Prototypical Cases

Selecting municipalities for the construction of prototypical cases

Jean-Paul Bousset, March 2009

 

Introduction

 

This document reports preliminary thoughts to select municipalities for the construction of prototypical cases in PRIMA project.

 

PRIMA project aims at developing models of municipality dynamics to analyse policy impacts on multifunctional land uses and on the economic activities on a set of municipality case studies. The models will address the structural evolution of the populations (appearance, disappearance and change of agents) depending on the local conditions for applying the structural policies on a set of municipality case studies.

 

The municipality is the level of scale at which the main actors can be identified; they interact at this level; last many measures start at this level. Munipality case studies will be used for building a set of virtual municipality prototypes, which will show contrasted features and dynamics that are relevant at regional level.

 

This paper deals with the ways which can be used for the selection of municipality case studies representing typical, contrasted macroeconomic features and multifunctional aspects of land use in a given region (Section 1Methodology). An application of the suggested methodology in Auvergne region provides WP3 with appropriate data for the construction of a pilot municipality case (Section 2 Mapping the Socio-economic diversity of rural Auvergne). This work refers to Task 1.5 (¹) and Task 3.2 (²) of PRIMA project.

 

1 Methodology for the selection of municipality case studies

 

Today it is widely recognized that regions have different characteristics that shape their potential path of development. This is especially true since the use of EU Structural Funds (García-Solanes and María-Dolores, 2002; Puigcerver 2007; EPSON 2006). Appendix A lists the eligibility criteria for Policy Programmes linked to EU Structural Funds. Structural Funds have been designed on the basis of three main assumptions: (i) gaps exist between EU regions, (ii) EU structural policies are able to reduce those gaps and (iii) regional growth and convergence leads to cohesion. One of the crucial questions is whether and to what extent it is possible to make links between regional features and the impacts of EU structural funds. This in turn has raised a number of questions as:

• Which are the underlying dimensions that characterize the diversity that exists across a given region?

• What is the spatial distribution of these dimensions?

• What is their meaning for the impact assessment of rural development policies?

 

1.1 A review of concepts and empirical research

 

The problem faced in this study is that of classifying a set of observations. Classification is a fundamental concern in any field of research and policy analysis. In order to make sense of complex realities and phenomena, analysts are often required to organize the observations by ‘types’, which are not identical, but rather tend to behave alike. In the context of spatial analysis, this classificatory work is defined as regionalisation (Rogers, 1971). Thus, regionalisation is the process of classifying and grouping small territorial units into larger aggregations that share elements of similarity or commonality.

 

Regional typologies serve as an analytical tool to characterise regions by similarities in a certain combination of criteria. These typologies generalise and condense the individual characteristics of a region, so that the regions can more easily be compared. The aim is to group regions in such a way that those of one type significantly differ from those of another type concerning the same combination of criteria.³ If the selection of criteria is adequate and the similarity within one group is high and finally if there are clear differences between the groups, one can ‑‑ ideally ‑‑ transfer the knowledge gained by looking at one region of one group to other regions of the same group. However, if this knowledge is to be transferable, it must reflect the criteria used to derive the typology. This is possible if the topology is designed to answer certain questions or describe certain problems that can adequately be represented by a certain number of indicators and their combination.

Typologies cannot be “true” or “false”. They are appropriated or not. The appropriateness of a typology itself should be evaluated against the purpose that it is intended to serve. In this regard, two broad alternatives can be identified. Some typologies are intended to address specific policy measures. For instance, it is possible to develop a typology of regions based on unemployment structure. In this case the attention can be restricted to a single or a few indicators. In other cases, the interest is on typologies that have a broad analytical or policy purpose that attempts to embrace a wide range of demographic, social and economic indicators.

Typologies which are directly addressed to policy measures

 

On the one hand, typologies are often used as a spatial corridor to address policy measures to those areas that fulfil certain criteria. This is possible, if the policy objectives can adequately be transferred into criteria and corresponding indicators. For example, measures of the Regional Policy in the European Union are directed to selected regions, which fulfil the criteria defined by the objectives of Policy Programmes (eligible areas). Mostly, this kind of typology does not cover the entire national territory and only consists ‑‑ as in this case ‑‑ of two types of regions: regions which fulfil the criteria and those which do not.

 

Typologies with a predominantly analytical and policy advise purpose

 

Mostly, typologies are designed to discover similarities in regional structures. So far, they firstly aim to gain information for regional diagnosis as a base of policy advice and, in a second step, develop their importance as a relevant tool for policy. Examples are the numerous analytical investigations concerning regional competitiveness at the beginning of the 90s in the European Union. They served policy as an overview on regional competitiveness from an economic point of view, evaluating the regional chances and weaknesses in the European single market. Other examples are typologies of economic structure. The transformation of post‑industrial economic systems to service based economies differs in space and time. Apart from individual regional particularities in economic structure an adequate typology characterises the current stage in the transformation process.

 

When typologies are designed to discover similarities in regional structures, the similarities between regions are set up and measured by empirical analysis. This means that the theoretical issues are put into the selection of the criteria and not into the typology itself. The creation of the typology itself is only based on the empirical analysis and the empirically observed similarities.

When the interest is in a broad range of regional characteristics, there is a major methodological distinction between ways to proceed in defining and analyzing ‘regional types’. On one hand, it is possible to define, a priori and based on theoretical reasoning, a set of criteria that will be used to assign each area to a regional type. For instance, it is possible to define population thresholds or thresholds based on distance from major urban areas. Each municipaloty can be assigned to a certain group based on these criteria and then the researcher can compare the various groups on a range of other indicators (e.g. income, unemployment).

 

Alternatively, it is possible to follow an exploratory type of approach and to use the range of data to construct types of regions. This means that the data set is ‘explored’ in an attempt to recognize any non-random patterns or structure in the existing set of variables, generally without imposing any pre-determined model of relationship between these variables.

