Table 2 shows some data regarding the levels of resident employment and resident employment by sector in the analysed area. Obviously, these percentages are correlated to the population size. In fact, in order to compare the employment data of the two analysed cities and to give more specific information about the levels of employment, some rates can be calculated.
As an example, the regional employment rate gives an idea about the levels of employment by considering employed persons as a percentage of the population.
Analogously, the regional unemployment rate can be calculated, by considering unemployed persons as a percentage of the economically active population labour force. Table 3 shows some data regarding the employment in the analysed area. ISTAT provides the data regarding economic activities, through the decennial census of the industrial and service activities [ 24 ].
The enterprises are generally small, with a staff of 4. While in Cosenza most of people are employed in the sector of the public services, the enterprises located in Rende refer prevalently to the business activities. Census data of the population [ 23 ] also provides the data referred to the daily trips made by people from home to work and study places commuter trips. The trips are distinguished into trips with destination in the place of residence internal trips , and trips with destination outside the place of residence external trips.
However, it is necessary to observe that among the trips from Cosenza some trips have destination in Rende and vice versa. Therefore, these trips are internal trips for the urban area. In order to quantify these, some information collected by previous surveys are taken into account, and specifically a survey realized on the occasion of the urban traffic plan drafting of Cosenza [ 25 ].
The survey, effected in May , was addressed to households 2, members out of 28, resident households [ 26 ]. From the survey data it follows that there are 32, trips per day made for all purposes by persons resident in the city with destination in other places, but a relevant part of these 17, trips had their destination in Rende This percentage can be used for estimating the number of commuter trips with origin in Cosenza and destination in the urban area.
Analogously, from the survey realized in the occasion of the urban traffic plan drafting of Rende [ 27 ], a number of 7, trips per day made for all purposes by persons resident in Rende with destination in other places was estimated. Also in this case, a relevant part of the trips 5, had their destination in Cosenza This percentage can be used for estimating the number of commuter trips with origin in Rende and destination in the urban area.
The trips with destination in Cosenza and those in Rende are been considered as internal trips. As shown in the Fig. The highest values are concentrated in the urbanized parcels. In Rende these are along the state roads n. Furthermore, some parcels have numerous daily trips but also a great area.
The others census parcels have less internal trips and are localized in the suburban areas which have low values of population and housing. The Fig. They vary between 0 to about 80 daily trips. However, it is necessary to point out that census data refer to the trips made for work and study purposes only, but a relevant part of the daily trips is made for other purposes. This value could be further increased in order to take into account the non home-based amount of trips.
Clustering techniques have emerged as a potential approach for analysing complex spatial data in order to determine whether or not inherent geographically based relationships exist. The measures of global and local spatial autocorrelation, defined in the Section 2 , were applied and implemented in a GIS environment for analysing the spatial association of the internal and external daily trips made in the urban area of interest.
The computer program ArcGIS contains methods that are most appropriate for understanding broad spatial patterns and trends. The purpose of the application of global techniques is to understand the spatial distribution of trips among the census parcels in the entire urban area. It calculates the Getis-Ord General G statistics and associated Z score which is a measure of statistical significance.
When the absolute value of the Z score is large, the null hypothesis can be rejected. The higher or lower values of the Z score involve the strong intensity of the clustering. A Z score near zero indicates no apparent clustering within the study area, whereas a positive and a negative Z score indicates clustering of high and low values, respectively. This statistics is very useful to understand the pattern of daily trips in the urban area of Cosenza and Rende. In the case of the application to the external trips, the outcomes Table 6 indicate that the Z score value is negative but his absolute value is lower; therefore, the null hypothesis cannot be rejected.
In the Fig. Probably, this result is caused by the data set, which for external trips contains low values respect to the internal trips. To determine if the Z score is statistically significant, it is compared to the range of values for a particular confidence level. When the p value is small and the absolute value of the Z score is large enough to fall outside of the desired confidence level, the null hypothesis can be rejected. Analysing the spatial distribution of the internal trips, it is evident that the Z score value is high and the null hypothesis can be rejected Table 7.
