Empirical data
Data analytics
Applied science: improve the efficiency of movements / spatial constraints
Why in this unit?
Distance
Accessibility: the capacity of a location to be reached by, or to reach different locations
Spatial interaction: movement of people, freight or information between an origin and destination
Transportation and land use models
Source: Rodrigue (2020)
Source: Rodrigue (2020)
Abstraction
Represent the structure not the appearance
Terminal = node
Node (vertex)
Link (edge)
Sub-graph - Loop (buckle)
Planar graph
Non-planar graph
Cycle, circuit
Tree \((e = v-1)\)
Source: Rodrigue (2020)
\(\beta = e / v\), where \(e\) is the number of links & \(v\) the number of nodes
\(Gamma\) AKA network density (number of liks / maximum number of links)
planar: \(\gamma = \frac{e}{3(v-2)}\)
non-planar: \(\gamma = \frac{2e}{v(v-1)}\)
Degree centrality
Eccentricity: the distance from a given node to the farthest node from it in the network
Shimbel index, or nodal accessibility, or Fareness (see Lecture 3
\(c_𝑖= \sum_j d_{ij}\)
This is a purely topological accessibility metric, remember this for later.
Which node has the shortest distance to other nodes
Instead of focusing on the number of links, the focus turns to the network distances
Different definitions:
Closeness, \(c_{i} = 1/\sum_{j} d_{ij}\)
Fareness, \(c_{i} = \sum_{j} d_{ij}\)
igraph
calculates closeness
Inequality measure
Ordered X and Y, cumulative percentage
Mostly used for income inequalities, but can be more widely used
\(Gini = A / (A + B)\)
Source: Rodrigue (2020)
Source: Rodrigue (2020)
Source: Rodrigue (2020)
Degree of concentration of a certain activities
Very common for regional analysis too
\(M_{ti}\) is the traffic of a merchandise \(t\) at a terminal \(i\)
\(Mi\) is the traffic of all merchandise at a terminal \(i\)
\(M_{t}\) is the total of all merchandises of type \(t\) for all terminals, and
\(M\) is the total of all types of merchandises for all terminals
\(LQ = \frac{\frac{M_{it}}{M_i}}{\frac{M_t}{M}}\)
\(LQ <1\): traffic of merchandise \(t\) in terminal \(i\) is under-represented compared to the same merchandise in all terminals
\(LQ = 1\) traffic of merchandise \(t\) in terminal \(i\) is proportional to its participation to total traffic
\(LQ > 1\) traffic of merchandise \(t\) in a terminal \(i\) is preponderant in total traffic.
Employment in manufacturing sector
Source: ONS
A spatial interaction is a realised movement of people, freight or information between an origin and a destination
It is a transport demand/supply relationship expressed over geographical space.
Conditions for spatial interaction to be materialised
Complementarity
Intervening opportunity
Transferability
Source: Rodrigue (2020)
Origin/destination matrices
Very large matrices
Missing data/0s
Estimation of flows
\(T_{ij} = f(V_i, W_j, S_{ij})\)
\(T_{ij} = f(V_i, W_j, S_{ij})\)
\(T_{ij}\): Interaction between location \(i\) (origin) and location \(j\) (destination)
\(V_i\): Attributes of the location of origin \(i\) (e.g. population, number of jobs available, industrial output, GDP); push factors; the potential of origins
\(T_{ij} = f(V_i, W_j, S_{ij})\)
\(W_j\): Attributes of the location of destination \(j\), pull factors; attractiveness of destinations
\(S_{ij}\): Attributes of separation between \(i\) and \(j\) (e.g. distance, transport costs, or travel time); cost of overcoming the separation between origins and destinations
\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)
\(\beta\): transport friction parameter
\(\lambda\): Potential to generate movements
\(\alpha\): Potential to attract movements
\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)
Known: \(V\), \(W\), and \(d\)
Define: \(\lambda=1\), \(\alpha=1\), \(\beta=2\), and \(k=0.00001\)
These are some standard results from past empirical studies
Big unknown: \(T\)
Example from Tranos, Gheasi, and Nijkamp (2015)
Fairly good estimation of reality for such an oversimplified model, but…
… not good enough.
Known: \(T\), \(V\), \(W\), \(d\) and \(k\)
Estiamte: \(\lambda=1\), \(\alpha=1\), and \(\beta=2\)
Why? To understand the effect of distance, pull and push factors
How? Regression
\(T_{ij} = k\frac{V_i^\lambda W_j^\alpha}{d_{ij}^\beta}\)
Look up properties of logarithms, e.g. here
\(T_{ij} = kV_i^\lambda W_j^\alpha d_{ij}^{-\beta}\)
\(ln T_{ij} = ln (kV_i^\lambda W_j^\alpha d_{ij}^{-\beta})\)
\(ln T_{ij} = lnk + lnV_i^\lambda + ln W_j^\alpha + lnd_{ij}^{-\beta}\)
\(\color{red}{ln T_{ij}} = \color{blue}{lnk} + \lambda \color{green}{lnV_i} + \alpha \color{orange}{ln W_j} -\beta \color{purple}{lnd_{ij}}\)
\(\color{red}{y} = \color{blue}{c} + \lambda \color{green}{x_1} + \alpha \color{orange}{x_2} + \beta \color{purple}{x_3}\)
Multivariate linear regression
\(c = lnk = 13.84\)
\(\lambda = lnV_i = 0.727\)
\(\alpha = lnW_j = 0.464\)
\(\beta = lnd_{ij} = -0.624\)
What did we learn?
How can we use these coefficients
The potential of opportunities for interaction
Ease of spatial interaction
Attractiveness of a node in a network taking into account the mass of other nodes and the costs to reach those nodes via the network
Different typologies (Holl 2007)
Network access
distance to access the network
travel opportunities
Travel cost measures
Market potential accessibility
Geographical indicator
Spatial structure (e.g. distance) and economic activities (e.g. population)
The potential for interaction
Opportunities