ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Quantile Composite-based Path Modeling formeasuring equitable and sustainable well-being

C. Davino 1, P. Dolce 2, V. Esposito Vinzi 3, S. Taralli 4

1University of Macerata 2University of Naples3ESSEC Business School 4ISTAT

Dealing with Complexity in Society: from Plurality of Data to Synthetic Indicators

17th-18th September 2015, Padua (Italy)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 1 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 2 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Aim of the paper

Combining PLS Path Modeling and Quantile RegressionQuantile Composite-based Path Modeling (QC-PM)

Application framework:measuring equitable and sustainable well-being

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 3 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Aim of the paper

Combining PLS Path Modeling and Quantile RegressionQuantile Composite-based Path Modeling (QC-PM)

Application framework:measuring equitable and sustainable well-being

The main goals of the paper:

• Regressor effects on the whole dependent variable distribution

• Heteroscedastic relationships

• Presence of outliers

• Skewed dependent variable

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 3 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Aim of the paper

Methodological framework: multivariate analysis

• PLS Path Modeling (PLSPM)

• Quantile Regression (QR)

• Quantile Correlation (QC)

• Quantile Composite-based Path Modeling (QC-PM)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 4 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 5 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Measuring well-being

A short agenda

2007 OECD World Forum: The Istanbul Declaration - measuring the

progress of societies in all dimensions toimprove policy making,

democracy and citizens wellbeing

2007 European Commission: Beyond GDP - Measuring progress,

true wealth, and the well-being of nations

2008 Commission on the Measurement of Economic Performance

and Social Progress (Stiglitz-Sen-Fitoussi Commission)

2011 ONS starts developing new measures of national well-being

Horizon 2020 states that country performance and best practices must be

addressed and monitored

Europe 2020 strategy for smart, sustainable and inclusive growth

...C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 6 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 7 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Measuring well-being

The BES project

• Italian project to measure equitable and sustainable well-being(BES - www.misuredelbenessere.it)

• National and regional level

• Italian National Institute of Statistics (Istat)

• National Council for Economy and Labour (Cnel)

Provinces BES - 2014• Measuring BES at local level according to the BES framework

• Nuts3 level

• Italian National Institute of Statistics (Istat)

• National network of the Provinces Statistical Offices (Cuspi)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 8 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 9 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Basic notation

The data structure

• Q blocks of manifest variables (MVs):

• Q latent variables (LVs)

Model representation

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 10 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Partial Least Squares Path Model (PLSPM)

(Wold, 1985) (Tenenhaus et al. 2005) (Esposito Vinzi et al., 2010)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 11 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

PLSPM: the main steps of the algorithm

1 Data pre-processing

2 Initialization

3 Inner estimation (structural model)

4 Outer estimation (measurement model)

5 Latent score estimation

6 Weight convergence

7 Final output

1 LV scores2 path coefficients

(Lohmoller 1987, 1989)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 12 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Quantile Composite-based Path Model

A quantile approach in the main steps of the PLSPM algorithm

1 Data pre-processing

2 Initialization

3 Inner estimation (structural model)

4 Outer estimation (measurement model)

5 Latent score estimation

6 Weight convergence

7 Final output1 LV scores2 Path coefficients

(Davino and Vinzi, 2015)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 13 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 14 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Classical vs quantile linear regression

Classical linear regression(conditional expected value)

estimation of the conditional mean of aresponse variable (y) distribution as afunction of a set X of predictorvariables

E(y | X) = Xβ

βi = ∂E(y)∂xi

Quantile regression(conditional quantiles)

estimation of the conditional quantilesof a response variable (y) distributionas a function of a set X of predictorvariables

Qθ(y | X) = Xβ(θ)

where: (0 < θ < 1)

βi (θ) = ∂Qθ(y)∂xi

(Koenker and Basset, 1978) (Koenker, 2005) (Davino et al., 2013)C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 15 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Classical vs quantile linear regression

Classical linear regression(conditional expected value)

estimation of the conditional mean of aresponse variable (y) distribution as afunction of a set X of predictorvariables