 

There is a third major distinction in methodologies that derive regional typologies. The applied research on regionalisation has tended to emphasize two alternative aspects: homogeneity and nodality or functionality (Rogers, 1971). When the emphasis is on homogeneity, the researcher aggregates areas that tend to be uniform with respect to a set of characteristics ‘contained’ within each unit of observation. However, the focus on nodality or functionality implies the aggregation around a relevant pole (generally an urban centre) on the basis of the linkages and functional relationships between areas (for instance, using commuting flows or trade linkages).

 

1.2 An overview of alternative methods

 

Attempts to develop regional or rural typologies have generally relied on multivariate statistical techniques and used population census or census-type data for this purpose (see Blunden et al., 1998). In regional applications, the dominant approach has been either factor analysis or a combination of principal component and cluster analysis (see also Rogers, 1971).

 

Factor analysis is a multivariate statistical technique that helps to answer questions such as, “Can a small number of unobservable factors explain the variability in many observable variables?” The main assumption of this statistical method is that observable outcome indicators can be accounted for by a limited number of underlying factors, which can be used to explain complex phenomena. For instance, conceptual constructs such as economic health or social distress are not directly observable. Nor they can be measured directly. What a researcher can do is to measure a number of outcome indicators, as for instance income level, unemployment rate, number of low-income families, and so on. One then postulates “factors” as latent variables, or underlying dimensions, which are in some way correlated to variables that are directly observable and measurable.

 

The application of factor analysis to the study of spatial diversity became known as factorial ecology and had a rapid expansion (Berry, 1971).Critics of this method indicated as a major weakness the exploratory nature of this research, which resulted in fragile theoretical foundations for the conclusions provided. A weakness that, on the contrary, was seen as a strength by some scholars, because the understanding of a certain situation was “learned” rather than “imposed” by a priori theory (Berry, 1971). There is no doubt that factor analysis, like all the exploratory data techniques, is exposed to a certain degree of subjectivity, particularly in the selection of the variables and the interpretation of the factors. Once the limitations of this method are recognized, it is clear that this technique can still provide a useful characterization of territorial units. Indeed, factor analysis has continued to be widely used in applied regional studies.

 

More recently, principal component analysis (⁴) -- in combination with cluster analysis, was used in France to develop a typology of agricultural areas (SEGESA 1992). Another study in France by Chapuis and Brossard (1989) used factor analysis to identify homogeneous regional types based on demographic structure and dynamics. In these studies, principal component analysis is used as a data reduction method, which allows the extraction of linear combinations of the original variables. In the second phase, cluster analysis is performed using principal component scores to identify grouping of areas with similar profiles in terms of component scores. Using this approach, Shields and Deller (1996) produced a classification of counties in Wisconsin. Quadrado et al. (2001) applied a similar approach, combining also other inequality measures, to classify 20 counties in Hungary. Montresor and Mazzocchi (2001) used this two step approach to classify 100 EU regions from agricultural-related indicators.

 

Recently other data reduction or exploratory methods have found application in regional classificatory exercises.A variant of traditional clustering methods was put forward by Lipshitz and Raveh (1998) in an application to Israel. The method is defined as “co-plot” by the authors and is in essence a graphical display-based technique, where geographic units are grouped on the basis of a measure of dissimilarity between each pair of observations. Blunden et al. (1998) presented a particularly interesting methodology for the classification of rural areas in the European context, which relies on a neural network application. Neural networks belong to a set of exploratory data techniques that have received increasing attention in recent years. In order to generate optimal outcomes the neural network needs to be “trained”, using data from typical examples of typologies. However, in the application presented by Blunden et al. (1998), the network was trained on the basis of the expert knowledge of practitioners who identified examples of five generic rural categories.

 

1.3 The method used for the selection of municipality case studies in Auvergne region

 

Assuming that impacts of EU structural funds depend on the spatial distribution and the dynamics of communities playing as 'growth poles' in regions (Parr 1999), the approach taken in this research aims at classifying and grouping the 115 rural municipalities which play as 'pôles de services intermédiaires' in Auvergne region (⁵) into larger aggregations that share elements of similarity about their dynamics. Such aggregations will define different classes of municipalities representing typical, contrasted macroeconomic features in the Auvergne region. Appendix B lists the rural municipalities playing as 'pôles de services intermédiaires' in Auvergne region.

 

The data set includes a range of commonly used geographic, demographic, social and economic variable. The selection of the indicators among those available was guided by findings from the literature (Chakravorty, 2005, Quentin et al 2004) and criteria defined by the objectives of Policy Programmes (e.g. population density, dependence, rate of unemployment; Appendix A lists the eligibility criteria for Policy Programmes linked to EU Structural Funds)..

 

The method combines cluster analysis, discriminant analysis and factorial analysis, in four stages. First stage consists of performing cluster analysis to identify grouping of municipalities with similar dynamical profiles. Second stage consists of performing discriminant analysis to identify the main factors explaining the differences between clusters, referring to dynamics indicators. Third stage consists of performing factorial analysis to identify colinearities between the factors of dynamics profiles and the current demographic, social, and economic features of municipalities. Fourth stage consists of performing cluster analysis to identify grouping of municipalities with similar demographic, social, economic, functional and dynamical profiles, by using factor scores

 

2 Mapping the socio-economic diversity of rural Auvergne

 

2.1 Identifying municipalities with similar dynamical profiles

 

Dynamics indicators includes: change in total population between 1990 and 1999; natural balance in total population between 1990 and 1999; change in yougness index between 1990 and 1999; and change in unemplyement rate between 1990 and 1999.

 

All the variables considered are rating scales computed from INSEE⁶ data, rather than absolute dimension of indicators (⁷). Hence, the comparison among municipalities focuses on the structural characteristics of the territorial unit and not on the absolute size. Given the enormous diversity among municipalities in term of size, the introduction of absolute values would force the results in a certain direction, which might not reflect the structural characteristics of a locality. Appendix C presents the used rating scales and the complete database. Table 1 presents the average values and standard deviation for the used variable.

