Geographical Variation of the Quality of the School Offer in the City of Mbujimayi (Dr Congo): Data Processing by the Method of Multivariate Spatial Analysis

This article presents spatial data related to the quality of school infrastructures in the city of Mbujimayi so as to bring out their characteristics and the typology of quarters which contain these infrastructures. The variables used are presented in the spatial information matrix. The principal components analysis and factorial analysis of correspondences helped make the description of associations based on these variables. The correlation matrix gave birth to channels of the strongest positive correlations (r ≥ 0.60) and resulted in the principal component analysis. The main results are: • The cartography of quarters containing schools. • The spatial disparity between the variables having degrees of affinity with the location and topography of adequate school site, sanitation, access to public services, and matching buildings. These variables are opposite to those related to unsanitary, localization and indecent topography of the site as well as non-school access to public services. • A strong interaction between sanitation and access to public services, including running water and electricity, determining the quality of schools.


Introduction
Mbujimayi is a postcolonial city whose size is about 135.2 km 2 .Geographically located in the centre of the DR Congo, in the humid tropical zone (between 6 °5' and 6 °10 ' southward latitude and 23 °27 ' and 23 °40 eastward latitude), it is the capital city of the province of Kasai-Oriental.The city is peopled by about 3 000 000 inhabitants in agglomeration or some 4% of the total population of the DR Congo (Institut National des Statistiques).From age group perspective, in the first half of 2015, the population of Mbujimayi was made up of 58% of youth (0-18 years old) of which 40% were schoolable (5-19 years old).In 2010 there were 303 school infrastructures comprising 693 schools of which 78 kingergartens, 428 primaries and 187 secondaries within the agglomeration ( see figure 1

below).
This study has its place in the domain of " area structuring of the education system in the city of Mbujimayi ".Although specific studies have been conducted on the educational system of the DR Congo including the Eastern Kasai in general, the education system of Mbujimayi, however, has got some characteristics of its own.This article is a contribution to the deepening of knowledge about geographical variation as far as the quality of school offer in the city of Mbujimayi is concerned.It also looks at the typology of quarters that contain schools.Basically, this work revolves around a methodological approach based on the collection and multivariate spatial analysis of data on the quality of school offers.

Problem
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The Descriptive and Explanatory Method
This method is a participatory method in that it allows the shift from theory to practice.It consists in describing the facts as they are for the purpose of achieving the explanation by an inductive approach (Racine and Reymond, 1973).In other words, this method leads to the explanation of the variables under study thanks to many other explanatory variables.It also helps to explain several other independent variables from a numerical variable.

Quantitative Methods
These methods are concerned with the statistical analysis of data in order to compare the existing realities and those found on the field to see whether they match.Statistical analysis of quantified data has facilitated our task in the skimming, providing therefore the explanation in order to verify the empirical observations mathematically ( Kakese et al., 2012).

The Analysis Methods
Factorial analysis of multivariate data mainly covers two sets of techniques: the first set of techniques from the Euclidean geometry lead to the extraction of values and vectors of their own.The second set of techniques, so-called automatic classification are characterized by the choice of an index of proximity and an aggregation or disaggregation algorithm that achieve a score or classification tree as written in Pages et al. (1979).
Of these sets of techniques, the former occupies a special place because they are used either alone or together with the latter, while the latter are rarely applied alone (Escofier and Pages 1988).In this study, we are especially interested in the factorial analysis focusing on main component analysis (much used in English-speaking countries) and correspondence factorial analysis (popular in France), two most used methods.
According to Beguin (1979), factorial analysis is a method that seeks to achieve parsimony in the description while minimizing the loss of information.It constitutes, therefore, a help to the synthesis of data.The main components analysis and correspondence analysis are part of the basic methods of data analysis (Volle, 1978;Chadule Group, 1987;Paegelow,1996;Tenenhaus, 2007).
In essence, the goal of factorial analysis methods is to investigate subsets of small dimensions that best adjust the points of individuals and the clouds of points of variables.
This study draws on methods of factorial analysis of statistical data processed by statistics by using IT tools, capable of processing large masses of data on the characteristics of the investigation area.
Data analysis was mainly intended to present and handle multi-dimensional data of the studied variables.Thus, there may be three situations: absence of affinity, high binding or affinity and homogeneous groups.

Geographic Information System (GIS)
According to Burrough, "The G.I S. is a powerful instrumental equipment for the acquisition, representation, processing and transformation of localized data for the real world " (Paegelow, 1996).The G. I. S. is "a high performance computer system for processing data and geographic information: capturing, storing, updating, deploying and manipulating information, and spatial data for making regional maps" (Rubenstein, 1996, Knox & Marston, 2001).In short, it is storage of geographic information in the form of piled up folders (arranged in layers or sheets).So, they are information and digital data from several different sources on different subjects and at different scales, which can be in relationships and merged to the need for mapping and / or a reflection on area planning.This is possible because the G.S.I. has a great analytical capacity (Haring et al., 1992).Overall, the G.S.I. is a tool for storage, management and exploitation of spatial information; a computer software used in the production of maps from a spatial database.
In this study the following techniques were used: -Library research, indispensible in any scientific work for accessing new knowledge made available by predecessors who have addressed similar topics, -Direct observation consisted in inspecting the field in order to construct facts, events and phenomena to be studied; -Data collection on the field was intended to establish a representative repository to better ground truth using a survey questionnaire; -The direct collection georeferenced information was conducted mainly using a GPS "Garmin 60 CSX map " to capture simultaneously the geographic object and its location.
Overall, the interpretation of the first two axes of the factorial design reveals that they represent 33.41% of information and 1st quadrant quarters associated with variables related thereto (see the analysis of the 1st axis above) are relatively well sanitized quarters containing the renowned schools and also relatively safe.By contrast, quarters of the 3rd quadrant in association with variables relating thereto (see the analysis of the second axis above) are mostly peripheral quarters with substandard schools.
The quarters of the 2nd quadrant , in line with the variable related thereto, (see the analysis of the second axis above) are generally not cleaned quarters of Mbujimayi.They contain essentially secular private schools of the second class.Conversely, quarters of the 4th quadrant variables related thereto (see the analysis of the 1st axis above) are safe quarters containing, clean and fairly well sanitized non-subsidized, Catholic and private-treaty Miba schools

Conclusion
This research on geographical variation in the quality of school offer in the city of Mbujimayi by multivariate spatial analysis helped to detect the quality of the education system of this city by its infrastructure.Indeed, multivariate analysis of survey data helped to understand that the quality of school offer is determined by a strong interaction between school sanitation and access to public services including running water and electricity.Several maximum associations between variables came to light thanks to solid relationships.
The chains of correlations have shown that there is a spatial disparity between variables with links to the location and topography of adequate school site, sanitation, access to public services and matching of school buildings.
Conversely, the variables related to unsanitary, localization and indecent topography of the site and the lack of access to public services have come to the open.
All in all, the study under consideration has allowed us to distinguish two types of quarters in the city of Mbujimayi.On one hand, there are quarters with urban amenities and safe and clean, non-agreed, Catholic agreed, Catholic and private Miba schools on non-erosive sites located along the main thoroughfares.On the other hand, there are peripheral, urban-rural and unsafe quarters containing secular unsafe schools on erosive sites.
It follows from the above that to remedy the precarity of the peripheral quarters and of the schools they contain a balanced, holistic and long lasting sectoral planning of quarters is needed.This includes the programming of investments in road infrastructure equipped with gutters, schools sanitation and their access to public services (running water and electricity.Moreover, maintenance culture should be imparted to managers of public properties, here schools.