Exploring Poverty and SDG Indicators in Italy: An Identity Spline Approach to Partial Least Squares Regression

Abstract

Poverty is a complex global issue, closely linked to economic and social inequalities. It encompasses not only a lack of financial resources but also disparities in access to education, healthcare, employment, and social participation. In alignment with the United Nations’ Sustainable Development Goals—specifically SDGs 3 (Good Health and Well-being), 4 (Quality Education), and 8 (Decent Work and Economic Growth)—this study investigates the relationship between poverty and a set of socioeconomic indicators across Italy’s 20 regions. To explore how poverty levels respond to different predictors, we apply an identity spline transformation to simulate controlled changes in the poverty indicator. The resulting scenarios are analyzed using partial least squares regression, enabling the identification of the most influential variables. The findings offer insights into regional disparities and contribute to evidence-based strategies aimed at reducing poverty and promoting inclusive, sustainable development.

1. Introduction

Poverty remains one of the most pervasive and complex issues affecting societies worldwide. Closely intertwined with economic and social inequalities, poverty reflects not only a lack of financial resources but also disparities in access to education, healthcare, employment, and social participation. Reducing these inequalities is among the most urgent challenges for achieving sustainable and inclusive development (Xhafaj & Nurja, 2014). As noted by Lanza (2015), economic inequality can be influenced by income and wealth disparities across different social groups, while social inequality—highlighted by Neckerman (2004)—manifests in unequal access to rights, services, and opportunities based on factors such as gender, ethnicity, or physical ability. Understanding the root causes and dimensions of poverty is essential for informing effective policy responses aimed at promoting equity, social cohesion, and long-term stability.

In Italy, the poverty risk indicator, calculated by ISTAT, measures the share of individuals living in households with an equivalent net income below the poverty risk threshold, defined as 60% of the median of the national distribution of the net income. In 2020, 20% of people residing in Italy were at risk of poverty (based on the previous year’s income), a percentage consistent with that of the preceding year (20.1% in 2019), despite the outbreak of the pandemic. Additionally, 5.6% of people were in conditions of severe material deprivation, and 11.7% were living in households with low work intensity. The composite indicator, based on these two components and on the risk of poverty, i.e., the share of the population at risk of poverty or social exclusion, indicates that 25.3% of the population was at risk of poverty or social exclusion, similar to 2019 (25.6%). This indicator is part of Sustainable Development Goal (SDG) 10. The risk of poverty or social exclusion varies significantly between regions, displaying a clear North-South gradient (Figure 1). Several central-southern regions (Lazio, Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria, Sicily, and Sardinia) have a percentage greater than 25.3%, whilest the north-central regions (Piedmont, Valle d’Aosta, Liguria, Lombardy, Trentino-Alto Adige, Veneto, Friuli-Venezia Giulia, Emilia-Romagna, Tuscany, Umbria, Marche) have percentages below 25.3%. In particular, among the north-central regions, only 11% of the resident population in Emilia-Romagna was at risk of poverty or social exclusion, whereas in Campania, among the central-southern regions, half of the population faced this risk (50.2%). The risk of poverty or social exclusion remained almost stable between 2019 and 2020 but remained high compared to other European countries, placing Italy near the bottom of the EU rankings. Over the past decade, regional disparities in poverty have persisted, showing no significant convergence between northern and southern Italy (Ciommi et al., 2021).

Socio-economic inequalities are shaped by a wide range of interrelated factors, including income, education, employment status, family structure, gender, ethnicity, and access to quality healthcare (Mackenbach et al., 2002; Timmis et al., 2022; Camminatiello et al., 2023). Previous research has shown that economically less developed countries tend to exhibit higher rates of NEET (Not in Education, Employment, or Training) individuals (Caroleo et al., 2020), whereas countries with more structured school-to-work transition systems experience lower NEET rates. Addressing these inequalities requires comprehensive and targeted interventions at the social, economic, and political levels (Schmidt et al., 2015). Moreover, several studies that analyze panel data report a negative correlation between economic growth and poverty (Garcés-Urzainqui, 2024; Marrero & Servén, 2022; Dollar et al., 2016).

In this study, we analyze the risk of poverty and social exclusion in Italy—hereafter referred to simply as poverty—and identify the socio-economic indicators most strongly associated with Sustainable Development Goals (SDGs) 3, 4, and 8, using data from the 20 Italian regions. When examining regional poverty levels, which are shaped by heterogeneous predictors, the research question can be framed around how poverty can be alleviated in the most disadvantaged areas and which variables exert the greatest influence in specific contexts. From a policy perspective, the short- to medium-term objective may consist in reducing the number of regions affected by poverty, a goal that can be pursued by perturbing the response variable through the use of an identity spline (Durand et al., 2025), which allows for the exploration of different poverty scenarios. Naturally, scenarios of varying complexities might be considered. Thus, the primary approach is to transform the response variable, poverty, with the aim of reducing poverty in specific areas. Furthermore, the analysis aims to identify the most influential predictors contributing to the attainment of this objective. To identify the most influential socio-economic indicators affecting poverty, this study employs partial least squares (PLS) regression (Wold, 1966). Unlike logit models (Xhafaj & Nurja, 2014) or quantile regression (Piketty & Saez, 2003; Lynch et al., 2004), PLS effectively addresses issues of multicollinearity among predictor variables, making it particularly suitable for analysing complex socio-economic phenomena.