 

Table 1 Variables used for the construction of the typology of dynamics

 

Code	Dynamics indicators	Average	Standard Deviation
POPCH2	change in total population between 1990 and 1999	6,122	2,820
NPOBAL	natural balance in total population between 1990 and 1999	5,165	3,179
YINDCH	change in yougness index between 1990 and 1999	5,896	2,261
UEMPCH	change in unemplyement rate between 1990 and 1999	4,043	3,079

 

Data characteristics

 

Change in total population between 1990 and 1999

Municipalities with the most positive change (3 to 20 %) are located arround big towns:

- in Puy de Dome: Billom, Champeix, Ennezat, Les Martres-de-Veyre, Maringues, Pont-du-Château, Saint-Amant-Tallende, Vertaizon; Vic-le-Comte.

- in Haute Loire: Bas-en-Basset, Monistrol-sur-Loire, Sainte-Sigolène, Saint-Didier-en-Velay, Tence, Yssingeaux.; Saint-Julien-Chapteuil, Vorey; Paulhague

- in Allier: Ébreuil, Marcillat-en-Combrailles, Montmarault 

- in Cantal: Laroquebrou.

 

Municipalities with the most negative change (-9 to -20 %) are located in mountaneous areas:

- in Cantal: Condat, Pleaux, Riom es Montagnes, Saint-Martin-Valmeroux, Allanche, Chaudes-Aigues, Murat, Saint-Flour.

- in Puy de Dome: Le Mont-Dore, Pontaumur, Saint-Éloy-les-Mines, Saint-Gervais-d’Auvergne; La Monnerie-le-Montel, Olliergues, Viverols

- in Haute Loire: Allègre, Craponne-sur-Arzon, ou volcanique : Fay-sur-Lignon, Landos, Montfaucon.

- in Allier (plaine areas): Ainay-le-Château Commentry.

 

Municipalities with no siginificant change in population are:

- in Allier : Cérilly, Chantelle, Bellenaves, Cosne-d’Allier, Lurcy-Lévis ; Gannat, Le Mayet-de-Montagne, Saint-Germain des Fossés.

- in Cantal : Saignes, Ydes ; et Haute-Auvergne : Massiac, Pierrefort.

- in Haute Loire : Retournac, Rosières.

- in Puy de Dome : Ambert, Courpière, La Chaise-Dieu, Puy-Guillaume; Aigueperse, Combronde, Le Rouget, Sainte-Florine.

 

Natural balance between 1990 and 1999.:

Positive balances are mostly located in big towns:.

- in Allier, only Moulins shows a positive balance.

- in Cantal, only Aurillac shows a positive balance.

- in Haute-Loire, positive balances are mainly located in Le Puy-en Velay and Yssingeaux.

- in Puy-de-Dôme, even if some rural municipalities show positive balances, the most part of positive balance is located arround Clermont and Issoire.

 

Municipalities with negative balances are located in the West side of the Auvergne region: Val de Sioule in Allier, Cézallier in Cantal, Nordest part of Livradois Forez.

 

Change in yougness index between 1990 and 1999

Only 7 municipalities among 115 municipalities playing as services poles, show positive changes in yougness (proportion of population with – 200 years old) between 1990 and 1999. They are the following: Ébreuil, Fay-sur-Lignon, Les Martes-de-Veyre, Marcillat-en-Combraille, Saint-Amant-Tallande, Vorey, Viverols. An only two municipalities demonstrated a stable value: Chantelle and Pionsat.

 

All other municipalities showed a negative index. Most negative index are located in Dompierre-sur-Besbre, Ennezat, La Monnerie-le-Montel, Mauriac, Pont-du-Château, Riom-ès-Montagnes, Saint-Flour, Saint-Georges-de-Mons, Sainte-Sigolène, Vic-le-Comte, Ydes.

 

Cluster analysis

 

The dendogramme in Appendix D represents how the algorithm works to group the observations, then the sub groups of observations. The dotted line represents the automatic truncation, leading to six groups (cluster number varies from 1 to 6, from the left side to the right side of the figure). Dissimilarities between the six clusters represent 58% of the dissimilarities existing between the 115 municipalities. Appendix D also shows how the 115 municipalities are clustered.

 

Each cluster can be represented by the barycenter of the observations in the class, which is a virtual observation that is meant to be particularly representative of the population of the class. Table 2 shows the value of the dynamics indicators for each barycenter of clusters.

 

Table 2 Typology of Municipalities from Dynamics Indicators: Description of Clusters

 

			Dynamics Indicators
Group	Cluster	Frequency	POPCH2	NPOBAL	YINDCH	UEMPCH
B	Cluster1	22	4,182	3,909	4,909	7,227
	Cluster2	17	4,118	8,471	3,882	5,294
	Cluster3	17	9,059	5,647	8,353	5,824
	Cluster4	14	9,143	9,143	3,429	3,214
A	Cluster5	31	7,097	2,645	7,161	1,645
	Cluster6	14	2,857	4,143	6,571	1,500

 

The dendogramme in Appendix D shows that municipalities can be split in two main groups (A and B). Group A puts together cluster 5 and cluster 6, while Group B puts together the four other clusters. Table 2 shows that municipalities belonging to Group A and municipalities belonging to Group B mainly differ from natural balance in population, change in yougness index and change in unemplyement rate. Cluster 5 and Cluster 6 (Group A) put together municipalities with the lowest natural balance, the lowest change in unemplyement rate and the highest change in yougness rate since 1990.

 

Dendogramme in Appendix D also shows that municipalities belonging to Cluster 1 and municipalities belonging to Cluster 2 have strong similarities, which differentiate them from municipalities belonging to Cluster 3 and Cluster 4. Table 2 shows that municipalities belonging to Cluster 1 and Cluster 2 share low change in yougness index between 1990 and 1999 and low change in total population between 1990 and 1999 -- which is high in municipalities belonging to Cluster 3 and Cluster 4. Municipalities belonging to Cluster 3 and municipalities belonging Cluster 4 mainly differ from change in yougness index between 1990 and 1999 – which is high in Cluster 3 and low in Cluster 4.

 

2.2 Explaining differences between clusters

 

Factors explaining differences between clusters (howmuch clusters differ among them and which are the main explatory factors of differences between clusters) were identified by applying Discrimant Analysis (DA) technology on the data used for cluster analysis – as explanatory variables, with cluster number as dependent variable.

 

Table below shows that, as the computed p-value is lower than the signifiance level alpha, one should reject the null hypothesis (the within class covariance matrices are equal). This means that clusters are significantly different.

