IS415 AY2022-23T2 - Lesson 6: Spatial Weights and Applications

What is geographically referenced attribute?

Rows: 323
Columns: 12
$ SUBZONE_N        <chr> "MARINA SOUTH", "PEARL'S HILL", "BOAT QUAY", "HENDERS…
$ SUBZONE_C        <fct> MSSZ01, OTSZ01, SRSZ03, BMSZ08, BMSZ03, BMSZ07, BMSZ0…
$ PLN_AREA_N       <fct> MARINA SOUTH, OUTRAM, SINGAPORE RIVER, BUKIT MERAH, B…
$ PLN_AREA_C       <fct> MS, OT, SR, BM, BM, BM, BM, SR, QT, QT, QT, BM, ME, R…
$ REGION_N         <fct> CENTRAL REGION, CENTRAL REGION, CENTRAL REGION, CENTR…
$ REGION_C         <fct> CR, CR, CR, CR, CR, CR, CR, CR, CR, CR, CR, CR, CR, C…
$ YOUNG            <dbl> NA, 1100, 0, 2620, 2840, 2910, 2850, 0, 1120, 30, NA,…
$ `ECONOMY ACTIVE` <dbl> NA, 3420, 50, 7500, 6260, 7560, 8340, 50, 2750, 210, …
$ AGED             <dbl> NA, 2110, 20, 3260, 1630, 3310, 3590, 10, 560, 50, NA…
$ TOTAL            <dbl> NA, 6630, 70, 13380, 10730, 13780, 14780, 60, 4430, 2…
$ DEPENDENCY       <dbl> NA, 0.9385965, 0.4000000, 0.7840000, 0.7140575, 0.822…
$ geometry         <MULTIPOLYGON [m]> MULTIPOLYGON (((31495.56 30..., MULTIPOL…

Describing attribute distribution

The dependency ratio values by planning subzone are normally distributed.

Geographical distribution question

Are the planning subzones with high proportion of dependency ratio randomly distributed over space?

Geographical distribution question

Are the planning subzones with high proportion of dependency ratio randomly distributed over space?

]

What are Spatial Weights (wij)

A way to define spatial neighbourhood.

Defining Spatial Weights

Contiguity Neighbours

Contiguity (common boundary)
What is a “shared” boundary?

Beyond the basic contiguity neighbours

There are also second-order, third-order, forth-order, etc contiguity

Weights matrix: Adjacency-based neighbours

Quiz: With reference to the figure below, list down the neighbour(s) of area 1202 using Rook case.

Weights Matrix: Distance-based neighbours

Quiz: With reference to the figure below, create a weights matrix for d = 650.

Weights matrix: Measured distances

Row standardisation

In practice, row-standardised weights instead of spatial weights will be used.

Applications of Spatial Weights

Formally, for observation i, the spatial lag of yi, referred to as [Wy]i (the variable Wy observed for location i) is:

where the weights wij consist of the elements of the i-th row of the matrix W, matched up with the corresponding elements of the vector y.

Spatially Lagged Variables

Spatial lag with row-standardized weights.

Spatial window sum

The spatial window sum uses and includes the diagonal element.

References

Chapter 2. Codifying the neighbourhood structure of Handbook of Spatial Analysis: Theory and Application with R.
François Bavaud (2010) “Models for Spatial Weights: A Systematic Look” Geographical Analysis, Vol. 30, No.2, pp 153-171.
Tony H. Grubesic and Andrea L. Rosso (2014) “The Use of Spatially Lagged Explanatory Variables for Modeling Neighborhood Amenities and Mobility in Older Adults”, Cityscape, Vol. 16, No. 2, pp. 205-214.