In Section 2, we introduce the identity spline and briefly discuss the PLS regression model. Section 3 presents an application using poverty-related data from the Sustainable Development Goals of Agenda 2030 for Italy, suggesting potential avenues for poverty alleviation. Section 3.3 compares three different scenarios related to poverty reduction in specific regions of Italy. Finally, Section 4 provides a final discussion.

2. Materials and Methods

This study makes use of an identity spline for transforming the response variable; this spline is designed to simulate controlled changes in the response variable within a partial least squares regression model.

2.1. Identity Spline

Before introducing the identity spline function, we first briefly define splines and B-splines.

A spline function s for a continuous variable y on the open interval $(a,b)$ is constructed from piecewise polynomials of degree d (or order $m=d+1$). These polynomials are joined at K points, ${\tau }_1,\dots ,{\tau }_K$, known as knots, with continuity constraints determined by the knot multiplicity, which ranges from 1 to m and indicates how many knots coincide at the same location. The functional space of splines has dimension $m+K$, and the most commonly used basis functions for splines are the B-splines (Shumaker, 1981). The user specifies K interior knots, which, together with the polynomial degree, act as tuning parameters. A spline function s is then expressed as linear combination of a set of $m+K$ B-splines:

$$s(y,\mathit{\beta })=\sum _{l=1}^{m+K}{\beta }_l{B}_l^m\left(y\right),$$

where ${\left\{B_l^m(.)\right\}}_{l=1,\dots ,m+K}$ denotes the set of B-spline basis functions. For simplicity, a spline can be written as $s\left(y\right)$. In regression settings, the weight vector $\mathit{\beta }$ is typically estimated. However, when using specific functions, such as the identity spline, $s_{id}$, it can also be modified by the users (Durand et al., 2025). The identity spline $s_{id}$ (Marsden, 1970), is defined by nodal weights ${\mathit{\beta }}_{\mathrm{nodal}}$, also known as Greville points (Greville, 1967) in approximation theory. Regardless of $d>0$ or the knot multiplicities, the identity spline satisfies

$$s_{id}\left(y\right)=s(y,{\mathit{\beta }}_{\mathrm{nodal}})=y,\forall y\in [a,b],$$

where

$${\left[{\beta }_{\mathrm{nodal}}\right]}_l={\displaystyle \frac{1}{d}}\sum _{k=1}^d{\tau }_{l+k},\mathrm{for}l=1,\dots ,m+K.$$

In any regression model involving a functional transformation of the response y, it is crucial to control the transformation to ensure both a good fit and predictive accuracy. By introducing small additive modifications $\mathit{\delta }$ to the nodal coefficients (${\mathit{\beta }}_{\mathrm{nodal}}+\mathit{\delta }$), one can dynamically adjust the response y, while preserving both goodness of fit and predictive performance. The properties of such variations around the identity spline—through the choice of degree, number, location, and knot multiplicity—allow for precise local control of these adjustments.

Here, a new response, denoted $y_{new}$, is defined as an alteration of the observed response y via a spline transformation, expressed as a deviation from the identity spline and controlled by the parameter $\delta$. When $\delta =0$, the transformation reduces to $y_{new}=y$ (Durand et al., 2025). Such an easy exploration of new scenarios, based on local or global, continuous or discontinuous, functional changes of the observed response, plays a strategic role, particularly for policymakers.

2.2. Partial Least Squares Regression

Partial least squares (PLS) is a statistical regression technique developed to identify linear relationships between one or more response variables and one or more predictor variables. PLS regression represents a non-parametric modeling approach which, unlike classical econometric models, does not rely on a priori assumptions regarding the distribution of the error terms. Consequently, neither the response variables nor the errors are assumed to follow a specific probability distribution, and traditional inferential tests can be applied through resampling techniques such as bootstrap procedures, as employed in this paper. This method is particularly advantageous when the set of predictors is large and characterised by multicollinearity or strong intercorrelations, and when the sample size is small relative to the number of variables (Wold, 1966, 1975, 1985).