 

Test de la statistique de Box (approximation asymptotique du F de Fisher)
F (valeur observée)	2,087
F (valeur critique)	1,352
DF 1	50
DF 2	8843
p-value unilatérale	< 0,0001
Alpha	0,05

The next table shows that 80% of the variance – i.e. the dissimilarities among cluster -- is represented with the two first factors.

	F1	F2	F3	F4
Eigen value	2,995	2,001	0,912	0,257
% variance	48,573	32,458	14,796	4,173
% total	48,573	81,031	95,827	100,000

 

Table below shows how the initial variables are correlated with the factors. We can see that the factor F1 is strongly negatively correlated with natural balance in total population between 1990 and 1999 and highly positively correlated to change in yougness index between 1990 and 1999. F2 is strongly correlated with change in total population between 1990 and 1999. F3 is strongly correlated with change in unemplyement rate between 1990 and 1999.

 

DA demonstrates the dissimilarities among clusters mainly come from variations in natural balance in total population and change in yougness index, secondly from variations in changes in total population, and only very few from variation in changes in unemployement rate. In addition, Table below indicates that -- as expected, changes in unemployment rate and changes in total population are not significantly correlated together, neither to natural balance in total population, nor to change in the yougness index. However, natural balance in total population is negatively correlated to change in the yougness index between 1990 and 1999.

 

Variable	F1	F2	F3	F4
POPCH2	0,407	0,896	0,056	-0,170
NPOBAL	-0,636	0,534	-0,225	0,509
YINDCH	0,794	-0,073	0,290	0,530
UEMPCH	-0,472	0,066	0,879	0,023

The next table displays the discriminant functions. When we assume the equality of the covariance matrices, the discriminant functions are linear. When the equality is not assumed, which is the case in this study, the discriminant functions are quadratic. The rule based on these functions is that we allocate an observation to the group corresponding to the function that gives the greatest value.

Variable	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5	Cluster 6
Constant value	-16,033	-17,648	-36,616	-28,195	-22,079	-14,218
POPCH2	1,509	1,405	3,263	3,204	2,576	1,016
NPOBAL	0,700	1,740	0,899	1,817	0,271	0,686
YINDCH	1,854	1,317	3,419	1,193	3,111	2,780
UEMPCH	1,468	1,103	1,067	0,679	0,159	0,141

These functions can be used in predictive mode on new observations to allocate them to a group. The confusion matrix of the cross-validation is displayed below.

	vers 1	vers 2	vers 3	vers 4	vers 5	vers 6	Somme
de 1	20	1	0	0	0	1	22
	17,39%	0,87%	0,00%	0,00%	0,00%	0,87%	19,13%
de 2	1	15	1	0	0	0	17
	0,87%	13,04%	0,87%	0,00%	0,00%	0,00%	14,78%
de 3	1	0	16	0	0	0	17
	0,87%	0,00%	13,91%	0,00%	0,00%	0,00%	14,78%
de 4	0	0	0	14	0	0	14
	0,00%	0,00%	0,00%	12,17%	0,00%	0,00%	12,17%
de 5	1	0	1	1	26	2	31
	0,87%	0,00%	0,87%	0,87%	22,61%	1,74%	26,96%
de 6	0	0	0	0	1	13	14
	0,00%	0,00%	0,00%	0,00%	0,87%	11,30%	12,17%
Somme	23	16	18	15	27	16	115
	20,00%	13,91%	15,65%	13,04%	23,48%	13,91%	100,00%

Taux d'erreur apparent (taux de resubstitution sur les données d'apprentissage) : 9,57 %

 

 

2.3 Exploring colinearities between dynamics profiles and current features of municipalities

 

Third stage of the methodology consists of performing principal factor analysis to identify colinearities between the variables used to define the dynamics profiles (ref. 2.1, Table 1) and the current features of municipalities.

 

Capacity of municipalities for econoomic and social development depends fundamentally on resources available: natural resources; human resources; social resources and economic resources – including infrastructures. So, variables used for the description of the current features of municipalities include: environmental, demographic and socio-economic indicators. Environmental indicators include altitude and biodiversity. Demographic indicators include population density and youngness rate. Socio-economic indicators include: unemployment rate, access time to municipalities, distances between municipalities, number of secondary houses, and number of marketed beds for tourism.

 

Like for variables used for the cluster analysis, all the variables considered are rating scales rather than absolute dimension of indicators. Biodiversity index was derived from the presence or not of ZNIEFF and/or Natura 2000 areas on municipality area. Social and economic indicators come from the "INSEE Local Statistics" (2000). Appendix E presents the used rating scales and the complete database used to explore colinearities between dynamics profiles and current features of municipalities. Table 1 presents the average values and standard deviation for the variables used for the description of the current features of municipalities.

 

Table 3 Variables used for the description of the currents situation of municipalities

 

Code	Dynamics indicators	Average	Standard Deviation
ALTITU	Altitude	6,922	2,520
BIODIV	Biodiversity	3,200	1,917
PODENS	Population density	4,991	3,158
YOUNG	Youngness rate (population < 20 years old%total poulation)	5,635	2,496
UNEMP	Unemployment rate	3,600	2,913
ACCESS	Access time to municipalities	8,357	1,948
DIST	Distances to other municipalities	6,104	3,500
SEHOUS	Number of secondary houses	5,530	3,402
MARKB	Number of marketed beds	2,852	2,996

 

Data characteristics

 

Altitude

With 1,180 m altitude, Fay-sur-Lignon is the higher municipality, while Vallon-en-Sully is the lower one, with 190 m altitude. 53 municipalities (46%) have more than 600 m altitude, and 15 municipalities among have about or more than 1,000 m altitude (Besse-Saint-Anastaise, Le Mont-Dore, La Tour d’Auvergne, Saint-Germain-l’Herm, La Chaise-Dieu, Allègre, Landos, Fay-sur-Lignon, Montfaucon-en-Velay, Saint-Anthème, Saugues, Le Monastier-sur-Gazeille, Allanche and Pierrefort).

