Development of a Catastrophe Model to Assess the Allocation Efficiency of Competitive Sports Resources in China - Advanced Research on Computer Education, Simulation and Modeling - page 401

resources and material resources, and with the maximum outputs. Under such circum-
stances, the “input-output” evaluation framework for resource allocation efficiency
assessment, proposed by Woidasky (2009) [7], was chosen as the basis for defining
indices to assess the allocation efficiency of competitive sports resources. Besides,
indices selection in this study was guided by the principles of integrity, simplicity,
dynamic response, geographical accuracy, and data availability and the “three-step”
method proposed by Su et al. (2010) [6]. We referred to previous studies and the
framework as well as the principles explained above to generate a set of assessment
indices. Initially, a set of 60 indices was developed. Subsequently, we established a
three-round Delphi Process from which 18 indices were selected and 2 indices were
added. After performing principal component analysis to reduce data dimensionality,
a total of 7 indices were generated: Input (Funding amount for competitive sports,
Total number of full-time coaches, Total area of sports venues) and Output (Gold
metals at national level and above level, Number of persons doing regular physical
activities, Total output of sports patent, Sports lottery sales).

2.2 Data Source and Standardization

Statistical data between 2003 and 2008, obtained from “China Statistical Yearbook”,
“China Sports Yearbook”, “State Patent Database” and “China Statistical Database”,
were used in this paper. Given the different dimension and distribution of indices, it
was difficult to directly compare or operate among them. Data standardization was
thus performed to make the original data of indices dimensionless using the following
equations:

xx −

'

x =

i i min

(1)

i

x − x

i max i min

Where i is the index, xi is the original value of i, x imax and x imin are respectively the
maximum and the minimum value of i.

2.3 Application of Catastrophe Theory

Catastrophe theory uses mathematical models to describe, predict qualitative changes
of natural phenomena and social activities. Catastrophe theory focuses on the poten-
tial function [V = V (x, u)], which describes the system behavior using the state
variables x and the external control parameter u. When the state variable is one di-
mensional, there exist four catastrophe models [8] (Table 1). The assessment index
system can be divided into hierarchical sub-systems. If the index at higher level (re-
sponse variable) contains two lower level indices (control variable), it can be assumed
as a cusp system. The relative importance of these two control variables should be
determined (u 1 , important; u 2 , less important), and control variable can then be ob-
tained from the membership function. Similarly, when the index at higher level con-
tains one, three or four lower level indices, it can be respectively calculated based on
fold, swallowtail and butterfly membership function. The catastrophe assessment
model for China's allocation efficiency of competitive sports resources was therefore
developed following such approach.