PLS operates by constructing A centered and uncorrelated latent variables, $t_1,\dots ,t_A$, known as PLS components, which are linear combinations of the original p predictors, $x_1,\dots ,x_p$. These components are designed to maximize their covariance with the response variable. The number A of retained components is usually determined by cross-validation or generalized cross-validation (Lombardo et al., 2009). The basic form of the PLS regression model for estimating a response variable $\widehat{y}$ can be expressed as follows:

$$\widehat{y}\left(A\right)=\sum _{j=1}^p{\widehat{\beta }}_j\left(A\right)x_j$$

where ${\widehat{\beta }}_j\left(A\right)$ is the coefficient associated with the jth predictor, which depends on the number A of retained PLS components. When A equals the rank of the predictor matrix $\mathbf{X}$, then PLS coincides with the ordinary least squares (OLS) regression.

A generalization of PLS for situations in which non-linear relationships exist between the response and predictor variables is provided by the partial least-squares splines (PLSS) model (Durand & Sabatier, 1997; Durand, 2001). This model extends PLS to the non-linear case by using B-splines as bases to transform the predictors.

In this study, we apply a linear PLS model, as the relationships between the response and the predictors appear to be linear.

3. Results

3.1. SDG-Based Variable Selection

Before using the linear PLS regression model to identify the most relevant predictors of poverty and its scenarios (see Section 3.2), the priority is to select the SDG indicators that will be used to predict poverty in Italy. This will be followed by the identification of three poverty scenarios, generated using three different identity spline transformations of poverty (see Section 3.2).

The Sustainable Development Goals (SDGs) are a set of 17 goals adopted by the United Nations General Assembly in 2015, aimed at promoting sustainable development, eradicating poverty, protecting the planet, and ensuring prosperity for all. Several studies have analyzed the SDGs in different ways. For instance, Alaimo and Maggino (2020) focus on composite indicators for SDGs 1–3 at the regional level in Italy, providing methodological insights useful for monitoring progress toward the 2030 Agenda. Similarly, D’Adamo et al. (2025) develop a multi-criteria decision analysis framework for regional assessment of the SDGs in Italy, using 61 indicators that cover social, economic, and environmental domains.

In this context, we focus on Italy’s Strategy for the SDGs (see the SDGs 2021 Report: Statistical Information for the 2030 Agenda in Italy, published by ISTAT), which assesses sustainable development across the 20 Italian regions.

We investigate poverty—a key aspect of SDG 10 (Reduced Inequalities)—in conjunction with indicators collected under SDG 3 (Good Health and Well-being), SDG 4 (Quality Education), and SDG 8 (Decent Work and Economic Growth). Accordingly, our analysis focuses on examining the dependence of poverty on several socio-economic indicators aligned with SDGs 3, 4, and 8, gathered from the 20 regions of Italy. These include 49 predictor variables described in

Table 1. Description of the 49 indicators of the SDGs 3, 4 and 8. The most relevant predictors in Scenarios 1, 2, and 3 are highlighted in bold.

Label	Predictor Description
HWB1	Probability of death under 5 years
HWB2	Excess weight (standardized rates)
HWB3	Healthy life expectancy at birth
HWB4	Diabetes (standardized rates)
HWB5	Hypertension (standardized rates)
HWB6	Percentage of births with more than 4 prenatal check-up visits
HWB7	Day-Hospital beds in public and private healthcare institutions
HWB8	Ordinary ward beds in public and private healthcare institutions
HWB9	Dentists
HWB10	Pharmacists
HWB11	Nurses and midwives
HWB12	Doctors
QEdu1	Inadequate literacy skills (students in Grade II of upper secondary school)
QEdu2	Inadequate literacy skills (students in Grade III of lower secondary school)
QEdu3	Inadequate literacy skills (students in Grade V of upper secondary school)
QEdu4	Inadequate numeracy skills (students in Grade II of upper secondary school)
QEdu5	Inadequate numeracy skills (students in Grade III of lower secondary school)
QEdu6	Inadequate numeracy skills (students in Grade V of upper secondary school)
QEdu7	Inadequate listening comprehension skills in English (students in Grade III of lower secondary school)
QEdu8	Inadequate listening comprehension skills in English (students in Grade V of upper secondary school)
QEdu9	Inadequate reading comprehension skills in English (students in Grade III of lower secondary school)
QEdu10	Inadequate reading comprehension skills in English (students in Grade V of upper secondary school)
QEdu11	Early exit from the education and training system
QEdu12	Nurseries and integrated services for early childhood per 100 children aged 0–2 years
QEdu13	Ministry of Education, Universities and Research
QEdu14	Students with disabilities: nursery school
QEdu15	Students with disabilities: primary school
QEdu16	Students with disabilities: lower secondary school
QEdu17	Students with disabilities: upper secondary school
QEdu18	Participation in continuous training
QEdu19	At least basic digital skills
QEdu20	Advanced digital skills
QEdu21	Graduates and other tertiary titles (aged 30–34)
QEdu22	Graduates in STEM disciplines
QEdu23	Physically accessible schools
QEdu24	Schools with students with disabilities for the presence of adapted computer workstations: primary school
QEdu25	Schools with students with disabilities for the presence of adapted computer workstations: lower secondary school
QEdu26	Schools with students with disabilities for the presence of adapted computer workstations: upper secondary school
QEdu27	Physically inaccessible schools
WG1	Annual growth rate of real GDP per employed person
WG2	Annual growth rate of value added in volume per employed person
WG3	Annual growth rate of value added in volume per hour worked
WG4	Employees in fixed-term jobs for at least 5 years
WG5	Involuntary part-time
WG6	Unemployment rate
WG7	Non-participation rate in the workforce
WG8	Employment rate (aged 20–64)
WG9	Young people not in employment, education, or training (NEET)
WG10	Young people not in employment, education, or training (NEET) (aged 15–24)

.