 

Biodiversity

Protected areas (Natura 2000, ZNIEF..) mainly are locted in mountaneous areas and hydrographic corridors. However, they can be found also in dry hilly areas (Coteaux de Limagne) and forestry in plain areas (Tronçais, Colettes). Finally, 15% of municipalities are located on/in protected areas. Only 15% of municipalities is far from proted site.

 

Population Density

Munipality area varies from 2 km² for Le Montet in Allier to 92 km² for Pleaux in Cantal. Referring to Population Census 1999, population density veries from 12 p/km2 to 487 p./ km², respectively in Saint-Anthème and Brioude.

 

Municipalities can be grouped in 3 different classes:

1 – Municipalities located in very structured rural areas (50 to 30 p./ km²): Ambert, Brioude, Saint-Eloy-les-Mines, Saint-Pourçain-sur-Sioule, Varennes-sur-Allier, Yssingeaux; Champeix, Maringues, Puy-Guillaume, Randan; Bas-en-Basset, Combronde, Courpière, Dunières, Montfaucon-en-Velay, Saint-Germain-Lembron, Saint-Rémy-sur-Durolle, Saint-Julien-Chapteuil; La Bourboule et Le Mont-Dore, Saignes et Ydes, Retournac et Vorey.

2 – Municipalities located in semi-structured areas (30 to 17 p./ km²): Bort-les-Orgues, Cosne-d’Allier, Lapalisse, Langeac, Mauriac, Murat, Saint-Flour; Arlanc, Bourg-Lastic, Craponne-sur-Arzon, Maurs, Montsalvy, Paulhaguet, Pleaux, Rochefort-Montagne Saint-Matin-Valmeroux, Tauves; Vic-sur-Cère, Le Rouget, Saint-Cernin, Le Monastier-sur-Gazeille, Saint-Paulien, Jaligny-sur-Besbre, Dompierre-sur-Besbre, Lurcy-Lévis, Huriel, Manzat, Pontgibaud; Bellenaves, Chantelle, Cunlhat, Ebreuil, Montmarault, Olliergues, Paulhaguet, Saint-Gervais-d’Auvergne, Saint-Martin-Valmeroux.

3 – Municipalities located in sparse areas (17 to 5 hab./ km²), most often in high altitude: Allanche, Allègre, Ardes, Besse-et-Saint-Anastaise, Blesle, Chaudes-Aigues, Condat, La Chaise-Dieu, Landos, La Tour d’Auvergne, Le Mayet-de-Montagne, Massiac, Pierrefort, Riom-ès-Montagnes, Saint-Anthème, Saint-Germain-l'Herm, Saugues, Viverols; or far from Clermont-Ferrand as Cérilly, Giat, Laroquebrou, Le Donjon, Marcillat-en-Combraille, Pionsat, Pontaumur.

 

Yougness Rate

Proportion of young people in population is especially low in the following municipalities: Ainay-le-Château, Cérilly, Cosne-d’Allier, Bellenaves dans l’Allier, Bort-les-Orgues, Condat, Pleaux, Laroquebrou, Maurs, Montsalvy, Pierrefort, Saint-Martin-Valmeroux dans le Cantal, Allègre, Retournas et Saugues en Haute-Loire, Bourg-Lastic, Giat, La Tour d’Auvergne, Pionsat, Saint-Anthème, Saint-Germain-l’Herm, Tauves, Viverols, disposent de la plus faible proportion de jeunes.

In other hand, youngness rate is especially high in Villefranche-d’Allier dans l’Allier, Monistrol-sur-Loire, Saint-Didier-en-Velay, Sainte-Sigolène, en Haute-Loire, Champeix, Ennezat, Les Martes-de-Veyre, Pont-du-Château, Vertaizon, Vic-le-Comte.

 

Access time to municipalities

Referring to isochrone curves computed from ChronoMap of MapInfo software, only a few number of municipality areas have points needing more than 15 to access the munipality. They are mainly located in montaneaous areas (Margeride, Aubrac, Monts du Cantal, Cézallier, Montagne Bourbonnaise, Forez, Haut-Livradois, Mézenc).

 

Distance to other municipalities

Distance between a given municipality and its closest neighbour varies from 8.4 km for Lempdes to 43 km for Pierrefort. Average distance is 18,3 km. Distances are greather in montaneous areas than in plain. (e.g: Allanche (26), Chaudes-Aigues (29), Le Mayet-de-Montagne (26,9), Montsalvy (28,6), Murat (28), Pierrefort (29,8), Saint-Cernin (26,1), Saint-Flour (28,2), Saint-Germain-L’Herm (25,4), Saugues (27,1), Vic-sur-Cère (27,8). Municipalities whith low distance to neighbours are Sainte-Sigolène (10,9), Saint-Rémy-sur-Durolle (12), La Bourboule (11,4) and Lempdes (8,4).

 

Market beds for tourism

Referring to INSEE data on tourism, municipalities can be grouped in 4 different classes :

1- Municipalities with more than 2,000 market beds (19 municipalities): La Bourboule 13 370 lits, Besse-et-Saint-Anastaise 12 760, Saint-Flour 6 860, Tence 6 430, Vic-sur-Cère 5 280, Le Mont-Dore 5 160, Murat, 4 730, Mauriac 4 580, Riom-ès-Montagnes 3 850, Murol 3 510, Langeac 3 010, La Tour d’Auvergne 2 770, Champeix 27 20, Ambert 2 640, Chaudes-Aigues 2 580, Brioude 2 510, Pleaux 2 410, Le Mayet-de-Montagne 2 110, Yssingeaux 2 000.

2- Municipalities with 1,000 to 2,000 market beds (22 municipalities) : Ainay-le-Château, Bas-en-Basset, Bourbon-l’Archambault, Condat, Craponne-sur-Arzon, La Chaise-Dieu, Lapalisse, Laroquebrou, Le Monastier-sur-Gazeille, Massiac, Maurs, Monistrol-sur-loire, Pontaumur, Pontgibaud, Rochefort-Montagne, Saint-Éloy-les-Mines, Saint-Gervais-d’Auvergne, Saint-Pourçain-sur-Sioule, Saint-Rémy-sur-Durolle, Saugues, Vorey.