E(y | X) = Xβ

βi = ∂E(y)∂xi

Quantile regression(conditional quantiles)

estimation of the conditional quantilesof a response variable (y) distributionas a function of a set X of predictorvariables

Qθ(y | X) = Xβ(θ)

where: (0 < θ < 1)

βi (θ) = ∂Qθ(y)∂xi

(Koenker and Basset, 1978) (Koenker, 2005) (Davino et al., 2013)C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 15 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Classical vs quantile linear regression

Classical linear regression(conditional expected value)

estimation of the conditional mean of aresponse variable (y) distribution as afunction of a set X of predictorvariables

E(y | X) = Xβ

βi = ∂E(y)∂xi

Quantile regression(conditional quantiles)

estimation of the conditional quantilesof a response variable (y) distributionas a function of a set X of predictorvariables

Qθ(y | X) = Xβ(θ)

where: (0 < θ < 1)

βi (θ) = ∂Qθ(y)∂xi

(Koenker and Basset, 1978) (Koenker, 2005) (Davino et al., 2013)C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 15 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Quantile Regression (QR)

The conditional quantile estimator

β (θ) = argminβ(θ)

∑ni=1 ρθ

(yi − x>i β(θ)

)ρθ =

θ (u) if u > 0(θ − 1) u if u ≤ 0

• No parametric distribution assumptions are required for theerror distribution

• θ regression lines

• 100(1-θ)% of points above the QR line and 100θ% below

• Coefficients inference using a bootstrap approach

(Koenker and Basset, 1978) (Koenker, 2005) (Davino et al., 2013)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 16 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

A very simple example

x

y

OLSq10q50q90

020

4060

8010

0

1 2

• Slopes: rate of change ofthe y θth conditionalquantile per unit changeof the regressor

• Fitted values reconstructthe conditional quantiles

intercept slope y |(x = 1) y |(x = 2) mean(y)OLS 27.13 -7.53 19.60 12.07 17.34θ = 0.1 6.80 -3.07 3.73 0.66 2.81θ = 0.5 18.98 -5.71 13.27 7.56 11.55θ = 0.9 66.56 -18.00 48.56 30.56 43.16

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 17 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 18 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Quantile Correlation (QC)

Q covarianceqcovθ Y ,X =

cov I (Y − Qθ(Y ) > 0) ,X =

E ψθ [Y − Qθ (Y )] [X − E (X )]

- Y, X : random variables- θ ∈ (0, 1): a quantile- I (·): indicator function

- ψθ (u) = θ − I (u < 0)

Q correlation (QC)

qcorθ Y ,X = qcovθY ,X√varψθ[Y−Qθ(Y )]var(X )

= qcovθY ,X√(θ−θ2)var(X )

QC distribution convergence√n (qcorθ Y ,X − qcorθ Y ,X)→d N (0,Ω1)

- qcorθ: sample QC

- Ω1: asymptotic variance

Li G., Li Y., Tsai C.L. (2015)Quantile correlations and quantile autoregressive modeling

Journal of the American Statistical Association, 110(509).

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 19 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Outline

Objectives

BackgroundMeasuring well-beingThe BES project

MethodsPartial Least Squares Path ModelQuantile RegressionQuantile CorrelationQuantile Composite-based Path Model

Results

Conclusions

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 20 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

QC-PM

A quantile approach in the main steps of the PLSPM algorithm

1 Data pre-processing

2 Initialization

3 Inner estimation (structural model)

4 Outer estimation (measurement model)

5 Latent score estimation

6 Weight convergence

7 Final output1 LV scores2 Path coefficients

(Davino and Vinzi, 2015)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 21 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

QC-PM: the inner estimation

Path weighting scheme (quantile θ)

ξj : successor LV ⇒ Quantile Regression

Qθ

(ξj |Ξ→j

)= Ξ→j β (θ) Ξ→j : matrix of the predecessor LVs

ξj : predecessor LV ⇒ Quantile Correlation

qcovθ ξj , ξj→ = cov I (ξj→ − Qθ(ξj→) > 0) , ξj

qcorθ =qcovθξj ,ξj→√

varψθ[ξj→−Qθ(ξj→)]var(ξj )=

qcovθξj ,ξj→√(θ−θ2)var(ξj )

-I : indicator function −1 ≤ qcorθ ≤ 1-Qθ(ξj→): unconditional θth quantile-ξj→: a successor LV

-ψθ (u) = θ − I (u < 0)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 22 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

QC-PM: the inner estimation

Factorial and centroid scheme (quantile θ)

ξj : predecessor LV ⇒ Quantile Correlation

qcovθ ξj , ξj→ = cov I (ξj→ − Qθ(ξj→) > 0) , ξj

qcorθ =qcovθξj ,ξj→√

(θ−θ2)var(ξj )

The direction of the links in the structural modelis taken into account!