It should be noted that only those indicators for which data were available across all Italian regions were considered, with 2019 selected as the reference year. A brief description of SDGs 3, 4, and 8 is provided in Table 1 and below:

–

SDG 3: “Ensure healthy lives and promote well-being for all at all ages” (HWB), described by 12 indicators aimed at measuring progress towards this goal.

–

SDG 4: “Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all” (QEdu), explained by 27 indicators.

–

SDG 8: “Promote sustained, inclusive, and sustainable economic growth, full and productive employment, and decent work for all, and enhance productive capacity for the least developed regions” (WG), related to 10 indicators.

3.2. Poverty in Italy: Three Scenarios

We consider three scenarios corresponding to simulated controlled changes in poverty, generated using the identity spline described in Section 2. The choice of the $\delta$-perturbation applied to the nodal coefficients of the identity spline depends on the specific target of the analysis—for example, in our poverty study, it is determined by the number of impoverished regions that we aim to move below the national average poverty threshold. Accordingly, different values of the $\delta$-perturbation were adopted for the three hypothetical poverty scenarios.

3.2.1. Scenario 1

First, poverty—with observations ranging from 0 to 1—is transformed using second-degree B-splines with a multiple knot at 0.25 (the average poverty level in Italy) and a multiplicity of 3. According to B-splines smoothness property, a knot of multiplicity 3 at the poverty threshold 0.25 introduces a discontinuity in the six-dimensional spline functions. The nodal coefficients are perturbed by $\delta =(0,0,0,-0.1,-0.05,-0.05)$ as indicated in the top-left corner of Figure 2.

On the right side of Figure 2, which displays both real and simulated poverty values, only the nine regions above the national poverty average have their values modified. Consequently, the nodal coefficients of the identity spline are modified by these delta values.

This adjustment results in a reduction in poverty in central-southern regions (Lazio = 12, Abruzzo = 13, Molise = 14, Campania = 15, Puglia = 16, Basilicata = 17, Calabria = 18, Sicilia = 19, and Sardinia = 20), while other regions remain unaffected (Piedmont = 1, Valle d’Aosta = 2, Liguria = 3, Lombardy = 4, Trentino-Alto Adige = 5, Veneto = 6, Friuli-Venezia Giulia = 7, Emilia-Romagna = 8, Tuscany = 9, Umbria = 10, Marche = 11). Notably, the delta perturbation substantially affects the risk of poverty for the Lazio region (12 = Lazio), bringing it below the national average.

The right side of Figure 2 illustrates the regions where the poverty value decreases. Note that the knot’s multiplicity is marked by overturned ‘k’ letters on the horizontal axis and that the identity spline is the red dotted line.

3.2.2. Scenario 2

Figure 3 shows the second scenario. The nodal coefficients have been perturbed by $\mathit{\delta }=(0,0,0,-0.1,-0.15,-0.1)$. Due to the smoothness property of B-splines, a discontinuity arises in the function at 0.25 (with a knot multiplicity of 3). Since the first three values of $\mathit{\delta }$ are zero, poverty remains unchanged in the less impoverished regions within the first knot interval, as in Scenario 1. Conversely, the distinct $\mathit{\delta }$ values in the subsequent interval induce nonlinear changes in areas with high poverty, decreasing the values in the central-southern regions. In particular, for two regions—Lazio (12) and Abruzzo (13)—this adjustment results in a reduction in poverty, bringing the risk of poverty or social exclusion below the Italian average.

3.2.3. Scenario 3

Figure 4 shows the third scenario. The nodal coefficients have been perturbed by different constant values, $\mathit{\delta }=(0,0,0,-0.15,-0.5,-0.05)$. Since the first three values of $\mathit{\delta }$ are zero, as in the first two scenarios, poverty remains unchanged in the northern, less impoverished regions within the first knot interval. However, the $\delta$ values in the subsequent interval induce significant changes in the central-southern regions. Now, in three regions—Lazio (12), Abruzzo (13), and Sardinia (20)—the reduction in poverty is substantial, bringing the risk of poverty or social exclusion in these regions below the Italian average.

In summary, decision-makers can make real-time adjustments to specific components of the statistical model by locally modifying the observed response. The choice of the appropriate scenario, $s_{\mathrm{new}}\left(y\right)=y_{\mathrm{new}}$, depends on the available resources and time required to reach it. The decision process allows for online control of the changes in the response (target to pursue) and the immediate evaluation of a new model (here, PLS).

