Using ClustOfVar to Construct Quality of Life Indicators for Vulnerability Assessment Municipality Trajectories in Southwest France from 1999 to 2009

Abstract

Climate change is increasingly accepted as a major worldwide issue, bringing with it a host of long-term consequences for both human beings and ecosystems. To more effectively limit the damage caused by natural hazards and global change, it is essential that we gain a greater understanding of the complex question of social vulnerability—a subject that has been widely discussed in the literature. This paper examines the use of a conceptual “human wellbeing” framework to analyse vulnerability. It also proposes an innovative statistical method (ClustOfVar) to capture the multidimensional nature of that vulnerability. Using our approach, it is possible to construct composite indicators of residents’ living conditions at municipality level. To test our methodology, we carried out a comprehensive evaluation of the development of residents’ quality of life for two specific years (1999 and 2009) in areas close to the Garonne and Gironde rivers in southwest France. The results reveal different municipality trajectories in terms of quality of life profiles. This study helps to understand the multivariate characteristics of communities with higher social vulnerability.

Appendices

Appendix 1: The Definition of Variables for Year 1999

Life domain	Variable	Description	Mean
Housing conditions	SingleFamilyRes	$\ge\! 90\,\%$ of single-family primary residences$^\diamond$	0.64
	Owner	Prop. of dwellings occupied by owner	74.5
	SocialHousing	$\ge\! 5\,\%$ of social housing primary residences$^\diamond$	0.11
	NbRoomsDwell	Number of rooms per dwelling	4.4
	Dwellings15_48	Prop. of dwellings built between 1915 and 1948	7.8
	Dwellings49_74	Prop. of dwellings built between 1949 and 1974	13.8
	Dwellings75_89	Prop. of dwellings built between 1975 and 1989	21.2
	DwellingsAfter90	Prop. of dwellings built after 1990	10.8
Labour market and working conditions	WorkDepartment	Prop. of working-age people employed within the department	56.9
	WorkMunicip	Prop. of working-age people employed in their municipality of residence	32.4
	EmployZone	Prop. of working-age people employed in the employment zone	48.8
	EmployUrbanCenter	Prop. of working-age people employed in the urban center	5.1
	WorkingAgeEmploy	Prop. of working-age people in employment	88.1
	15_24Employ	Level of employment of people aged 15–24	22.9
	25_54Employ	Level of employment of people aged 25–54	78.1
	55_64Employ	Level of employment of people aged 55–64	33.6
Standard of living—economic inequality	Income	Average net taxable income of households	8489894.9
	Farmers	Prop. of farmers	7.1
	TradeSelfEmploy	Prop. of tradesmen, other self-employed people, business owners	4.3
	HighlyQualified	Prop. of managers and other highly-qualified jobs	3.6
	IntermediateProf	Prop. of workers and other employees	9.4
	MiddleLevelWorkers	Prop. of middle-level workers	27.5
	NoDiploma	Prop. of people having no diploma	21.5
Social interaction and lifestyles	PopDensity	Population density	80.0
	CpleNoChild	Prop. of households composed chiefly of couples with no children	31.9
	CpleWithChild	Prop. of households composed chiefly of couples with children	36.0
	SingleParent	Prop. of single-parent households	6.8
	SingleWoman	Prop. of households made up of a single woman	11.9
	SingleMan	Prop. of households made up of a single man	11.0
	Retirees	Prop. of retirees	28.3
	NotActive	Prop. of people not in active employment	20.0
Natural environmental conditions	DvpedSurfaceArea	Prop. of developed surface area	3.7
	AgriLand	Prop. of agricultural land	70.5
	ForestVegetation	Prop. of land with forest of other vegetation	24.7
	WaterBodies	Prop. of water bodies	1.0
	DistceRiverEstuary	Distance from river/estuary in kilometers	23.9
Accessibility and quality of services	Banks	Presence of banks$^\diamond$	0.12
	Butchers	Presence of butchers and delicatessens$^\diamond$	0.22
	Bakeries	Presence of bakeries$^\diamond$	0.33
	PostOffices	Presence of post offices$^\diamond$	0.30
	Supermarkets	Presence of supermarkets$^\diamond$	0.09
	Veterinary	Presence of veterinary surgeries$^\diamond$	0.08
	Restaurants	Presence of restaurants$^\diamond$	0.41
	Petrol	Presence of petrol station$^\diamond$	0.23
	Tobacco	Presence of tobacco shops$^\diamond$	0.42
	BarCoffee	Presence of bars and coffees$^\diamond$	0.49
Educational facilities	Schools	Presence of schools$^\diamond$	0.08
	ColNurseries	Presence of collective nurseries$^\diamond$	0.05
	FamNurseries	Presence of familial nurseries$^\diamond$	0.09
	PrimarySchools	Presence of primary schools$^\diamond$	0.38
	PreSchools	Presence of pre-schools$^\diamond$	0.47
	AfterSchoolCenters	Presence of after-school centers$^\diamond$	0.46
	DayCares	Presence of daycare centers$^\diamond$	0.10
Health conditions	GPs	Presence of GPs and specialist doctors$^\diamond$	0.25
	Pharmacies	Availability of pharmacies$^\diamond$	0.20

