.3 Formulating Two Submodels to Be Estimated
				Formulation of the Entry Structure Model
				Formulation of the Shop-Around or Kaiyu Structure Model
		5 The Estimated Model
			5.1 The Entry Structure Model
			5.2 The Shop-Around or Kaiyu Structure Model
			5.3 Evaluating the Estimated Model
		6 Forecasting Consumers´ Shop-Around or Kaiyu Behaviors After the Redevelopments
			6.1 Defining Cases for Simulation
			6.2 Results of Simulations
			6.3 Assessing Redevelopment Programs
		7 Conclusion and Future Challenges
		References
	Estimation of Disaggregate Huff and Kaiyu Markov Model: A Lecture Note on Conditional Logit Model
		1 Introduction
		2 A Dice Model
			2.1 Random Utility Function
			2.2 Calculation of the Probability PA
			2.3 Reformulation of the Dice Model
				A Method to Find the Distribution of εA - εB
				A Method Similar to Convolution
				Generalization to the Continuous Case
		3 Conditional Logit Model
			3.1 Introducing Unknown Parameters
		4 Gumbel Distribution
			4.1 Definitions of Gumbel Distribution
			4.2 Distributional Properties of Gumbel Distribution
				Density of Gumbel Distribution
				Cumulative Distribution Function of Gumbel Distribution
				Distribution of Difference Between Two Independent Gumbel Distributions: Logistic Distribution
		5 Properties As the Extreme Value Distribution: Gumbel Is Closed for Maximization Operations
		6 Mean of Gumbel Distribution and Euler´s Constant
			6.1 Euler´s Constant
			6.2 Convergence of Euler´s Constant
			6.3 Integral Forms of Euler´s Constant
			6.4 Gamma Function and Euler´s Constant
				Gamma Function
				The Infinite Product Form of Gamma Function
				Derivative of the Logarithm of Gamma Function
			6.5 Equivalence of Mean of Gumbel Distribution to Euler´s Constant
			6.6 Characteristic Function of Gumbel Distribution and Its Moments
				Characteristic Function and Its Properties
				Characteristic Function of Gumbel Distribution
				The Variance and Means of Gumbel Distribution
		7 Maximum Likelihood Estimation of Logit Model
			7.1 Estimation Problem
			7.2 Logit Models and Their Likelihood
				Logit Models
				Likelihood
			7.3 Maximum Likelihood Estimate for Logit Models
		8 Numerical Examples
			8.1 Numerical Example of the Logit Model with Dummy Explanatory Variables
			8.2 Numerical Example of the Logit Model with Continuous Explanatory Variables
		9 Estimation of Disaggregate Huff Model
			9.1 Defining the Disaggregate Huff Model
			9.2 Numerical Example of Estimation of Disaggregate Huff Model
			9.3 Least Square Estimation of Disaggregate Huff Model for the Case when Repetitions of Observations Exist
		10 Conclusion and Further Research
		11 Notes on the Literature and Further Readings
		Appendix 1: Elements of Statistics, Algorithm to Compute Maximum Likelihood Estimation, and Computation by Python and SAS Codes
			Expectation
			Cumulative Distribution Function
			Joint and Marginal Distributions
			Independence of Random Variables
			Convolution
			Newton-Raphson Method
			Newton-Raphson Algorithm to Find Maximum Likelihood Estimates of Conditional Logit Models: Derivation of Eq. (79)
			Python Code
			SAS Code
		Appendix 2: Primers for Analysis, Complex Analysis, Fourier Analysis, Measure, and Lebesgue Integral: Convergence of e, Gamma ...
			Proof of the Convergence of e: From Natural Number to Real Number
			Proof of Related Inequalities of the Convergence of e: From Euler´s Number to Exponential Function
			Lebesgue Convergence Theorem and Proof of Eq. (41): Interchange of Integration and Limit
			Uniform Convergences of Digamma and Trigamma Functions: Derivatives of Logarithm of Gamma Function
			Properties of Characteristic Function: Elements of Complex Analysis
			Fourier´s Integral Theorem and Levy´s Inversion Formula: Fourier´s Transform of Distribution Function Gives Reformulated Levy´...