3.3. Comparing Poverty Scenarios

To understand which socio-economic indicators most affect changes in poverty across Italian regions, we first analyze the non-transformed poverty variable—named $y_0$—using PLS regression model, i.e., ${\mathrm{PLS}}_0=\mathrm{PLS}(X,y_0)$. The model shows good fit and predictive accuracy. Specifically, the coefficient of determination $R^2$ is 0.90 and the PRESS value is very good (0.11) suggesting to retain only one component. Therefore, since PLS is the simpler and more parsimonious model, requiring only one component, we retain this linear model without seeing the need to construct a non-linear PLS model.

When the goal is to alleviate poverty in one of the most impoverished regions, we can consider Scenario 1 (see Figure 2), which produces the new response $s_{id}\left(y\right)=y_1$. This response differs from $y_0$ by a slight decrease in poverty in the nine most impoverished regions (12 = Lazio, 13 = Abruzzo, 14 = Molise, 15 = Campania, 16 = Puglia, 17 = Basilicata, 18 = Calabria, 19 = Sicilia, 20 = Sardegna), bringing the Lazio region below the Italian average for poverty, while leaving the northern, less impoverished regions unaffected. This poverty scenario is then compared to the original observed ${\mathbf{y}}_0$ in Scenario 0 through the corresponding ${\mathrm{PLS}}_1$ = PLS($X,y_1$) model, see

Table A1. Predictor coefficients of the original linear (PLS) model applied to poverty (subscript 0) and its three different scenarios (subscripts 1, 2, and 3), with all predictors increasingly ordered.

${\mathbf{PLS}}_0$	Beta	${\mathbf{PLS}}_1$	Beta	${\mathbf{PLS}}_2$	Beta	${\mathbf{PLS}}_3$	Beta
QEdu20	−0.041	QEdu20	−0.038	QEdu20	−0.035	QEdu20	−0.031
HWB3	−0.040	HWB3	−0.035	HWB3	−0.032	QEdu12	−0.028
QEdu12	−0.037	QEdu12	−0.034	QEdu12	−0.032	QEdu18	−0.027
QEdu18	−0.036	QEdu18	−0.033	QEdu18	−0.031	QEdu23	−0.027
HWB8	−0.035	HWB8	−0.032	HWB8	−0.030	HWB8	−0.026
QEdu19	−0.035	QEdu19	−0.032	QEdu23	−0.030	QEdu19	−0.025
WG8	−0.035	QEdu23	−0.032	QEdu19	−0.029	WG8	−0.025
QEdu23	−0.034	WG8	−0.032	WG8	−0.029	QEdu21	−0.022
QEdu21	−0.029	QEdu21	−0.027	QEdu21	−0.026	HWB3	−0.021
HWB6	−0.013	HWB6	−0.013	HWB6	−0.013	HWB11	−0.014
HWB11	−0.012	HWB11	−0.012	HWB11	−0.011	HWB6	−0.012
QEdu25	−0.011	QEdu25	−0.009	HWB9	−0.008	HWB10	−0.010
QEdu24	−0.010	HWB9	−0.008	QEdu25	−0.008	HWB9	−0.009
WG1	−0.009	HWB10	−0.008	HWB10	−0.007	WG1	−0.007
HWB9	−0.008	QEdu24	−0.008	WG1	−0.007	WG3	−0.007
HWB10	−0.008	WG1	−0.008	QEdu24	−0.006	WG2	−0.006
WG3	−0.008	WG2	−0.007	WG2	−0.006	QEdu24	−0.004
WG2	−0.007	WG3	−0.007	WG3	−0.006	QEdu25	−0.004
QEdu17	0.003	QEdu17	0.002	QEdu17	0.001	QEdu17	−0.002
HWB12	0.005	HWB12	0.003	HWB12	0.002	QEdu22	−0.002
QEdu14	0.005	QEdu14	0.003	QEdu14	0.002	HWB12	0.002
QEdu15	0.006	QEdu15	0.005	QEdu22	0.004	QEdu14	0.004
HWB7	0.007	QEdu22	0.005	QEdu15	0.005	HWB7	0.006
QEdu22	0.007	HWB7	0.006	HWB7	0.006	QEdu15	0.009
QEdu16	0.009	QEdu16	0.008	QEdu16	0.008	QEdu16	0.010
QEdu26	0.017	QEdu26	0.016	QEdu26	0.015	QEdu26	0.016
QEdu13	0.027	HWB1	0.026	HWB2	0.024	QEdu10	0.019
HWB1	0.028	HWB2	0.026	QEdu13	0.024	HWB2	0.020
HWB2	0.028	QEdu13	0.026	HWB1	0.025	QEdu8	0.020
QEdu8	0.030	QEdu6	0.028	QEdu6	0.025	QEdu6	0.021
QEdu6	0.031	QEdu8	0.028	QEdu8	0.025	QEdu27	0.021
QEdu10	0.031	QEdu10	0.028	QEdu10	0.025	QEdu13	0.022
QEdu27	0.031	QEdu27	0.029	WG4	0.026	WG4	0.022
WG4	0.032	WG4	0.029	QEdu27	0.027	QEdu1	0.023
QEdu11	0.033	QEdu3	0.030	QEdu1	0.028	QEdu3	0.023
QEdu1	0.034	QEdu1	0.031	QEdu3	0.028	WG5	0.023
QEdu3	0.034	QEdu4	0.031	QEdu11	0.028	HWB1	0.024
QEdu9	0.034	QEdu9	0.031	WG5	0.028	QEdu4	0.024
WG5	0.034	QEdu11	0.031	QEdu4	0.029	QEdu7	0.024
QEdu4	0.035	WG5	0.031	QEdu5	0.029	QEdu5	0.025
QEdu5	0.035	QEdu5	0.032	QEdu7	0.029	QEdu9	0.025
QEdu7	0.035	QEdu7	0.032	QEdu9	0.029	QEdu11	0.026
QEdu2	0.036	QEdu2	0.033	QEdu2	0.031	HWB5	0.027
WG6	0.037	WG6	0.034	WG6	0.031	QEdu2	0.027
WG7	0.037	WG7	0.034	WG7	0.031	WG7	0.027
WG9	0.038	WG9	0.035	WG9	0.032	WG6	0.028
WG10	0.038	WG10	0.035	WG10	0.032	WG9	0.028
HWB5	0.039	HWB5	0.036	HWB5	0.033	HWB4	0.029
HWB4	0.040	HWB4	0.037	HWB4	0.034	WG10	0.029