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 23 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

QC-PM: the outer estimation

Outwards-directed Inwards-directed

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 24 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

QC-PM: the outer estimation

Mode Q

an innovative outer estimation mode measured through QC

Mode QOutwards−directed Mode QInwards−directed

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 25 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The proposed QC-PMs

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 26 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data structure

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 27 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data structure

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 28 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data structure

Dimensions

1 health

2 education and training

3 work and life balance

4 economic well-being

5 social relationships

6 politics and institutions

7 security

8 landscape and cultural heritage

9 environment

10 research and innovation

11 quality of services

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 29 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data structure

Dimensions (sub-dimensions) [# indicators]

1 health (life expectancy, mortality) [8]

2 education and training (educational attainment, participation in

education, competencies, lifelong learning) [8]

3 work and life balance (work participation, employment, unemployment,

safety at work) [9]

4 economic well-being (income, wealth, inequality, financial difficulties) [11]

5 social relationships (disability, immigration, civil society) [8]

6 politics and institutions (political participation, institutional

representation, local government) [10]

7 security (crime rate, physical integrity) [6]

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 30 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data structure

Dimensions (sub-dimensions) [# indicators]

8 landscape and cultural heritage (cultural heritage, landscape) [5]

9 environment (quality of environment, environmental resources consumption,

environmental sustainability) [8]

10 research and innovation (innovation, research) [7]

11 quality of services (provision of public services, access to public services)

[7]

Data matrix

110 provinces11 Dimensions31 sub-dimensions87 indicators

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 31 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES structural model

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 32 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Data pre-processing

• Indicator selection : not reliable indicators, related to districts,uncorrelated

• Missing data imputation: regional values

• Multicollinearity analysis: redundant indicators

• Preliminary PLSPM using Mode PLS: low weights,multidimensional blocks

Final data matrix

110 provinces11 Dimensions29 sub-dimensions63 indicators

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 33 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES hierarchical model

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 34 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES dataset

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 35 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES dataset

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 36 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES dataset

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 37 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The BES dataset

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 38 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

The proposed QC-PMs

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 39 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Health results

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 40 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Health: PLSPM results

Path coefficients

life expectation mortality−0.

6−

0.4

−0.

20.

00.

20.

4

Outer weights

I.1 I.2 I.3 I.8

−0.

4−

0.2

0.0

0.2

I.1 Life expectancy at birth (male) I.2 Life expectancy at birth (female)I.3 Infant mortality rate I.8 Avoidable mortality rate (0-74 years old)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 41 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Health: PLSPM and QC-PM results

Path coefficients

quantile

path

coe

ffici

ents

−1.

0−

0.5

0.0

0.5

0.1 0.25 0.5 0.75 0.9

life expectation mortality

Outer weights

0.1 0.25 0.5 0.75 0.9 plspm

I.1 I.2 I.3 I.8

−0.

6−

0.4

−0.

20.

00.

20.

4

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 42 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Education and training results

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 43 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Education and training: PLSPM results

Path coefficients

attainment participation competencies lifelong l.

−0.

4−

0.2

0.0

0.2

0.4

Outer weights

II.1 II.2 II.3 II.4 II.6 II.7 II.8

−0.

2−

0.1

0.0

0.1

0.2

0.3

II.1 Early leavers from education and training II.2 People in working age with lower secondary educ.II.3 Participation in upper secondary education II.4 Participation in tertiary education (19-25y)II.6 Level of literacy II.7 Level of numeracyII.8 Participation in lifelong learning (25-64y)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 44 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Education and training: PLSPM and QC-PM results

Path coefficients

quantile

educ

atio

n p

ath

coef

ficie

nts

−0.