3- Municipalities with 500 to 1 000 market beds (33 municipalities): Allanche, Allègre, Arlanc, Cérilly, Cosne-d’Allier, Courpière, Cunlhat, Dompierre-sur-Besbre, Ébreuil, Gannat, Giat, Le Rouget, Lurcy-Lévis, Manzat, Montmarault, Montsalvy, Olliergues, Paulhaguet, Pierrefort, Pont-du-Château, Puy-Guillaume, Retournac, Saint-Anthème, Saint-Georges de Mons, Saint-Germain-Lembron, Saint-Germain-l’Herm, Saint-Julien-Chapteuil, Saint-Martin-Valmeroux, Saint-Paulien, Sainte-Sigolène, Varennes-sur-Allier, Vic-le-Comte, Ydes.

4- Municipalities with less than 500 market beds (41 municipalities): Ardes, Billom, Blesle, Brassac-les-Mines, Lezoux, Randan, … .

 

Factor analysis

Factor analysis was ran to identify colinearities batween the above variables and to determine the fewer underlying factors of variations among the current situations of municipalities. We have applied it here to generate seven factors, and we have done a varimax rotation to facilitate the interpretation of the results.

Colinearities

Cronbach's alpha equal to 0.522 means that there are only a few numbers of redundancies among the selected variables. Table 4 below presents the correlation matrix.

 

 

Table 4 Correlations matrix

 

 

	ALTITU	BIODIV	ACCESS	POPCH2	PODENS	NPOBAL	YOUNG	YINCH	UNEMP	UEMPCH	SEHOUS	MARKB	DIST
ALTITU	1	-0,186	0,227	0,328	0,283	-0,104	0,037	0,054	-0,417	0,038	0,095	-0,367	0,230
BIODIV	-0,186	1	-0,170	-0,124	-0,133	0,005	-0,076	0,085	-0,054	0,222	-0,132	0,325	-0,141
ACCESS	0,227	-0,170	1	0,374	0,508	0,158	0,299	0,175	-0,226	0,043	0,080	-0,359	0,464
POPCH2	0,328	-0,124	0,374	1	0,414	0,121	0,408	0,184	-0,194	-0,088	0,330	-0,186	0,411
PODENS	0,283	-0,133	0,508	0,414	1	0,469	0,624	-0,074	-0,309	0,109	0,335	-0,240	0,618
NPOBAL	-0,104	0,005	0,158	0,121	0,469	1	0,736	-0,339	0,003	0,149	0,177	0,112	0,341
YOUNG	0,037	-0,076	0,299	0,408	0,624	0,736	1	-0,137	-0,077	-0,012	0,283	-0,075	0,428
YINCH	0,054	0,085	0,175	0,184	-0,074	-0,339	-0,137	1	-0,046	-0,113	0,094	-0,172	0,154
UNEMP	-0,417	-0,054	-0,226	-0,194	-0,309	0,003	-0,077	-0,046	1	0,245	-0,108	0,085	-0,137
UEMPCH	0,038	0,222	0,043	-0,088	0,109	0,149	-0,012	-0,113	0,245	1	-0,228	0,057	0,116
SEHOUS	0,095	-0,132	0,080	0,330	0,335	0,177	0,283	0,094	-0,108	-0,228	1	0,138	0,217
MARKB	-0,367	0,325	-0,359	-0,186	-0,240	0,112	-0,075	-0,172	0,085	0,057	0,138	1	-0,317
DIST	0,230	-0,141	0,464	0,411	0,618	0,341	0,428	0,154	-0,137	0,116	0,217	-0,317	1

 

En gras, valeurs significatives (hors diagonale) au seuil alpha=0,050 (test bilatéral

 

Colinearities among indicators of current situation:

Altitude is positively correlated to distance between municipalities, population density and changes in population between 1990 and 1999. It is negatively correlated to unemployement and market beds. In other hand, biodiversity is positively correlated to market beds. Access to municipalities also is positively correlated to population density and distance between municipalities. In addition, population density is positively correlated to youngness rate and distance between municipalities, and it is negatively correlated to unemployement. There are no correlation between second houses and market beds

 

Colinearities between Dynamics indicators and Indicators of current situations

Change in total population is mainly correlated to altitude, access time, and population density. Natural balance between 1990 and 1999 is positively correlated to youngness and population density

 

Factors

Table below demonstrates that 4 factors capture 81 % of the variability of the initial data.

 

	F1	F2	F3	F4	F5	F6	F7
Eigen value	3,323	1,715	1,042	0,828	0,736	0,501	0,312
% total variability	25,559	13,189	8,014	6,367	5,665	3,856	2,396
% sum	25,559	38,748	46,762	53,129	58,794	62,650	65,046
% common variability	39,293	20,276	12,321	9,789	8,708	5,928	3,684
% sum	39,293	59,569	71,890	81,679	90,387	96,316	100,000

 

Next table shows that the varimax rotation has changed the way each factor explains part of the variance. The varimax rotation makes the interpretation easier by maximizing the variance of the squared factors loadings by column. For a given factor, high loadings become higher, low loadings become lower, and intermediate loadings become either lower or higher.

 

% de variance totale après rotation Varimax :
	F1	F2	F3	F4	F5	F6	F7
% variance totale	25,212	18,579	11,412	11,901	11,161	11,054	10,681
% cumulé	25,212	43,791	55,203	67,104	78,266	89,319	100,000

 

The next results are the factor loadings after the varimax rotation. These results are used to interpret the meaning of the (rotated) factors.