. The coefficient $R^2$ is 0.88, and the PRESS value is 0.13, indicating that the goodness of fit and predictive accuracy are very similar to those of the original model. The left panel of Figure 5 shows the bar plot of the effects of the predictor variables on poverty ($y_0$) in Scenario 0, while the right panel displays the corresponding bar plot for poverty ($y_1$) in Scenario 1. In both scenarios, ${\mathrm{PLS}}_0$ and ${\mathrm{PLS}}_1$, the seven most important predictors with positive coefficients—HWB4 (Diabetes), HWB5 (Hypertension), WG10 (NEET, aged 15–24), WG9 (NEET), WG7 (Non-participation rate in the workforce), WG6 (Unemployment rate), and QEdu2 (Inadequate literacy skills, students in Grade III of lower secondary school)—are identical, as is their order of importance, although their values differ (see Figure 5 and Table A1). All of these predictors are statistically significant at the $\alpha =0.01$ level, as shown in

Table A2. Bootstrap confidence intervals for PLS regression coefficients ($A=3$). Significant coefficients at $\alpha =0.05$ are marked with **.

Predictor	Estimate	Lower	Upper
HWB1 *	0.028	0.002	0.057
HWB2 **	0.028	0.018	0.036
HWB3 ***	−0.040	−0.071	−0.028
HWB4 **	0.040	0.027	0.054
HWB5 **	0.039	0.026	0.064
HWB6	−0.013	−0.037	0.022
HWB7	0.007	−0.008	0.023
HWB8 ***	−0.035	−0.049	−0.022
HWB9	−0.008	−0.040	0.012
HWB10	−0.008	−0.027	0.011
HWB11	−0.012	−0.033	0.006
HWB12	0.005	−0.010	0.018
QEdu1 **	0.034	0.025	0.046
QEdu2 **	0.036	0.024	0.049
QEdu3 ***	0.034	0.025	0.040
QEdu4 **	0.035	0.024	0.045
QEdu5 **	0.035	0.025	0.046
QEdu6 **	0.031	0.023	0.037
QEdu7 **	0.035	0.027	0.042
QEdu8 **	0.030	0.023	0.036
QEdu9 **	0.034	0.025	0.047
QEdu10 **	0.031	0.023	0.041
QEdu11 *	0.033	0.021	0.042
QEdu12 ***	−0.037	−0.044	−0.027
QEdu13 *	0.027	0.009	0.054
QEdu14	0.005	−0.013	0.030
QEdu15	0.006	−0.013	0.029
QEdu16	0.009	−0.014	0.029
QEdu17	0.003	−0.019	0.017
QEdu18 ***	−0.036	−0.042	−0.028
QEdu19 ***	−0.035	−0.040	−0.027
QEdu20 ***	−0.041	−0.047	−0.032
QEdu21 ***	−0.029	−0.037	−0.019
QEdu22	0.007	−0.031	0.024
QEdu23 ***	−0.034	−0.088	−0.019
QEdu24	−0.010	−0.050	0.005
QEdu25	−0.011	−0.026	0.014
QEdu26	0.017	−0.003	0.040
QEdu27 **	0.031	0.020	0.058
WG1	−0.009	−0.031	0.014
WG2	−0.007	−0.029	0.015
WG3	−0.008	−0.026	0.011
WG4 **	0.032	0.018	0.038
WG5 **	0.034	0.023	0.048
WG6 **	0.037	0.027	0.046
WG7 **	0.037	0.029	0.043
WG8 ***	−0.035	−0.040	−0.027
WG9 **	0.038	0.030	0.045
WG10 **	0.038	0.029	0.047

.