			Fourier Series and the Value of ζ(2): Fourier Series Solve the Basel Problem
			Proofs of  Using Fourier´s Transform and Cauchy´s (Complex) Integral Theorem
			Measure, Lebesgue Integral, and Convergence Theorems: Proof of Lebesgue Dominated Convergence Theorem
		References
Part IV: Frequency-Based Retail Models for Forecasting the Number of Visitors and Sales of Commercial Districts
	A Disaggregate Kaiyu Markov Model to Forecast the Sales of Retail Establishments Based on the Consumers´ Frequency of Visits
		1 Introduction
			1.1 Motivation
			1.2 Purpose
		2 Previous Studies
			2.1 Kaiyu Markov Model Without Covariates
			2.2 Covariates to Explain Entrance Choice and Shop-Around Probabilities
			2.3 The Number of Incoming Trips Increased by Redevelopment Programs
			2.4 A Money-Based Kaiyu Markov Model
			2.5 The Distinctive Feature of Frequency-Based Modeling
		3 A Disaggregate Kaiyu Markov Model to Forecast Sales of Retail Establishment Based on Frequency of Consumers´ Visits
			3.1 The Frequency-Based Sales Forecasting
			3.2 Disaggregating the Previous Kaiyu Markov Model
			3.3 Constructing the Disaggregate Kaiyu Markov Model to Forecast Sales of the Retail Establishment
		4 Application to the City Center Commercial District of Kitakyushu City
			4.1 Data
			4.2 Shopping Sites in the City Center Retail Environment
		5 Estimation of Sales Forecasting Model for the City Center Commercial District of Kitakyushu City
			5.1 Estimation of a Purchase Model to Forecast the Amount of Expenditure per Visit at Shopping Sites
			5.2 Estimation of the Disaggregate Entry Choice Model
			5.3 Estimation of the Disaggregate Kaiyu Choice Model
		6 Sales Forecasts for the City Center Commercial District of Kitakyushu City
		7 Conclusion
		References
Part V: Multivariate Poisson Models with Hub Functions and Intervening Opportunities
	How Would the Kyushu Super-Express Railway Opening Change the Flow of Tourists from the Kansai Region within the Kyushu Wide A...
		1 Aim and Purpose
		2 The Outline of the Kyushu Shinkansen Line
		3 Analysis Framework
			3.1 Procedure to Estimate the Number of Tourists
			3.2 Data Used
				Survey of Consumer Behavior Related to the Opening of the Whole Kyushu Shinkansen Line
				Supplementary Data
					Travel Time and Costs by Travel Mean for Respondents
						Private Cars
						Railway
						Airplane
					Travel Time and Costs by Travel Means for Municipalities
						Private Car
						Railway
						Airplane
				Population Data
				Data on Retail Floor Area
		4 Estimation of Logit Model for Travel Means Choice
			4.1 Logit Model for Modal Choice
			4.2 Estimated Results of Modal Choice Logit Model
		5 Estimation of the Poisson Model for Forecasting the Frequency of Visits
			5.1 Poisson Model for Forecasting the Frequency of Visits
			5.2 Estimated Results of Parameters in the Poisson Model for Forecasting the Frequency of Visits
		6 Forecasting the Number of Sightseeing Visitors from the Kansai Region Before and After the Opening of the Kyushu Shinkansen
			6.1 Changes in Modal Choices
			6.2 Predicting the Increase in the Number of Sightseeing Visitors from the Kansai Region to Kyushu
				Case Without Considering Hub Functions
				Case with Considering Hub Functions
		7 Predicting Changes in the Number of People Traveling Among Fukuoka, Kumamoto, and Kagoshima Due to the Opening of the Whole ...
			7.1 Data Used
				Data Used for the Estimation of the Parameters
					The Survey Data
					Supplementary Data
				Data Used for the Prediction
			7.2 Estimated Parameters
				Estimated Results of Transport Means Choice Model
				Estimated Results of Visit Frequency Poisson Model
			7.3 Prediction of People Flow Between Fukuoka, Kumamoto, and Kagoshima Before and After the Opening of Kyushu Shinkansen
		8 Conclusion and Future Challenges
		References
	A Micro Behavior Approach to Estimating and Forecasting the Intervening Opportunity Effects with a Multivariate Poisson Model:...
		1 Purpose
		2 Intervening Opportunities
			2.1 City Center Commercial District of Fukuoka City
			2.2 Intervening Opportunities from Micro Behavior Viewpoint
		3 Research Framework
			3.1 Research Procedure
			3.2 Data Used
				The 15th Survey of Consumer Kaiyu Behavior at the City Center of Fukuoka City
				Supplemented Data by GIS
				Greater Fukuoka Metropolitan Area
				Population Data of Greater FMA
				Shop-Floor Area Data
		4 Estimating a Multivariate Poisson Model for Visit Frequency with Intervening Opportunity
			4.1 Model Formulation
			4.2 Estimated Results of Parameters
		5 Forecasting the Number of Visitors to Tenjin and Hakata before and after JR Hakata City´s Opening
		6 Hakata´s and Tenjin´s Intervening Opportunity Effects on the Destinations Tenjin and Hakata Estimated and Predicted by the N...
