# Spatial data analysis

### INTRODUCTION

'Spatial'refers to phenomena occuring in a geographical location,or occupying space on the Earth surface which could be referenced in relation to its coordinates-ie its longitude and latitude respectively,and sometimes ,such referencing could be in relations to other objects around it;example,a parcel of land or a brown jaguar car located in warwick,longitude 13 degree ,North,20 degree East,or the car is parked directly behind the Asda supermarket(Luc Anselin 1992)

In the above description of the object-car, is referenced to other objects existing and occupying space over time in the study area.

Spatial phenomena can be represented as points(zero dimension),2-demension,one -demension,etc for analytical purposes;hence it is a data which could be the subjects of analysis to obtain vital informations(wong and Lee 2005,p25).

Though,spatial data are quite unique compared to other types of data because it is geographically referenced data-ie observations,or occurence dependent on location or relatively positioning(Luc Anselin 1992).

Spatial data are of many different types, thus informing different types of its analysis,eg data from an object,and data from a surface.(Haining 2003,p2)

Spatial data also exhibits patterns due to there characteristics or influenced by human actions resulting in changes in patterns(spatial) over time.To identify and describe the process of changes in spatial data and the elements that necessitated these changes(ie human and environmental elements) with a view to enable comparisons,promote desirable phenomena associated with these change process,therefore a tool /system is necesary for its analysis-Geographical information systems(Gis)(Wong and Lee 2005,p327-3330).

Gis is a system that captures,organizes,manipulates,checking,analysing and dispalying spatially referenced data(Grimshaw1994,p22)

Spatial data analysis,/statistics in a geographical information systems environment can be used to analyse and describe spatial patterns,processess relating to these patterns,forms,changes etc and there relationship to other geographical objects within the neighbourhood for comparison in there different respective environment.(wong and Lee 2005,p327-330).

Gis has the capabilities to transforms data between different spatial scale of observations,execute query,interpolates,overlay, and execute other operations to produce new geogarphical results(Luc Anselin 1990)

Spatial data analysis seek to investigate patterns in spatially referenced data and there relationships(strength and direction) including attributes data and modelling such relationship across the study area with the intent of understanding or predicting a hypothetical situation of a pattern and or produce maps based on spatial data sample's attributes, test ,support,or derive a theorem(fotheringham and Rogerson1994,p15-16).

Spatial data analysis involves the various processess in manipulating and analyzing cartographic data using there geomatric or topographic characteristics as well as incorporating attributes informations into different forms resulting in the extractions of useful informations of a geographic nature(fotheringham and Rogerson 1994,p15).

Spatial data analysis relies on some fundamental concepts in the analysis of data,which are mostly statistical,such as scale measurements,use of mathematical notations,and scale and projections (Wong and Lee 2005,p13)

- Scale Measurement-This is necessary to ascertain the limits to which geograhical phenomena can be measured either for analytical comparative or recognition and differentaition.Examples are mesurements based on norminal scale,ratio scale or interval scale.(Wong and Lee 2005,p13-15).
- Mathematical Notations-spatial data analysis uses complex and simple algebraic expressions to derive a formulae to explain effectively and efficiently the relationships between geographical phenomena .Examples are the relationship between a points and the neighbouring points,strength of these relationships etc,which can be expressed using mathematical notaions as inversely1/d,summations,factorials! etc.(Wong and Lee 205,p22-25).
- Scale and projections-all spatial phenomena have dimensions in the real world,so it is important to represent them accurately in relation to the size on the map to the real world using ratios,eg 1:500 ie 1units of the observed variable on the map represent 500 units in the real world distance.It can also be expressed literally as 1metre on the map to represent 500km.(Wong and Lee 2005,p13-22)

On the other hand,displaying spatial phenomena and patterns of distribution from the real world into 2-dimensional surface (paper map) often results in distortions and loss of data,therefore,appropriate projections is necessary to quantify them.In a computer environments,maps can be zoomed to reasonable required scale to obtain informations.(Wong and Lee 2005,p27)

There are varierties of spatial data analytic techniques,but the following techniques would be discussed in this paper due to restriction-

Nearest neighbour Analysis- Developed by Clark and Evans(1954) to explore the distance between the points(average distances) and that of the nearest neighbour with a view to predicting the distance(ie pattern of the probable next events based on area occupied per point) between the next possible points in a randomly selected event or in a clustered occurence.