Regarding the seven most important predictors with negative coefficients, six of them are identical (in position but not in value) across both scenarios: QEdu20 (Advanced digital skills), HWB3 (Healthy life expectancy at birth), QEdu12 (Nurseries and integrated services for early childhood), QEdu18 (Participation in continuous training), HWB8 (Ordinary ward beds in public and private healthcare institutions), and QEdu19 (At least basic digital skills). The remaining predictor differs in Scenario 1, where QEdu23 (Physically accessible schools) appears more relevant for Lazio than WG8 (Employment rate). Among these most influential predictors, HWB4 reflects the standardized prevalence of diabetes in the impoverished population and ranks first among the predictors with positive coefficients in Scenario 2 as well. Conversely, QEdu20 emphasizes that adequate digital skills are essential for lifting people out of poverty and is the most important predictor with a negative coefficient across all scenarios. For complete details on the predictor coefficients in the full model, and to check their statistical significance, see Table 1 and Table A2, respectively, in Appendix A.

Therefore, to alleviate poverty in the nine most disadvantaged regions—particularly in Lazio (Scenario 1)—greater efforts should be directed toward improving digital skills (QEdu20), increasing healthy life expectancy at birth (HWB3), expanding nurseries and integrated services for early childhood (QEdu12), enhancing participation in continuous training (QEdu18), increasing the availability of ordinary ward beds in public and private healthcare institutions (HWB8), and strengthening basic digital skills (QEdu19). Additionally, for Lazio in particular, attention should be given to increasing the number of physically accessible schools (QEdu23).

When the goal is to reduce the risk of poverty or social exclusion below the national average in two specific regions, Abruzzo and Lazio, we can consider Scenario 2 (see Figure 3), which leads to the new response $s_{id}\left(y\right)=y_2$ (see the $PL{S}_2$ model in Table A1). This response differs from $y_0$ by exhibiting a stronger decrease (compared to Scenario 1) in the nine regions with the highest poverty levels—Lazio (12), Abruzzo (13), Molise (14), Campania (15), Puglia (16), Basilicata (17), Calabria (18), Sicilia (19), and Sardegna (20)—while the northern regions remain largely unaffected.

The coefficient $R^2$ is 0.86 and the PRESS value is 0.15 when retaining one component. Thus, the model’s goodness of fit and predictive accuracy remain strong.

The left panel of Figure 6 presents the predictors for poverty ($y_2$) under Scenario 2. The seven most influential predictors with positive coefficients are consistent with those identified in Scenario 1, although their values differ. Notably, six of the seven most important predictors with negative coefficients are shared with Scenario 0. The only variable that distinguishes Scenario 2—and ranks first relative to Scenario 1—is QEdu23, which reflects an increase in the number of physically accessible schools aimed at mitigating poverty.

Overall, to effectively alleviate poverty in the two most disadvantaged regions—Abruzzo and Lazio—greater efforts should be directed toward increasing the number of physically accessible schools, along with improving all the other indicators.

Finally, when the goal is to reduce the risk of poverty or social exclusion below the national average in three specific regions—Abruzzo, Lazio, and Sardinia—we can consider Scenario 3 (see Figure 4), which produces the new response $s_{id}\left(y\right)=y_3$ (see the $PL{S}_3$ model in Table A1). Again, this response differs from $y_0$ by showing a stronger decrease—compared with Scenarios 1 and 2—in the nine impoverished regions: Lazio (12), Abruzzo (13), Molise (14), Campania (15), Puglia (16), Basilicata (17), Calabria (18), Sicilia (19), and Sardinia (20), while leaving the remaining regions unaffected. As a result, in Abruzzo, Lazio, and Sardinia, poverty falls below the national average.

The coefficient $R^2$ is 0.66 and the PRESS value is 0.38 when retaining one component. Thus, the model’s goodness of fit and predictive accuracy remain acceptable.

