  The concept of allometric growth is based on scaling relations, and it has
been applied to urban and regional analysis for a long time. However, most
allometric analyses were devoted to the single proportional relation between
two elements of a geographical system. Few researches focus on the allometric
scaling of multielements. In this paper, a process of multiscaling allometric
analysis is developed for the studies on spatio-temporal evolution of complex
systems. By means of linear algebra, general system theory, and by analogy with
the analytical hierarchy process, the concepts of allometric growth can be
integrated with the ideas from fractal dimension. Thus a new methodology of
geo-spatial analysis and the related theoretical models emerge. Based on the
least squares regression and matrix operations, a simple algorithm is proposed
to solve the multiscaling allometric equation. Applying the analytical method
of multielement allometry to Chinese cities and regions yields satisfying
results. A conclusion is reached that the multiscaling allometric analysis can
be employed to make a comprehensive evaluation for the relative levels of urban
and regional development, and explain spatial heterogeneity. The notion of
multiscaling allometry may enrich the current theory and methodology of spatial
analyses of urban and regional evolution.