The nearest neighbour analysis can be calculated as the ratio of the average distance between neraest neighbour of an occurence and the average distance of the expected nearest neighbour in adistribution(fotheringham and Rogerson1994,p25).

Mathematically,it is represented as D=observed average distance between nearest neighbour /exp.observed average distance between nearset nieghbour as determined by the hypothetical pattern,and where D is the nearest neighbour statistics.(Wong and Lee 2005,p238-241).

Spatial Autocorrelation- (Ismail 2006)- refers to measuring occurence,how they are related in terms of magnitude of there relationship( ie the variables) across a geographic space,and that of a neaby place; (locational similarities').Variables occuring due to geographical proximity are said to be clustered(positive Autocorrelation),(Fotheringham and Rogerson 1994,p31)

However,if the variables patterns are dissimilar or exhibit disperedness,this is a negative Autocorrelation.There is no autocorrelation in a randomly distributed variables.The techniques of spatial Autocorrelation draws its strength from the first law of geography;- Tobler(1970) 'things nearer are more related than distant things'(wong and lee 2005,p330,260-261 )

Spatially Autocorrelated variables are dependent of each other due to clustering,unlike nearest neighbour methods which considers only the average distance of each points and its nearest neighbour only,autocorrelation considers both locational proximity and similarity of their attributes in analysis.(wong and lee 2005,p260)and( Ismail 2006).

Spatial autocorrelations techniques find applications in may areas of human endeavors,eg(wong and lee 2005,p260-267) in the analysis of robbery incidences to predicts patterns and checked its spread,for analyzing and calculating routing features like roads ,railways and flights of similarities.It can be used in estaimting the values of real estate, ie properties of close proximity(Ismail 2006)

Spatial error dependence refers to errors occuring among the independent variables which could be due to correlations between latent variable,omission of variables or variables measurements.Example of such error is ecological fallacy(Ismail 2006)

Spatial lag dependence refers to error occuring between the correlated dependent variables .The impact of one dependent variable may influence its neighbouring variables;it can also arise from spatial spillover effect between dependent variables in the same region(Ismail 2006)

Isotropic Autocorrelation refers to variables correlating in the same direction but usually decline with distance,ie it follows the first law of geography by (Tobler 1970)'that things nearer are more related than distant things'(Ismail 2006).

Anisotropic autocorrelation on the other hand relates to variables correlating in both distance and direction.....(Ismail 2006)

The magnitude of the relationships of the variables can be measured using a statistical model knowns as the Moran's I index

Spatial Interaction-refers to the movement of the spatial entities over space,usually influenced by human activities.It is the interactions between geographical space induced by human activities such as migration,usage of public goods-roads,publicfacilities,landuse,transmission of informations,travels, etc interactions among many human related socio-economic activities that involves movement (ie from one point to another point ''from-to''or fron one origin to a destination(Haynes and fotheringham 1984),(fotheringhan and Rogerson 1994,p34-35)and( Rodigrue et al 2009).

Spatial interaction models are used to analyze and predicts patterns of spatial data interactions across a geogarphic space.Contempoary model of spatial interaction is the gravity model(Haynes and Fotheringham 1984)

The gravity model shares it's name from Newton's law of gravity that 'attractions between two variables in space is directly proportional to their mass and inversely proportional to their respective distances'(Rodigue 2009 et al). Gravity models relies on scale/size and distance in its analysis to measure and predicts spatial interactions patterns of variables.

Distance characteristics of the gravity model consider distance as a key factor i.e geographical space to overcome/travel across ;the farther the variables are apart,the less likelyhood of interactions between them,the nearer the places are the more chances of interaction.

Scale/size-the aresa with larger population size tends to attarcts more activities compared to areas with scanty population(Haynes and fotheringham 1984)

### Spatial Interpolation-

(Wong and Lee 2005,p267)and (J.Anita Dille 2002) is one of the many techniques of spatial analysis that involves estimating the value of a variable(unobserved) within a relative distance to predicts value from a known existing value(observed point).The rationale behind this techniques lies in the facts that variables in close proximity are correlated than farther variables.Spatial interpolation draws it's strength from the principle of spatial autocorrelation in analizing data.It uses neighbouring values to predicts values of unknown sample.There are many types,but this paper will discuss on two prominent types-(1) kriging and (2) Inverse Distance Weighted Interpolation (IDW).These techniques find many applications in the petrochemical industry,mining,geology,soil science,ecology,and geochemistry.