As represented in the Fig. The results of the spatial autocorrelation applied on the external trips follow the same trend as the previous one, as showed in the Table 8.
Therefore, the null hypothesis can be rejected and there is a clustered pattern of the data Fig. In fact, for internal trips, the first statistics establishes that there is clustering of low values, and the second one confirms the presence of spatial patterns.
The global measures of spatial association refer to the entire area and do not give indications about the clusters are localized. The local statistics of spatial association are useful in detecting places with unusual concentrations of hot spots. The output of the G i function is a Z score which represents the statistical significance of clustering for a specified distance and must be compared to the range of values for a particular confidence level.
A high Z score for a feature indicates its neighbours have high attribute values, and vice versa. A Z score near zero indicates no apparent concentration. The parcels with high values are localized on the boundary between Cosenza and Rende. In fact, this zone is a unique urban structure, which has similar characteristics, as said in the Section 4. Instead, the parcels with low values are localized in the old town of Cosenza and in areas with low population.
A positive value for I indicates that the feature is surrounded by features with similar values. A negative value for I indicates that the feature is surrounded by features with dissimilar values. The tool also provides a Z score value for each observation.
A group of adjacent features having high Z scores indicates a cluster of similarly high or low values. A low negative Z score for a feature indicates the feature is surrounded by dissimilar values. Finally, the tool provides a distinction between a statistically significant 0. In the Figs. There is an evident agreement between the two representations. The areas of the corresponding patterns are localized in the same place, even if their extensions and shapes are different.
In fact, both the statistics give an indication about the localization of the hot and cold spot, which is approximately the same. The application of the spatial association statistic to commuting trip data introduced new aspects which merit further consideration, as said in [ 20 ].
Moreover, the used measures can improve understanding of the strengths and weaknesses of the estimated models in terms of a spatial analysis.
This understanding can be incorporated into improved and more comprehensive models. The purpose of this paper is to investigate spatial association patterns in the distribution of daily trips made by people from home to work and study places commuter trips.
The trips have been distinguished into trips with destination in the place of residence internal trips , and trips with destination outside the place of residence external trips.
Exploratory spatial data analysis was conducted applying both global and local techniques of spatial association. The main contribution of the ESDA is to highlight potentially interesting features in the data, and to address the modelling process. The statistics were elaborated by using GIS, which allows the outcomes to be estimated with automatic proceedings and this aspect facilitates the application of techniques to large data sets.
In fact, the application of spatial analysis has obviously become easier with the recent advancements in computing and GIS, which have revolutionized the development of planning support systems to study and simulate the future of travel demand in urban areas. The results showed that the spatial distribution of trips among the census parcels displays clusters of similar values and there is spatial dependence in the data set.
This means that to model the phenomenon is necessary to use spatial regression models because the application of non-spatial regression models can lead to wrong results. The work presented in this paper is a step towards a wider work regarding the case study of Cosenza-Rende. Future developments will regard the analysis of interaction between land-use and transportation systems, the development of spatial regression models, and it will also comprise the supply transportation system, the localization of dwellings and economic activities, and the territorial features.
Moreover, further developments will concern the check if the results can be generalized to urban contexts with similar characteristics to that studied. Bertaud A, Stephen M The spatial distribution of population in 48 world cities: implications for economies in transition, the centre for urban land economic research. Eboli L, Forciniti C Spatial analysis and statistics as a tool for analyzing land-use and transportation systems. Libria, Melfi, pp 25— Google Scholar. GeoJ — Article Google Scholar.
In: Fischer M, Getis A eds Handbook of applied spatial analysis: software tools, methods and applications. Springer, Berlin Heidelberg. Getis A Reflections on spatial autocorrelation. Wilson Ed. DOI: This Topic is also available in the following editions: DiBiase, D. Global measures of spatial association. Spatial association is a general term that encompasses a number of ways in which events, measurements or places are related in space.
This relationship may be measured by determining the distance between nearby observations or by assessing whether the value of observations at nearby locations are similar. When similarity in both observations and locations is of interest, we invoke the first law of geography, "Everything is related to everything else, but near things are more related than distant things" Tobler , Measures of spatial dependence and spatial autocorrelation are based on this fundamental Geographic Information Science principle and these are the concepts most frequently encompassed within the term spatial association.