		7 Conclusion and Further Challenges
		References
Part VI: Integrated Modeling of Weighted Multivariate Poisson Models with Competitive Destinations and Kaiyu Markov Models
	How Would the Opening of JR Hakata City, a New Terminal Complex of the Kyushu Super-Express Railway, Change the Number of Visi...
		1 Purpose
		2 Framework
			2.1 City Center Commercial District of Fukuoka City
			2.2 Forecasting Framework
				Causal Path of Consumer Behaviors and Forecasting Procedure
				Model Estimation and Aggregation in Forecasting
				Forecasting Procedure Details
			2.3 Data
				The 15th Survey of Consumer Shop-Around Behaviors at the City Center of Fukuoka City
				Complementary Data by GIS
					By Car
					By Railway
					By Bus
			2.4 Greater Fukuoka Metropolitan Area
			2.5 Population Data
			2.6 Shop Floor Area Data
		3 The Number of Net Incoming Visitors to the Entire City Center Commercial District of Fukuoka City
			3.1 The Weighted Poisson Model for Estimating and Forecasting the Number of Net Incoming Visitors to the Entire City Center Di...
			3.2 Estimated Results
			3.3 Forecasted Results
				The Net Incoming Number of Visitors to the Entire City Center
				The Total Incoming Number of Visitors to the Tenjin and Hakata Station Districts and Their Intervening Opportunity Effects
		4 The Number of Net Incoming Visitors to Three Core Commercial Establishments at the City Center of Fukuoka City
			4.1 The Weighted Logit Model for Entrance Choice among Three Core Commercial Establishments
			4.2 Estimated Results
			4.3 Forecasted Results
		5 Consistent Estimation of Kaiyu Paths Density Among 45-Division Districts in the City Center of Fukuoka City
			5.1 Detailed Maps of Fukuoka City Center with District Divisions
			5.2 Consistent Estimation Method Employed
			5.3 Estimated Result of Kaiyu Paths Density
				Nodes and Zones Segmenting the City Center
				Estimated Kaiyu Path Density Over All Kaiyu Paths
			5.4 Transforming Kaiyu Paths Density into Kaiyu OD Flow Density
			5.5 Expansions of Estimated Kaiyu OD Flow Density to People´s OD Flows
			5.6 Aggregating 45-Division Kaiyu OD Flows into 25 Divisions
		6 The Number of Entrance Visitors to 25 Division Districts in the City Center Commercial District of Fukuoka City
			6.1 The 25-Entrance Choice Probability Logit Model
			6.2 Expanding Entrance Probabilities into the Numbers of Entrance Visitors: A Method by Conditional Probabilities
		7 Kaiyu Markov Model with Covariates for 24 Division Districts in the City Center of Fukuoka City
			7.1 Kaiyu Markov Model
				Formulation
				Estimation
			7.2 Estimated Results
		8 Changes in Kaiyu Flows and Retail Sales of Fukuoka City Center Before and After JR Hakata City´s Opening
			8.1 Forecasted Result of Changes in People´s Kaiyu Flows Among Tenjin, Hakata, and Canal City Before and After JR Hakata City´...
			8.2 Forecasted Result of Changes in Retail Sales of Tenjin, Hakata, and Canal City Before and After JR Hakata City´s Opening
		9 Did Our Prediction Fit with the Actual Values?: A Partial Verification by Newspaper Reports
			9.1 One Week After the Opening
			9.2 One Month After the Opening
			9.3 Three Months After the Opening
			9.4 Intervening Opportunity and Railroad Network
		10 Conclusion and Future Challenges
		References
	How Many Customers Would Be Brought Back from Suburban Shopping Malls to the City Center by Redeveloping the City Center Stati...
		1 Purpose
		2 The City Center of Oita City and Large-Scale Suburban Shopping Malls
			2.1 The City Center Commercial District of Oita City
			2.2 Large-Scale Suburban Shopping Malls
		3 Framework
			3.1 Analysis Procedure
				Forecasting the Changes in the Number of Incoming Visitors to the City Center Before and After JR Oita City´s Opening
				Forecasting the Changes in Visitor´s Kaiyu Flows Among JR Oita City, Tokiwa, and Shopping Streets in the City Center and Their...