The right panel of Figure 6 shows the fourteen most important predictors for poverty in Scenario 3. We note that the seven most important predictors with negative coefficients belong primarily to SDG 4 (Quality Education), unlike in Scenario 0. These include QEdu20, QEdu12, QEdu18, QEdu23, and QEdu19 (see also Table 1 and Table A1), all of which are statistically significant at the $\alpha =0.01$ level, as shown in Table A2. Furthermore, we observe the increased relevance of WG8 (Employment rate) compared with HWB3 (Healthy life expectancy at birth), which ranks second in Scenarios 0, 1, and 2. Therefore, to effectively alleviate poverty in Sardinia, greater efforts should be made to enhance knowledge of advanced digital skills (QEdu20), which recent studies have identified as particularly relevant for reducing social inequalities in general (Park, 2017; van Deursen & Helsper, 2015). As in Scenarios 1 and 2, Scenario 3 also shows that expanding nurseries and integrated services for early childhood (QEdu12), enhancing participation in continuous training (QEdu18), increasing the number of physically accessible schools (QEdu23), increasing the number of ordinary ward beds in public and private healthcare institutions (HWB8), strengthening basic digital skills (QEdu19), and improving the employment rate (WG8) are crucial for alleviating poverty overall, and especially in Lazio, Abruzzo, and Sardinia.

4. Discussion

This paper presents a novel application of the identity spline (Marsden, 1970) within the framework of partial least squares regression models (Wold, 1966; Durand, 2001). The innovative use of the identity spline allows researchers and decision-makers to move beyond analysis of the observed response variable by constructing alternative target scenarios that reflect hypothetical or desired outcomes. This methodological approach is particularly valuable in complex socio-economic contexts, where observed data may not fully capture the dynamics or potential trajectories of key societal challenges such as poverty.

By systematically deviating from the observed response using the identity spline, we can simulate and assess how changes in specific predictors influence poverty outcomes across Italian regions. This capability provides a more flexible and forward-looking tool for policy evaluation. Unlike traditional regression models that focus solely on present conditions, our approach facilitates the exploration of what-if scenarios, helping to identify actionable strategies for poverty reduction under constrained resources and varying policy priorities.

The application of this method to three distinct poverty scenarios has yielded several important insights. Specifically, our findings suggest that particular attention should be paid to enhancing advanced digital skills (QEdu20) among the population (OECD, 2021b; Park, 2017; van Deursen & Helsper, 2015), as this factor consistently emerges as a key lever for reducing poverty levels. Similarly, reducing the prevalence of diabetes (HWB4) and hypertension (HWB5), increasing the number of young people not in employment, education, or training (NEETs; WG9 and WG10), reducing the unemployment rate (WG6) and non-participation in the workforce (WG7), and decreasing inadequate literacy skills of students in Grade III of lower secondary school (QEdu2) are critical targets. These predictors are not only relevant but also carry clear policy implications, aligning with well-established socio-economic mechanisms that drive exclusion and vulnerability (Carcillo et al., 2015; Lanza, 2015; OECD, 2021a; Marrero & Servén, 2022).

Moreover, the scenario-based analysis highlights the importance of addressing public health concerns, particularly through indicators such as HWB4 and HWB5, which reflect the standardized prevalence of diabetes and hypertension in the population. This finding underscores the intersection between health and economic deprivation, suggesting that efforts to tackle chronic conditions could have downstream effects on poverty alleviation. Recent global reports indicate that diabetes disproportionately affects disadvantaged populations and contributes to long-term economic hardship (WHO, 2016; Narayan et al., 2006). Therefore, reducing its prevalence through improved prevention and healthcare access is not only a public health priority but also a strategic component of sustainable anti-poverty policies.

These multidimensional linkages reaffirm the need for integrated policy approaches that cut across sectors such as health, education, and labor markets. Nevertheless, we acknowledge the inherent complexity of poverty as a multidimensional phenomenon. The scenarios discussed here are illustrative rather than exhaustive. Future work could build on these findings by incorporating additional response scenarios and predictor variables (Marrero & Servén, 2022). The selection of such variables should be guided by both theoretical considerations and the practical feasibility of monitoring and influencing SDG indicators at the regional level. In particular, further research is needed to understand how local contexts mediate the relationship between structural predictors and poverty outcomes, and how regional disparities in policy implementation may affect these results.

5. Conclusions

This study demonstrates that the identity spline, when integrated within the PLS regression framework, provides an effective means of exploring alternative response scenarios and assessing the sensitivity of outcomes to changes in key predictors. Given the large set of predictors, characterized by strong intercorrelations, and the small sample size of the Italian regions, the PLS regression model is particularly suitable (Wold, 1966; Durand, 2001). However, the identity spline can also be applied within other regression models (Tibshirani, 1996), such as penalized regression models, to explore new response scenarios.

Applied to regional poverty in Italy, the model proves capable of identifying the most influential socio-economic determinants—such as education, employment, and health—while enabling the construction of hypothetical scenarios to support evidence-based policy design.

Beyond poverty analysis, the identity spline approach can be extended to other socio-economic and environmental domains where the capacity to model controlled changes in response variables is essential. For example, by using the national unemployment rate or the national average level of healthcare perfomance, the proposed method can help identify regional disparities and determine the main factors underlying such differences.

By enabling the formulation of what-if scenarios within a consistent statistical framework, this methodology offers a valuable contribution to scenario planning, policy evaluation, and sustainable development research.