kriging-is a geostastical method use to predict values of unobserved variables using values of data of known observed point together with a measure of error of uncertainty.It involves studying the data gathered in the study area(ie from one location to location) and modelling the variation in values in relation to locational difference between them and direction and a prediction can be made of an unknown value in the same study area(.mitas and mistova 1999)

Kriging draws its strength from spatial autocorrelation in that it uncovers and measures the magnitude of the relationship of the variables with a view to predicting the unknown values of the variable around the the prediction location.( mitas and mistova 1999),though it is fraught with the issue of time consuming of developing the variogram and it is subjective in nature,large number of samples is required to arrived in a reasonable variogram,and the assumptions that the data are stationary and isotropic(Li and Heap 2008).

The distinguishing features of kriging as a method of spatial analysis is the ability inherent in it quality of statistical prediction and uncertainty of spatial distribution.(Mitas and Mistova),it is the best linear unbiased values/estimate,(Li and Heap 2008).

Inverse Distance Weighted Interpolation(IDW)-this method employes the concepts of weight which is inversely proportional to a certain limit of distance to arrive at the approximate values of unsample points.The weights decreases as the distance increases as well as when the power function of the distance increases.

It is based on the assumptions of positive spatial autocorrelation ie that sample nearer the prediction locaion have a heavier weights than sample farthest away,(mitas and mistova 1999)

Inconclusion spatial data analysis involves a whole range of statistaical techniques and or mathematical models to analyse spatial phenomena's characteristics with aview to obtaining results of a geographic nature.(Fotheringhan and Rogerson1994,p15)

Also,spatial analysis uses simple and complex statistical formulae to derive a mathematical models to explain effectively and efficiently the various degrees of relationships occuring between the these spatial phenomena and the pattern's of exhibitions. (Wong and Lee 205,p22-25

The techniques of spatial data analysis cut across many disciplines without any conceptual framework(Fotheringhan and Rogerson1994,16).

Finally,Gis provides a medium for the operation of spatial analysis in that it has the capability to geographically visualize,data transformation and ease of accessing spatial relation that exits between spatial phenomena in the study location.(Fotheringhan and Rogerson1994,p21)

### References:

- Luc Anselin 1992 in Spatial Data Analysis with Gis:An Introduction To Application In The Social Science,(A Technical Report August 1992){online}Accessed 5-2-2010 http//www.ncgia.ucsb.edu/Publications/Tech_Reports/92/92-10.PDF
- David W.S Wong and Jay Lee (2005). Statistical Analysis Of Geographic Information, With ArcView GIS and ArcGIS. USA: John Wiley & Sons Inc.
- Robert .P.Haining (2003) in Spatial Data Analysis;'Theory and Practise' (online)accessed 12/2/2010. books.google.com/books?isbn=0521774373
- David .J.Grimshaw(1994) in 'Bringing Geographical Information Systems into Business ,published by longman group Ltd.
- Fotheringhan and Rogerson 1994 in Spatial analysis with GIS',(Accessed online 9-2-2010)http//www. books.google.com/books?isbn=0748401040
- Haynes E. and A.Steward Fotheringham (1984) in'Gravity and Spatial Interactions Model'(Access online) 12-2-2010. hpp//www.web.pdx.edu/stipkb/download/PA557/Reading/PA557sec1-2.pdf,
- Jean-Paul Rodrigue, Claude Comtois and Brian Slack (2009),2nd edition in 'The Geography of Transport Sytems published by Routledge, (Accessed online) 13/2/2010.http// people.hofstra.edu/geotrans/eng/content.html
- J.Anita Dille 2002 in How good is your weed:'A Comparison Of Spatial Interpolators' weedscience,hpp//www.arsweeds.cropsci.illnoise.edu/howgood.pdf,{Acessed online }10/2/2010
- Suriatini Ismail Ph,D (2006) in Spatial Autocorrelation and Real Estate Studies:A literature Review (accessed online)12/1/2010.hpp//www.eprints.utm.my/438/1/1-13.pdf.
- L.Mitas and H.Mistova 1999 .in Spatial Interpolation'Accessed online 9/2/2010 hpp//www.colorado.edu/geography/class_homepages/geog_4203_s08/mitas_mistova_1999_2005pdf