 

Table 5 Factor Scores

 

	F1	F2	F3	F4	F5	F6	F7
ALTITU	0,207	-0,056	-0,187	-0,825	-0,131	0,031	0,011
BIODIV	-0,134	0,018	-0,060	0,099	0,648	-0,088	0,104
ACCESS	0,628	0,110	-0,099	-0,099	-0,128	-0,039	0,149
POPCH2	0,367	0,257	-0,076	-0,271	-0,095	0,280	0,254
PODENS	0,749	0,333	-0,136	-0,143	-0,018	0,219	-0,177
NPOBAL	0,288	0,650	0,050	0,138	0,108	0,105	-0,397
YOUNG	0,335	0,925	-0,023	-0,016	-0,038	0,145	-0,064
YINCH	0,146	-0,167	-0,018	-0,006	0,052	0,059	0,711
UNEMP	-0,212	0,021	0,797	0,279	-0,108	-0,038	0,023
UEMPCH	0,250	-0,060	0,497	-0,175	0,481	-0,224	-0,231
SEHOUS	0,133	0,137	-0,069	-0,032	-0,079	0,773	0,056
MARKB	-0,393	0,030	-0,002	0,268	0,461	0,316	-0,201
DIST	0,696	0,224	0,039	-0,108	-0,059	0,115	0,096

 

From this table we can see that the first factor is highly positively related to population density, distance between municipalities and access time to municipalities. The second factor is loaded on yougness and natural balance between 1990 and 1999. The third factor is heavily loaded on unemplyement and change in unemplyement. The fourth factor is positively loaded on altitude. The biodiversity appears to be significant only on the fifth factor, second houses on the sixth factors and change in yougness rate on the eighth factors.

From these results, we can understand that the municipalities that have high scores on the first factor are municipalities located in sparse spaces. Municipalities with high coordinates on the second factors are municipalities with high human potential, while the municipalities that have high scores on the third factor are municipalities with low human potential, ect.

2.4 Combining dynamical profiles and current dimensions

 

Each dimension (or factor) that resulted from the factor analysis allows us to classify the municipalities belonging to each dynamics cluster according to the size of the factor scores after the varimax rotation for the given municipality. This section presents an example of how the results generated by the factor analysis can be further used to create regional types of municipalites that combine the values of more than one dimension (or factor).

 

The dendogramme in Appendix G represents how the algorithm works to group the observations, then the sub groups of observations. The dotted line represents the automatic truncation, leading to 13 groups (cluster number varies from 1 to 13, from the left side to the right side of the figure). Dissimilarities between the 13 clusters represent 60% of the dissimilarities existing between the 115 municipalities. Appendix F shows how the 115 municipalities are clustered. Appendix G presents the value of dynamics indicators and situation indicators for the barycenter of each cluster (virtual observation that is meant to be particularly representative of the population of the class).

 

Final cluster analysis includes three steps: identification of corresponces between Dynamics Profiles and Compound Clusters; description of Compound Clusters; selecting appropriate data for the construction of pilot municipality cases.

 

Correspondences between Dynamics Profiles and Compound Clusters

 

The table below presents the correspondences between the final typology – which refers both to dynamics and situation indicators, and the dynamics typology. Khi² independence test demonstrates that depndences between the two typologies are significative.

 

Correspondences between compound typology and dynamics typology

 

Compound Classes					Dynamics Classes
					Class Number	1	2	3	4	5	6	Total
Group	Sub-group 1	Sub –group 2	Sub-group 3	Class Number	Variability	34,46	28,28	24,11	13,48	56,97	32,52
A		A1		1	13,74	0	0	2	4	1	0	7
				2	21,33	0	6	1	1	0	0	8
		A2		3	10,37	0	2	3 **	0	1	0	6
				4	34,01	1	0	9	4	2	0	16
B	B1			5	18,98	4 *	0	1	0	5	0	10
				6	11,10	0	0	0	0	4	2	6
				7	28,90	1	0	1	0	8	3	13
	B2	B21		8	31,76	1	2	0	3	3	2	11
				9	27,01	3	5	0	2	2	0	12
		B22	B221	10	7,24	6	0	0	0	0	0	6
				11	12,56	1	2	0	0	0	1	4
			B222	12	11,05	2	0	0	0	2	4	8
				13	13,73	3	0	0	0	3	2	8
					Total	22	17	17	14	31	14	115

 

* e.g. Pontaumur

** e.g. Sainte-Florine

 

This dendogramme shows that -- referring to both dynamics and situation indicators, municipalities can be split in two main groups (A and B). Group A puts together clusters 1 to 5, while Group B puts together the other clusters. The above table shows that most of the municipalities belonging to Dynamics Cluster 5 and 6 – which share as common feature to have experienced low natural balances in total population and low changes in unemplyement rate but high changes in yougness index since 1990, belong to Group B. This means that Group A mainly includes municipalities in which natural balances and changes in unemployment rate were medium or high while changes in yougness index were low.

 

Dendogramme shows that Group A includes 4 differents types of municipalities (Compound Clusters 1 to 4). The above table indicates these compounds clusters have simple links with dynamics clusters, i.e. most of the municipalities belonging to each of these compound clusters belong to an only one specific dynamics cluster:

- Compoud Cluster1 mainly includes municipalities belonging to Dynamics Cluster4 -- in which change in total population were very high, while Compound Cluster2 mainly includes municipalities belonging to Dynamics Cluster2 in which change in total population was low. Although both Compound Cluster1 and Compound Cluster2 have experienced a very high change in natural balance.

- Compoud Cluster3 and more especially Compound Cluster4 mainly include municipalities belonging to Dynamics Cluster3 which have experienced a very high change in yougness index and total population since 1990. These two clusters mainly differ from situation indicators, not from dynamics indicators.

 

Next, the dendogramme shows that Group B includes 9 different types of municipalities (Compound Clusters 5 to 13). The above table indicates that only three of these compounds clusters have simple links with dynamics clusters, i.e. most of the municipalities belonging to these 3 compound clusters belong to a specific dynamics cluster.

- Compoud Cluster6 and Compound Cluster7 mainly include municipalities belonging to Dynamics Cluster 5, which have experienced a low natural balance in total population and a low change in unemplyement rate, but a high change in yougness index and change in total population since 1990. Like Compoud Cluster3 and Compound Cluster4 in Group A, these two clusters mainly differ from situation indicators, not from dynamics indicators.

- Compound Cluster10 mainly include municipalities belonging to Dynamics Cluster 1, which have experienced a low natural balance in total population and a low change in unemplyement rate, but a high change in yougness index and change in total population since 1990

 

Other Group B compound clusters have complex links with dynamics clusters, i.e. municipalities belonging to each of these compound clusters belong to many dynamics clusters.

