# Understanding Spatial Analysis

Spatial analysis encompasses everything we do with our geospatial data, from framing our research question to presenting our final results. It allows us to solve complex location-oriented problems and better understand where and what is occurring in a particular geographic space. In the present, spatial analysis goes beyond mere mapping to study the characteristics of places and the relationships between them, rather it involves using analytical techniques to examine geospatial data and answer questions by highlighting or creating new information. Thus, spatial analysis lends new perspectives to decision making in a number of ways. Whenever we look at a map, we inherently start turning that map into information by analyzing its contents and finding patterns, assessing trends, and making decisions. Thus, spatial analysis refers to statistical analysis based on patterns and underlying processes. It is a kind of geographical analysis that elucidates patterns of personal characteristics and spatial appearance in terms of geostatistics and geometries, which is known as location analysis. The entire process involves statistical and manipulation techniques, which could be attributed to a specific geographic database (Cucala et al„ 2018).

Classification of the techniques of spatial analysis is difficult because of the many different fields of research involved. They have been invented in many disciplines, including mathematics, geometry; statistics, spatial statistics and statistical geometry; and in geography and other earth sciences. Spatial analysis is a type of geographical analysis that explains the behavioral patterns of humans, animals, epidemics, etc., and their spatial expression in terms of geometry. Thus, the range of methods deployed for spatial analysis varies with respect to the type of the data model used. Measurement of length, perimeter, and area of the features is a very common requirement in spatial analysis (Clark and Evans, 1954). However, different methods are used to make measurements based on the type of data used, i.e., vector or raster. Invariably, the measurements will not be exact, as digitized features on a map may not be entirely similar to the features on the ground, and moreover, in the case of raster, the features are approximated using a grid cell representation (Oliver and Webster, 2007).

Spatial analysis is one of the most intriguing and remarkable aspects of GIS. Due to the flexibility of GIS, spatial analysis can constitute one simple task or a series of complex tasks. A simple spatial analysis process might consist solely of visualizing data on a map for users to inteipret, and a complex spatial analysis process can incorporate multiple datasets, spatial statistics, and Python scripts. These tools enable you to address critically important questions and decisions that are beyond the scope of simple visual analysis. However, complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research.

## Types of Spatial Analysis

### Autocorrelation

In order to detect the spatial pattern (spatial association and spatial autocorrelation), some standard global and new' local spatial statistics have been developed. These include Moran’s /, Geary’s C, and G statistics (Getis et al., 1992). All of these spatial analytical techniques have tw'o aspects in common. First, they start from the assumption of a spatially random distribution of data. Second, the spatial pattern, spatial structure, and form of spatial dependence are typically derived from the data (Bao, 1999). Spatial autocorrelation is simply looking at how w'ell objects correlate with other nearby objects across a spatial area. Positive autocorrelation occurs when many similar values are located near each other and vice versa in cases of negative autocorrelation. The importance of spatial autocorrelation is that it helps to define how important spatial characteristics affect a given object in space if there is a clear relationship (i.e., dependency) of objects with spatial properties. Strongly positive or negative results indicate that a clear spatial property is found in the object w'ith a high correlation (Griffith, 2011). Perhaps the most common way in which autocorrelation is measured is using Moran’s /. which allow's the correlation measure to determine correlation based on multiple dimensions across a given space. Results are generally used to measure how well an object correlates globally, that is across a given defined space for a dataset. Geary’s ratio C is another similar measure, w'here this measure is more sensitive to local variations and can be used to define local patterning within a dataset (O'Sullivan and Unwin, 2010).

### Spatial Interpolation

Spatial interpolation methods estimate the variables at unobserved locations in geospace based on the values at observed locations because it is often difficult to obtain height, magnitude, or concentration of a phenomenon from every location of a given area. Instead, one can measure the phenomenon at strategically dispersed sample locations (randomly or regularly spaced) and create a continuous surface by predicting values for all other locations. Various interpolation techniques such as Inverse Distance Weighted (IDW), Sapline and kriging interpolation, as well as polynomial trend and natural neighbor methods can be used to estimate rainfall, elevation, temperature, or other spatially continuous phenomena. IWD and Spline methods are deterministic interpolation methods because they assign values to locations based on the surrounding measured values whereas kriging is based on statistical models that include autocorrelation, the statistical relationship among the measured points. Analysts can also create non-traditional surfaces using various other functions (i.e., density surface showing the density of objects), such as persons per square kilometer of land area; distance-based surfaces showing distance to various features, such as a police station, petrol pump, bank, city market, etc. Using surface analysis in GIS, we can obtain elevation from a terrain surface, or density areas for crime analysis. These techniques not only have the capability to produce a prediction surface but also provide some measure of the certainty or accuracy of the predictions.

