Examine the relationship between population density and social sustainability with spatial autocorrelation models (Case Study: Orumiyeh)

Introduction
One of the growth patterns of the city, which known as a sustainable growth pattern, is intensive growth. Compactness is a mechanism for controlling and gradually reducing the growth of the city, which known for its high level of density, mixing of land uses, suitable transportation systems, and creating opportunities for pedestrians and cyclists. Socially, Density is associated with social justice and diversity because access to social infrastructure and
provides a more diverse environment by facilitating opportunities for all. Economically, the minimum density is necessary for the efficient use of urban resources in order to reduce costs and provide infrastructure. However, some studies in non-European cities suggest that these cities with increasing density, they have faced a decrease in social stability. In contrast, urban planners in Europe believe that the dense model of the city, in addition to increasing environmental and economic sustainability has led to increased social sustainability. Therefore, it is necessary to study the role of density in social sustainability with the characteristics of each city and the cultural characteristics of its citizens, far from prejudices. Therefore, the present study seeks to investigate the positive or negative role of density in social sustainability of Urmia city.
Methodology
The research is applied and the research method is descriptive-analytical. The required data for the research collected from the general population and housing census data within the statistical blocks and 30 indicators for the year 2006 and in Spss18 Software analyzed with using factor analysis method. However, the indicators reduced to six influential factors. Spatial autocorrelation, Moran index, G general statistics and Moran bivariate autocorrelation techniques used to analyze the relationships between population density and social stability in GIS software.
Results and discussion
The local Moran coefficient used to investigate the relationship between density and Social stability.
Four types of spatial correlations showed in this analysis:
 

High-high cluster: which has both high population density and high social stability. Which includes 564 statistical blocks that are spatially concentrated in the north, northeast of Urmia.
Low-low cluster: which has both low population density and low social stability. It includes 842 statistical blocks that are spatially concentrated in the northwest, east and south of Urmia.
High-low discomfort: which has low population density and high social stability. Which is concentrated in the northern part of the city and includes 261 blocks.
Low-high discomfort: which has high population density and low social stability. Which are spatially concentrated in the north, east and south of Urmia and contains 110 blocks.

Conclusion

The Moran coefficient of two variables (Moran s I =0.0371) that indicates a positive and not very strong relationship between Population density and social stability. Although, the Moran index is small, it partially confirms the fact that areas with high population density are to some extent consistent with areas of high social stability and the relationship between them is relatively positive but cannot be very reliable, because the coefficient value is very small.