1. The symbol $^\diamond$ indicates that the variable is categorical. The variables of the two last life domains may have two or more categories. But for simplicity reasons, we only give the mean value for the presence of the service, which could be one or more on the municipality

Appendix 2: Statistical Details on ClustOfVar

1.1 Ascendant Hierarchical Clustering

Let $\mathbf{X}$ and $\mathbf{Y}$ be the corresponding numeric and categorical data matrices of dimensions $n \times p_1$ and $n \times p_2$, where n is the number of observation units. For the sake of simplicity, we denote $\mathbf{x}_j \in \mathcal{R}^n$ the j-th column of $\mathbf{X}$ and $\mathbf{y}_j \in \mathcal{M}_j^n$ the j-th column of $\mathbf{Y}$ with $\mathcal{M}_j$ the set of categories of $\mathbf{y}_j$.

It builds a set of p nested partitions of variables in the following way:

• 1. Step $l=0$: initialisation. Start with the partition into singletons (p clusters).

• 2. Step $l=1,\ldots ,p-2$: aggregate two clusters of the partition into $p-l+1$ clusters to get a new partition into $p-l$ clusters. For this, choose clusters A and B with the smallest dissimilarity defined as:

  $$d(A,B)=H(A)+H(B)-H(A\cup B) =\lambda _A^1+\lambda _B^1-\lambda _{A\cup B}^1.$$

  (6)

  We can prove that $\lambda _{A\cup B}^1 \le \lambda _A^1+\lambda _B^1$, which implies that the merging of two clusters A and B at each step results in a decrease of criterion $\mathcal{{H}}$. This dissimilarity measures the loss of homogeneity observed when the two clusters are merged. The strategy therefore consists in merging the two clusters that result in the smallest decrease in $\mathcal{{H}}$. Using this aggregation measure the new partition into $p-l$ clusters maximises $\mathcal{{H}}$ among all the partitions into $p-l$ clusters obtained by amalgamation of two clusters of the partition into $p-l+1$ clusters.

• 3. Step $l=p-1$: stop. A single cluster consisting of all variables is obtained.

The height of a cluster $C=A\cup B$ in the tree is defined as $h(C)=d(A,B)$. This approach provides a tree which enables the user to see the successive aggregations between the variables, and gives a graphical illustration to aid in selecting the number of clusters to be used.

1.2 The Final Weigthing Scheme of the Quality of Life Indicators

The weighting scheme of $\mathbf{f}_k$ as linear combination of the initial variables (belonging to cluster) is:

$$\mathbf{f}_k= \beta _0+\sum _{k=1}^{p_1+m}\beta _k \mathbf{x}_k$$

(7)

where the vectors $\mathbf{x}_1,\ldots ,\mathbf{x}_{p_1+m}$ are the columns of $\mathbf{X}=(\mathbf{X}_k|\mathbf{G})$. The values of $\beta _0$ and $\beta _k,k=1,\ldots ,p_1+m$ are given in Appendix.

$$\begin{aligned} \beta _0&= -\sum _{l=1}^{p_1}v_{li}\frac{{\bar{\mathbf{x}}}_l}{\sigma _l} -\sum _{l=p_1+1}^{p_1+m}v_{li}\frac{n}{n_l} {\bar{\mathbf{x}}}_l\\ \beta _k&= v_{ki}\frac{1}{\sigma _k}, \text{ for } k=1,\ldots , p_1\\ \beta _k&= v_{ki}\frac{n}{n_k}, \text{ for } k=p_1+1,\ldots , p_1+m \end{aligned}$$

with ${\bar{\mathbf{x}}}_k$ and $\sigma _k$ respectively denote the empirical mean and standard deviation of the column $\mathbf{x}_k$.

Appendix 3: Complement Results for 1999

See Fig. 3; Table 5.

Fig. 3

Dendrogram of the hierarchy of the variables of the 1999 data set built with ClustOfVar (the line indicates a cutting into five clusters)

Table 5 Link between the initial variables and the synthetic variables for each cluster in 1999

Appendix 4: Some Results for Year 2009

See Tables 6, 7 and 8.

Table 6 Link between the initial variables and the synthetic variables for each cluster in 2009

Table 7 Reading of the five composite indicators for 2009

Table 8 Mean of the composite indicators for the five groups of municipalities in 2009