 

Description of Compound Clusters

 

Table below presents the value of indicators for each barycenter of clusters.

 

Typology of Municipalities from Dynamics and Situation Indicators: Description of Clusters

 

				Dynamics indic.				Situation indicators									Complementary ind
Cluster Group			CompoundClasses	POPCH2	NPOBAL	YINDCH	UEMPCH	Altitude	Biodiversity	Acces time	Pop. Density	yougness	Unemplyement	Scond houses	Market beds	Distance rating	Nombre exploitants total exclusifs, principals ou secondaires de tout âge en 2005	Nombre exploitants total exclusifs, principals de tout âge en 2005	Nombre exploitants secondaires de tout âges en 2005	Nombre exploitants avec salariés en 2005
A			1	9,7	8,9	5,4	2,6	5,1	1,1	9,6	8,6	8,9	6,0	12,3	3,7	9,3	185	160	17	24
			2	5,5	8,5	4,3	6,0	6,8	1,3	9,6	7,8	7,8	6,0	2,0	0,3	9,6	215	191	17	53
			3	6,7	6,0	6,0	7,0	9,0	3,7	10,0	9,7	6,0	0,0	5,0	0,7	10,0	206	176	17	42
			4	9,1	6,0	7,1	4,9	8,8	4,1	9,4	8,4	8,1	2,3	7,8	1,3	9,4	174	153	13	49
B	B1		5	5,2	1,6	6,2	5,4	9,0	2,2	7,8	2,6	2,4	6,0	4,8	2,2	4,5	315	286	17	55
			6	6,3	1,7	7,0	0,0	9,0	1,7	10,0	6,7	3,0	0,0	7,7	0,3	8,3	188	165	13	43
			7	6,3	2,9	7,4	1,8	7,7	3,2	8,5	2,3	4,8	1,4	3,4	1,4	4,6	235	213	13	40
	B2	B21	8	5,3	6,5	4,7	2,5	6,2	4,4	6,5	3,3	6,9	2,7	5,8	6,5	2,7	347	315	18	48
			9	5,5	6,5	3,5	3,8	7,8	2,0	7,7	5,0	5,7	2,5	6,0	3,3	4,2	256	227	17	45
		B22	10	4,0	4,0	4,7	8,5	6,0	5,0	6,0	2,7	2,7	5,0	3,3	6,0	1,7	314	289	12	46
			11	4,0	8,0	6,5	6,8	2,5	6,0	7,5	4,5	6,5	5,3	7,0	10,0	7,5	283	254	17	58
			12	3,8	4,3	6,3	1,1	3,3	3,5	7,8	2,3	3,8	3,8	4,3	3,5	4,4	184	159	13	19
			13	5,0	3,5	7,3	5,3	4,3	4,3	8,3	2,0	4,8	8,6	3,0	2,3	5,0	291	262	18	47

 

Selecting appropriate data for the construction of pilot municipality cases

 

In PRIMA project, selecting appropriate data for the construction of pilot municipality cases consists of finding municipalities which will be used as spatial corridors to address a given Policy Programmes, i.e. municipalities which fulfil certain criteria (eligible areas).

 

For example, selecting clusters for the construction of pilot municipality cases to address Objective 2 – ex 5b Policy Prgrammes, implies selecting municipalities which either have a low population density or have an above average rate of unemployment (ref. Appendix A). Such a selection can be achieved in many different ways.

 

First way consists of sorting municipalities from eligibility criteria, i.e. from population density and unemployment rate. In doing so, in Auvergne region, one might select the following 15 municipalities:

TOUR-D'AUVERGNE; CHAUDES-AIGUES; ALLANCHE; ARDES; ROCHEFORT-MONTAGNE; BESSE-ET-SAINT-ANASTAISE; PIERREFORT; MONASTIER-SUR-GAZEILLE; BOURG-LASTIC; PAULHAGUET; GIAT; GELLES; VIVEROLS; FAY-SUR-LIGNON; PONTAUMUR

 

Second way consists of sorting municipalities from links between eligibility criteria and other criteria, i.e. from factors scores including population density and unemployment rate. Appendix E presents the used data in Auvergne region. Appendix D present factor scores computed from the used data. Table 5 presents correlation between factors and variables. This table shows that population density and unemployment rate respectively are mainly positively correlated to F1 and F3. So, sorting municpalities from their coordinates on these two factors, one might select the following 15 municipalities: CHAUDES-AIGUES; MAYET-DE-MONTAGNE; MASSIAC; ALLANCHE; SAUGUES; PIERREFORT; PONTAUMUR; BESSE-ET-SAINT-ANASTAISE; BOURBON-L'ARCHAMBAULT; SAINT-FLOUR; RIOM-ES-MONTAGNES; CONDAT; PONTGIBAUD; MURAT; TOUR-D'AUVERGNE

 

Third way consists of sorting compound clusters from factors scores including eligibility criteria, i.e. highly correlated with population density and unemployment rate. Appendix H presents coordinates of barycenters on factors. In doing so, in Auvergne region, one might select rather the following municipalities, which play as cluster barycenters: MASSIAC (Compound Cluster8) and TOUR-D'AUVERGNE (Compound Cluster11).

 

The data sets describing these municipalities can be found in Appendix C (dynamics) and Appendix E (current situation).

 

Conclusion

 

Apart from the aspect that typologies generalise individual regional characteristics to a comparable level of information, one important use of regional typologies is the monitoring of development trends. As it is often not possible and not helpful to look at the dynamics of development separately for each unit, a typology serves as a general comparative classification to gain insight into the development patterns. The observation of development trends is useful in two ways: it enables, on the one hand, to evaluate the regional effects of previous political strategies and instruments and, on the other hand, to observe the development of regional disparities between the different types of regions and within the same type.

A typology, which can serve as a general typology, should ‑‑ ideally ‑‑ show correlation between the selected indicators and other indicators that were not used for the classification, but characterise regional development in a very complex way. .

It should be stressed that the results are largely determined by the variables included in the procedure. This is obvious in the sense that whether or not an indicator of a certain social or economic sphere of concern is included will determine the possibility to have this dimension in the results that are generated.

 

 

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