Mathematical and statistical modeling of hierarсhy and heterarchy of economic-geographical systems

The paper considers the structure of territorial economic-geographical system of Russian regions in the vertical (hierarchy) and horizontal (heterarchy) aspects using methods of mathematical modeling of a multilevel indicative function. It connects indicators of socio-economic development of regions and takes into account characteristics of the economic-geographical environment and regional spatial hierarchy. For the model calculations, we use data of dependence of the annual regional domestic in- vestment on the volume of industrial and agricultural production from 1999 to 2018. The calculated values of investment acceleration indicators vary in time and between regions. They reflect the variability of the economic-geographical environment at the different hierarchical levels. A logical chain of regression equations statistically describes the vertical hierarchy of the Russian economic system. Linear regional trends form groups, or congruencies, with similar norms of the socio-economic environment at the federal okrug level. The congruencies shape the all-Russian directive surface, or directress, and demonstrate diversity of the levels and directions of region development. Described in terms of the relationship between domestic investment and production volumes, the structure reflects the hierarchy of the Russian economic system at the regional, okrug and state levels and forms spatial heterarchical network of similarity of economic growth potentials.