Modeling Spatial Trends in Rural Population Based on the spatial moving average (SMA)

Introduction
Iran's total population in 2006 was about 70 million. In 2011, it reached 75 million. Many of those are settling down in rural areas. The geographic distribution of Iranian population is uneven. There are many reasons for the differences in geographic distribution of population. They can be divided into physical factors and social, economic, and political factors. The increase in human population in some area causes the pressure on natural resources such as water and soil also increases. It follows spatial inequalities. On the other hand, rural population needs must be met. Trends and geographic distribution affects regional planning policies. Census data are collected for individual households but are usually released in aggregate. Aggregation is often done on the basis of geographical location, and data are made available at some spatial scales such as statistical tracks, villages, cities, dehestan, bakhsh, shahrestan, provinces, and finally national levels. Surely, scale of aggregation affects results of analysis. The main objective of this paper is present a methodology for Modeling spatial trends in rural population.
Geographers deal with the distribution of a wide variety of geographical entities and phenomena. Geographers analyse their spatial distributions, the pattern of the distribution of objects, spatial variability and so forth. The concepts of spatial analysis deal discovery spatial patterns, cause and effect of phenomena, autocorrelation, etc. Some concepts must be considered: MAUP and problems of spatial units, spatial stationary, spatial weight, spatial moving average, and spatial trends.
The Modifiable Areal Unit Problem (MAUP) is a potential source of error that can affect spatial studies which utilize aggregate data sources. MAUP consists of two components; one is the scale problem or aggregation problem and the other is the grouping or zoning problem. The former concerns the different statistical inferences and estimates generated by the same data set that is aggregated into different spatial resolutions, especially aggregating small areas into a larger unit.
Stationary and none stationary. Any spatial process operating between neighbouring units can cause spatial heterogeneity. Inference from a pattern on the underlying process is further hindered by variation in the process in space or time as well as by the presence of additional, confounding processes. Spatial distribution displays stationary if the expected value at all places are the same. But the most geographic entities are none-stationary because of spatial variability.
Spatial trends. We define a spatial trend as a regular change of one or more non-spatial attributes when moving away from a given start object i. We use neighbourhood paths starting from i to model the movement and we perform a moving average analysis on the attribute values for the objects of a neighbourhood path to describe the regularity of change.
Spatial weight matrix. Spatial weights are central components of many areas of spatial analysis. In general terms, for a spatial data set composed of n locations (points, areal units, network edges, etc.), the spatial weights matrix expresses the potential for interaction between observations at each pair i, j of locations. There is a rich variety of ways to specify the structure of these weights.
Spatial moving average. in time series moving average is Mean of time series data (observations equally spaced in time) from several consecutive periods. And spatial moving average can computed locally using a geographical weighting scheme. The mean of individual cells computed by neighbourhood attribute.
Methodology
We use results of census of population and housing 2006 as Geodatabase. The following steps are used to perform research:
Step1: Preparing and pre-processing data.
Step 2: Making spatial units base on hexagonal forms.
Step 3: Spatial data aggregation
Step 4: Setting K nearest neighbours
Step 5: Calculation spatial weight
Step6: Calculation of SMA
Step7: Analysis results
Step 8: making maps
Conclusion
Spatial is variability and non-stationary. Exploration of spatial pattern is an important subject in spatial planning. Spatial analysis include some components such as spatial pattern, spatial autocorrelation and autoregressive. One of the favorites in spatial analysis is discovering spatial pattern and trend in spatial data. Several tools have been developed for analysing spatial trends. At this paper we suggest a model based on moving average. Charts and maps have been used to analyse the results. The result of present based on various orders of moving average. In each of orders result completely difference. To k= 20 the local trend configured and with increasing value of ka global trend are found.