Thus, these are the focus of this entry. Other forms of spatial association, such as spatial interaction and spatial clustering, are covered elsewhere in this collection. Spatial association can be assessed globally or locally.
In global measures, a single statistic is used to provide a general measure of the similarity between neighbors across the entire study region. Local measures call on the principle of spatial heterogeneity, which assumes that the relationships between locations are not constant over the study area; they provide a means of measuring local variation.
This entry explores global measures; a companion entry provides details on local measures. Measures of spatial dependence and spatial autocorrelation generally depend upon the creation of a spatial weights matrix in which the spatial relationships between observations can be recorded.
Thus, we begin with a brief introduction to the spatial weights matrix. The semivariogram, a method used to depict spatial autocorrelation between samples of continuous fields, is also introduced. Finally, we close the entry with an assessment of limitations, disciplinary applications and software environments of the measures. Typically denoted as W, a spatial weights matrix records a neighborhood structure for a set of data with n observations as an n x n matrix:.
There are various adjacency rules used to define neighbors. Figure 1 shows the simple adjacency neighbor structure of counties in Ohio using the county centroids. Figure 1. The two neighbor structures are very similar except for the top left corner and the top right corner where the counties share vertices but not edges. Source: authors. There are a variety of other spatial structure options for assigning neighbors, such as a distance threshold, k nearest neighbors, and Delaunay triangulation.
Spatial weights can also be measurements of interaction, such as number of commuters between places, or distance. The choice of a spatial weights matrix is critical for many spatial statistics calculations including spatial autocorrelation measures, and a spatial weights matrix should be carefully selected to reflect the underlying process of the problem being studied.
Spatial autocorrelation refers to the correlation of a variable with itself in a space — therefore it is "autocorrelation. Measures of spatial autocorrelation detect the dependence between the values of one attribute due to spatial proximity. In the case of testing for spatial autocorrelation in regression residuals, a statistically significant result implies that the predictor variables do not capture the variances properly.
The result is a misspecified regression model. Measures of spatial autocorrelation show spatial patterns in three categories: 1 Positive spatial autocorrelation that indicates similar values are nearby, 2 negative spatial autocorrelation that indicates dissimilar values tend to be together, and 3 zero spatial autocorrelation, or random distribution, meaning no significance in similar or dissimilar values in nearby locations. Figure 2 illustrates the three categories of spatial autocorrelation patterns.
Figure 2. Three categories of spatial autocorrelation patterns: Positive spatial autocorrelation, negative spatial autocorrelation, and no spatial autocorrelation random. Conceptually, one can measure spatial autocorrelation within any type of objects points, lines, polygons , but these measures are usually applied to polygon data area objects, called lattices in the spatial econometrics literature with ratio or interval scale data.
A join or joint count statistic is a global spatial autocorrelation measure for categorical variables described back in late s but not named until the s by Dacey Dacey A join count statistic assumes first-order homogeneity and tests whether the attribute values of a categorical variable at adjacent locations are the same.
As its name implies, a join count statistic counts the number of occurrences of each combination of two categories between neighboring pairs of polygons. Since the number of different joins possible between categories grows quickly, the join count statistic is usually only applied when the number of categories is a very small number e.
The second numerator portion includes a covariance portion -- the product of deviations from the mean of variable x of observations i and j and, its spatial weight element w ij indicating how the observations i and j are spatially related. The sum of this product would only equal to the auto-covariance if all elements of the weights matrix are equal to one. The second denominator is the sum of the non-diagonal elements of the weights matrix over the entire study region. A data variance term is used to normalize the value and to ensure that the index I is not large simply due to the large values or variability of x.
When there is a sufficiently large number of observations, we can test the statistical significance of the measure of spatial autocorrelation. An alternative option in testing for spatial autocorrelation is a random permutation test. Search this site. AP Project. Chat BOX! Carl Saucer's Cultural Landscape Theory. Space Time Compression. Cultural Ecology.
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