4.6.2 Construction of the Price Relation Matrix

4.6.2 Construction of the Price Relation Matrix

The Price Relation Matrix is constructed by transforming the value relationships represented in the Value Relation Matrix into corresponding price relationships.

Let

VRM=[rij]n×n,\mathbf{VRM} = [r_{ij}]_{n\times n},VRM=[rij​]n×n​,

where rijr_{ij}rij​ denotes the relative value relationship between spatial units iii and jjj.

The corresponding Price Relation Matrix is defined as

PRM=[pij]n×n,\mathbf{PRM} = [p_{ij}]_{n\times n},PRM=[pij​]n×n​,

where

pijp_{ij}pij​

represents the relative price relationship between the same pair of spatial units.

The transformation from value relations to price relations can be expressed generally as

PRM=Φ(VRM),\mathbf{PRM} = \Phi(\mathbf{VRM}),PRM=Φ(VRM),

where

Φ(⋅)\Phi(\cdot)Φ(⋅)

denotes the value-to-price transformation function.

The specific mathematical form of this transformation depends on the valuation framework and calibration strategy adopted in a particular application. Regardless of its implementation, the transformation must preserve the relative spatial structure established by the Value Relation Matrix.

Consequently, locations exhibiting stronger value relationships within the Urban Land Value Field are expected to maintain correspondingly stronger price relationships after transformation.