Location-Based Marketing. Gérard Cliquet. Читать онлайн. Newlib. NEWLIB.NET

Автор: Gérard Cliquet
Издательство: John Wiley & Sons Limited
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Жанр произведения: Маркетинг, PR, реклама
Год издания: 0
isbn: 9781119721291
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intended to develop sophisticated mathematical and statistical methods, it is nevertheless necessary to review a few tools in order to get the most out of the often tedious mapping work. It would be a pity to miss some conclusions because of a lack of knowledge of these tools. To do this, it is important to be familiar with spatial autocorrelation and related indices: Moran index, Geary index. Less specific to spatial analysis, however, the Gini coefficient (Gini 1921) is used in particular to show income inequalities by location as was done for the city of Athens (Panori and Psycharis 2018).

      Autocorrelation expresses the correlation of a variable with itself. This correlation can be measured either over time by comparing successive values of the variable (temporal autocorrelation) or over time by measuring the variable in different locations (spatial autocorrelation) (Oliveau 2017).

      Spatial data are characterized by their great heterogeneity, which is systematic, while temporal data encounter this type of difficulty less frequently (Jayet 2001).

      A distinction is made between heterogeneity of size (geographical entities such as cities, regions or countries are very diverse in size), heterogeneity of shape (regions do not have the same contours), heterogeneity of position (a northern region and a southern region of the same size and shape are not comparable), heterogeneity of structure in terms of qualification, economic activity or the size of establishments (Jayet 2001). It is therefore appropriate to use certain tools such as autocorrelation measurements to measure this heterogeneity.

      where

       – zi and zj are the coordinates of geographical entities;

       – zi is the value of the variable for entity i, its mean being

       – i is the geographical entity;

       – j is the neighbor of entity i;

       – n is the total number of geographical entities in the sample;

       – m is the total number of pairs of neighbors;

       – w is the weighting matrix, the elements of which take, for example, the value 1 for the neighboring i, j and 0 otherwise.

      Moran’s I formula compares the difference between the ratio of the value of a variable concerning an individual to the mean of these values, to the ratio of the value of the same variable for neighboring individuals to the same mean. This I index takes these values between –1 (negative spatial autocorrelation) and +1 (positive spatial autocorrelation). But the value of I can exceed 1 or be less than –1 (Oliveau 2011). A non-zero measure of this index shows a contiguous effect between close spaces:

       – if I > 0, the contiguous spaces have similar measures of the variable;

       – if I < 0, it means the absence of the significant variation or disparate values;

       – if I is close to 0, there is no negative or positive spatial autocorrelation.

      But the measurement of this index I is not without criticism and may not clearly reflect spatial structures. There are three limitations to the measurement of Moran’s I (Oliveau 2011):

       – the measurement of spatial autocorrelation obtained from Moran’s I is global unlike Geary’s C which provides a local measurement of spatial autocorrelation. This global character of Moran's I can lead not to a precise spatial structure, but to two different spatial configurations:- a configuration highlighting a central pole;- the presence of two peripheral poles;

        – Moran’s I considers the deviation from the mean without looking at neighboring individuals, but also with values close to the mean;

       – Moran’s I is sensitive, on the one hand, to the level of observation, and on the other hand, to the mode of neighborhood chosen.

      Moran’s I measured the spatial coherence of a chain of stores with a measure of the network’s territorial coverage by relative entropy (Rulence 2003). The influence of time on spatial dependence has been estimated by data on property prices (Devaux and Dubé 2016).

      Once again, Moran’s I has the disadvantage of being too global when looking at spatial structures over small areas (Brunet and Dollfus 1990), which requires the use of Geary’s C index. The Geary C index (Geary 1954) is also used to measure spatial autocorrelation and is presented as follows (Oliveau 2017) following a rewrite (Cliff and Ord 1973):

      where

       – zi and zj are the coordinates of geographical entities;

       – zi is the value of the variable for entity i, its mean being

       – i is the geographical entity;

       – j is the neighbor of entity i;

       – n is the total number of geographical entities in the sample;

       – m is the total number of pairs of neighbors;

       – w is the weighting matrix, the elements of which take, for example, the value 1 for the neighboring i, j and 0 otherwise.

      1.4.2.3. Simulation systems

      Spatial simulations based on multi-agent systems (MAS) or agent-based models (ABMs) (Amblard and Phan 2006; Banos et al. 2015) are based on artificial intelligence (AI) and artificial life. AI simulates intelligence using machines and software (Minsky 1986). Artificial life (Heudin 1997) is based on biomimicry, that is, the reproduction of biological phenomena with neural networks, genetic algorithms, cellular automatons represented by regular grids and used to define urban space simulation models (Langlois and Phipps 1997). Multi-agent systems (MAS) have been widely used in logistics management in connection with retail activities (Li and Sheng 2011; He et al. 2013; Heppenstall et al. 2013). An application of multi-agent systems has made it possible to develop a system called the Multi-agent System for Traders (MAST) to facilitate the consumer purchasing process