### Spatial Regression

Spatial regression method capture spatial dependency in regression analysis to avoid statistical problems such as unstable parameters and unreliable significance tests. It also helps to provide information on spatial relationships among the variables involved. Depending on the specific technique, spatial dependency can enter the regression model as relationships between the independent variables and the dependent one. Geographically Weighted Regression (GWR) is a local version of spatial regression which allows to study how a given phenomenon varies spatially in a particular area (Fotheringham et al„ 2002). For example, in crime-related studies, spatial regression method can be applied successfully to understand what variables (education, occupation, age, income, etc.) explain crime locations, which can be used for decision making. Spatial regression model can be used to predict future crime locations.

### Spatial Interaction

Much of the data gathered today contains at least one location component. Often times, there will be multiple location components or additional factors within a single data set. In such cases, there are many valuable questions to ask about how these location components or factors might impact one another. For this, one needs to draw on specific spatial techniques to plumb the depths of available data for answers to these questions. Various forms of spatial interaction models have been applied in aggregate analysis, most commonly the spatial interaction or gravity model. The gravity models provide a flexible approach for the analysis of spatial interactions between spatially separated nodes, being applied in a wide variety of studies, such as those devoted to migration, commodity flows, traffic flows, residence-workplace movement, market area boundaries, etc. In general terms, the gravity models state that the interaction between two centers is in direct proportion to their size and in inverse proportion to the distance between them. After specifying the functional forms of this interaction, the expert can estimate model parameters using observed flow data and standard estimation techniques such as ordinary least squares or maximum likelihood. Competing destinations versions of spatial interaction models include the proximity among the destinations in addition to the origin-destination proximity. This captures the effects of destination (origin) clustering on flows. Artificial Neural Networks (ANN) can also estimate spatial interaction relationships among locations and can handle qualitative data.

### Simulation and Modeling

In the present day, our ability to collect and organize observations and to combine and transform data to generate new information, including maps and models, make GISs an essential tool for designers and policy analysts. The observations (data) might be used together to understand real and hypothetical situations. Geographic models may be useful for developing and communicating an understanding of how things and conditions affect each other. This is the sort of information that designers and policy analysts often have to make. Geographical models can be useful for conducting hypothetical (what-if?) experiments that explore plausible ways that critical aspects of situations might be affected by change. Spatial interaction models are aggregate and top-down: they specify an overall governing relationship for flow between locations. This characteristic is also shared by urban models such as those based on mathematical programming. Important spatial simulation methods are cellular automata and agent-based modeling. Cellular automata modeling imposes a fixed spatial framework such as grid cells and specifies rules that dictate the state of a cell based on the states of its neighboring cells whereas Agent-based modeling uses software entities that have purposeful behavior and can react, interact and modify their environment while seeking their objectives. While cellular automata are of interest in spatial modeling and often used to model land cover changes, whereas agent-based models are being applied for many operations including managing traffic flow. Cellular automata and agent-based modeling are divergent yet complementary modeling strategies. They can be integrated into a common geographic automata system where some agents are fixed while others are mobile.

## Data Types in Spatial Analysis

According to Camara et al. (2004) the most used taxonomy to characterize the problems of spatial analysis consider three types of data:

Events or Point Patterns - phenomena expressed through occurrences identified as points in space, denominated point processes. Some examples are crime spots, disease occurrences, and the localization of vegetal species.

Continuous Surfaces - estimated from a set of field samples that can be regularly or irregularly distributed. Usually, this type of data results from natural resources survey, which includes geological, topographical, ecological, phitogeo- graphic, and pedological maps.

Areas with Counts and Aggregated Rates - means data associated to population surveys, such as census and health statistics, and that are originally referred to individuals situated in specific points in space. For confidentiality reasons, these data are aggregated in analysis units, usually delimited by closed polygons (census tracts, postal addressing zones, municipalities).

The previously mentioned data types are environmental and socioeconomic in nature, which requires solution through a set of chained procedures that aims at choosing an inferential model that considers the spatial relationships present in the phenomenon and their dependency patterns. In the case of point pattern analysis, the objective is to study the spatial distribution of the points under consideration, testing hypothesis about the observed pattern, if it is random or is regularly distributed (Table 1.1). For surface analysis, the objective is to reconstruct the surface from which the samples were removed and measured. For a real analysis, the areas are usually delimited by polygons with internal homogeneity, that is, important changes only occur in the limits.

## Geovisualization

Geovisualization combines scientific visualization with digital cartography to support the exploration and analysis of geospatial data and information, including the results of spatial analysis. Geovisualization is generally defined as the method of interactively visualizing geographic information in any of the spatial analysis measures, although it may also apply to the visual production (e.g., charts, maps, diagrams, 3D views) or the techniques associated with it. In contrast with traditional cartography, this method is typically three- or four-dimensional and user-interactive. GISs increasingly provide a range of such tools, providing static or rotating views, draping images over 2D surface representations, providing animations and fly-throughs, dynamic linking, and spatio- temporal visualisations. A key argument for geovisualization is that visual thinking using maps is central to the creation of scientific processes and theories, and the role of maps has expanded beyond communicating the end results of an experiment or documentation. As such, geovisualization integrates with a variety of disciplines including cartography, visual analysis, knowledge visualization, scientific visualization, statistics, computer science, art-and-design, and cognitive science.