50.

00.

51.

0

0.1 0.25 0.5 0.75 0.9

ed. attainmentparticipation ed.

competencieslifelong learning

Outer weights

0.1 0.25 0.5 0.75 0.9 plspm

II.1II.2

II.3II.4

II.6II.7

II.8

−0.

4−

0.2

0.0

0.2

0.4

0.6

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 45 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

PLSPM

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 46 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES and geographic areas

PLSPM - North west

−1.0 −0.5 0.0 0.5 1.0

0.08

0.09

0.10

0.11

0.12

0.13

0.14

LV averages

path

coe

ffici

ents

HEALTH

EDUCATION

WORKECONOMIC WELL−B

SOCIAL RELAT.

POLITICS

SECURITY

LANDSCAPE

ENVIRONMENT

RESEARCH

QUALITY SERV.

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 47 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES and geographic areas

PLSPM - North east

−1.0 −0.5 0.0 0.5 1.0

0.08

0.09

0.10

0.11

0.12

0.13

0.14

LV averages

path

coe

ffici

ents

HEALTH

EDUCATION

WORKECONOMIC WELL−B

SOCIAL RELAT.

POLITICS

SECURITY

LANDSCAPE

ENVIRONMENT

RESEARCH

QUALITY SERV.

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 48 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES and geographic areas

PLSPM - Center

−1.0 −0.5 0.0 0.5 1.0

0.08

0.09

0.10

0.11

0.12

0.13

0.14

LV averages

path

coe

ffici

ents

HEALTH

EDUCATION

WORKECONOMIC WELL−B

SOCIAL RELAT.

POLITICS

SECURITY

LANDSCAPE

ENVIRONMENT

RESEARCH

QUALITY SERV.

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 49 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES and geographic areas

PLSPM - South and islands

−1.0 −0.5 0.0 0.5 1.0

0.08

0.09

0.10

0.11

0.12

0.13

0.14

LV averages

path

coe

ffici

ents

HEALTH

EDUCATION

WORKECONOMIC WELL−B

SOCIAL RELAT.

POLITICS

SECURITY

LANDSCAPE

ENVIRONMENT

RESEARCH

QUALITY SERV.

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 50 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

PLSPM

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 51 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

QC-PM: θ=0.1

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 52 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

QC-PM: θ=0.25

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 53 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

QC-PM: θ=0.5

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 54 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

QC-PM: θ=0.75

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 55 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: path coefficients

QC-PM: θ=0.9

Security

Environment

Social relationships

Health

Research and innovation

Cultural heritage

Education

Politics and institutions

Quality of services

Work and life balance

Economic well−being

0.00 0.02 0.04 0.06 0.08 0.10 0.12

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 56 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

PLSPM

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.06 −0.02 0.02 0.04 0.06 0.08

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 57 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

QC-PM: θ=0.1

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.10 −0.05 0.00 0.05

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 58 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

QC-PM: θ=0.25

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.06 −0.02 0.02 0.04 0.06

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 59 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

QC-PM: θ=0.5

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.05 0.00 0.05 0.10

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 60 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

QC-PM: θ=0.75

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.05 0.00 0.05 0.10

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 61 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

BES: indirect effects

QC-PM: θ=0.9

mortalitycrime rate

physical integrityunemployment

educ. attainmentquality of env.

work participationinequality

financial diffic.safety at work

participation in educresources consump.

disabilityimmigration

political part.wealth

lifelong learningresearch

employmentlife expectancy

sustainabilityincome

institut. represent.local govern.

competenciescivil society

access to psprovision of ps

innovation

−0.05 0.00 0.05 0.10 0.15

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 62 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Concluding remarks

When to use what version - Inner scheme

• Path weighting/factorial/centroid: take into account thedirection of the links

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 63 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Concluding remarks

When to use what version - Outer weights

• Conceptual definition of the LVs

• Inwards/Outwards weights: discrete MVs

• QI /QO : simultaneously favouring dependence andinterdependence relationships

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 64 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Further developments