			3.2 Data Used
				The Second On-Site Survey of Consumer Kaiyu Behaviors at the City Center of Oita City
				Supplementary Data by GIS
				Oita Metropolitan Area
				Population
				Shop Floor Area Data
		4 A Multivariate Poisson Model with Competitive Destinations
			4.1 Incorporating the Competitive Destination Factors: Formulation and Estimation
				Formulation
				Estimation by the Weighted Multivariate Poisson Model
			4.2 Estimated Results
			4.3 Forecasted Results
				Forecasts for Visitors to Three Destinations Before and After JR Oita City´s Opening
				Decomposing on Each Destination by Log-Linearization
		5 Consistent Estimation of Kaiyu Density
			5.1 Consistent Estimation for On-Site Samples
			5.2 District Divisions for the City Center of Oita City
			5.3 The Consistent Estimate of Kaiyu Path Distribution
			5.4 The Consistent Estimate of the Kaiyu OD Density
			5.5 Validation of the Number of Net Incoming Visitors to the City Center
		6 Kaiyu Markov Model to Forecast the Changes in People´s Flows in the City Center of Oita City
			6.1 Entrance Choice Model
			6.2 Kaiyu Choice Model: Formulation and Estimation
			6.3 Estimated Result
		7 Forecasting the Changes in Kaiyu OD Flows Within the City Center of Oita City
		8 Forecasting the Changes in Retail Sales in the City Center of Oita City
			8.1 Forecasts of Changes in Retail Sales of the City Center of Oita City
			8.2 How Much Would Pedestrian Crossing Increase the Retail Sales of the City Center?
		9 Was the Forecast Accurate?
		10 Conclusion and Future Challenges
		References
Part VII: Other Applications of Kaiyu Markov and Related Models
	An Opportunity Cost Approach to Valuation of the River in a City Center Retail Environment: Another Application of the Kaiyu M...
		1 Purpose
		2 Method for Measuring the Asset Value of Rivers in City Center Commercial Districts
			2.1 Asset Value of Rivers in City Center Commercial Districts Viewed from Consumer Shop-Around or Kaiyu Behaviors
			2.2 Method for Measuring the Value of the River in Central Commercial District Using Shop-Around or Kaiyu Markov Model
		3 A Shop-Around or Kaiyu Markov Model Estimating Retail Sales at Shopping Nodes in the City Center Commercial District of Koku...
			3.1 Data Used
			3.2 Monetary-Based Disaggregate Consumer Shop-Around or Kaiyu Markov Model for the City Center Commercial District of Kokura i...
			3.3 Present State of the Division of City Center Commercial District Kokura by the Murasaki River
		4 Measuring the Value of the Murasaki River
			4.1 Measurement Method
			4.2 Results of Measuring the Value of the Murasaki River
				Comparison of the No-Detour State (n) and the Present State (a)
				Comparison of the No-Detour State (n) and the State with Only the Murasaki River Present (o)
				Measurement of the Net Value of the Murasaki River
		5 Conclusion and Future Topics
		Appendix
			Mathematical Formulation for the Net Value of the Murasaki River
		References
	Extraction of Long Sightseeing Kaiyu Routes in the Kyushu Wide Region, Japan
		1 Purpose of this Study
		2 Framework of the Analysis
			2.1 Method of Extracting Wide Sightseeing Routes from the Transition Probability Among Tourism Areas
			2.2 Method of Extracting Wide Sightseeing Routes from the Preference Order Index Over Tourism Areas Created by the Eigenvector...
			2.3 Estimation of the Tourism Area Shop-Around or Kaiyu Effect
		3 Characteristics of Survey Data
		4 Extraction of the Most Frequent Long-Sightseeing Route
		5 Estimation of Sightseeing Preference Order Index for Tourism Areas
		6 Estimation of the Sightseeing Kaiyu Effect
		7 Conclusion and Future Topics
		References
	A Bayesian Network Model of Consumers´ Kaiyu Behaviors
		1 Aim and Purpose of This Study
			1.1 Aim of This Study
			1.2 Positioning the Present Research in Previous Studies
			1.3 Purpose of this Study
		2 Bayesian Networks
		3 Data
		4 Analysis
			4.1 Structure Learning for a Network Between Shops
			4.2 Parametric Learning for a BN for Shop-Around Behaviors and Inference
				Model
				Data Preprocessing and Parameter Learning
				Inference
		5 Discussion
			5.1 Structure Learning for the Shop-to-Shop Relationship
			5.2 Inference in the BN for Shop-Around Behaviors
		6 Conclusion and Further Research
		References
Index