1 Data structure• Investigating an alternative QC measure more suited in case of

discrete values• Exploring QC-PM with highly collinear data• Analysing differences among the QC-PMs through simulated

data

2 Model assessment• Building goodness of fit measures in outwards and inwards

version

3 Model validation• Exploring a jackknife approach to evaluate the statistical

significance of the QC-PM coefficients• Testing the statistical significance of the differences among

QC-PM coefficients at different quantiles through interquantileregression (Gould, 1987)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 65 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Further developments

1 Data structure• Investigating an alternative QC measure more suited in case of

discrete values• Exploring QC-PM with highly collinear data• Analysing differences among the QC-PMs through simulated

data

2 Model assessment• Building goodness of fit measures in outwards and inwards

version

3 Model validation• Exploring a jackknife approach to evaluate the statistical

significance of the QC-PM coefficients• Testing the statistical significance of the differences among

QC-PM coefficients at different quantiles through interquantileregression (Gould, 1987)

C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 66 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Main references

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Esposito Vinzi V., Chin W.W:, Henseler J., Wang H. (2010) Handbook of PartialLeast Squares: Concepts, Methods and Applications. Springer.

Esposito Vinzi V., Russolillo G. (2012) Partial least squares algorithms andmethods. WIREs Comput Stat, 5, pp. 1–19.

Gould W.W. (1997) sg70: Interquantile and simultaneous-quantile regression.Stata Technical Bulletin, 38, pp. 14–22.

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ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Main references

Istat-Cnel (2014) Rapporto Bes 2014: il benessere equo e sostenibile in Italia.Roma, Istat.

Istat-Cuspi (2014) Il benessere Equo e Sostenibile delle Province. Roma, Cuspihttp : //www .besdelleprovince.it/

Kocherginsky M., He H., Mu Y. (2005) Practical Confidence Intervals forRegression Quantiles. Journal of Computational and Graphical Statistics, 14(1),pp. 41–55.

Koenker R. (2005) Quantile Regression. Cambridge University Press

Koenker R., Basset G.W: (1978) Regression Quantiles. Econometrica, 46, pp.33–50.

Li G., Li Y., Tsai C.L. (2014) Quantile correlations and quantile autoregressivemodeling. Journal of the American Statistical Association, accepted.

Lohmoller J.B. (1987) LVPLS Program Manual, version 1.8.. Technical Report,Zentralarchiv fur Empirische Sozialforschung, Universitat Zu Koln, Koln.

Lohmoller J.B. (1989) Latent Variable Path Modeling with Partial Least Squares.Physica-Verlag, Heildelberg.

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ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

Main references

OECD (2011) How’s Life? Measuring Well-being. Paris OECD.

OECD (2014) How’s Life in Your Region? Measuring Regional and LocalWell-being for Policy Making. Paris. OECD.

Sanchez G., Trinchera L. (2012) plspm: Partial Least Squares Data AnalysisMethods. R package version 0.2-2.

Stiglitz J. E., Sen A., Fitoussi J. (2009) Report by the Commission on theMeasurement of Economic Performance and Social Progress. Technical Report.Commission on the Measurement of Economic Performance and Social Progress,Paris. (www.stiglitz-sen-fitoussi.fr.)

Taralli S., Capogrossi C., Perri G. (2015) Measuring equitable and sustainablewell-being (BES) for policy-making at local level (NUTS3), Atti della LIIRiunione Scientifica della SIEDS, Societ Italiana di Economia Demografia eStatistica, Ancona-Fermo, maggio 2015 (in press).

Tenenhaus M., Esposito Vinzi V., Chatelin Y.M., Lauro C. (2005) PLS PathModeling. Computational Statistics and Data Analysis, pp. 159–205.

Tenenhaus M., Esposito Vinzi V. (2005) PLS regression, PLS path modeling andgeneralized Procustean analysis: a combined approach for multiblock analysis.Journal of Chemometrics, 19, pp. 145–153.C.Davino 17th-18th September 2015 QC-PM FOR MEASURING WELL-BEING 69 / 71

ObjectivesBackground

MethodsResults

ConclusionsUniversity of Padua

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