Modelling Social Inequalities With Identity Spline And Lasso Regression

Addressing socio-inequalities in the digital era requires the development of integrated policies informed by advanced statistical modelling. These policies often involve coordinated investment in digital infrastructure, education, inclusive technological design, and the regulation of dominant technology platforms, alongside efforts to promote equitable digital labour practices. From a statistical perspective, modelling the impact of such multifaceted interventions across geographically and economically diverse regions poses significant challenges, especially due to structural heterogeneity, correlated covariates, and the need for interpretable scenario analysis. Cross-sectional data provide a valuable setting for examining the relationships between socio-economic indicators and investment patterns in education, infrastructure, and technology. However, assessing the implications of different policy strategies under uncertainty necessitates flexible modelling tools that can accommodate complex dependencies and enable exploratory perturbations of the response. To this end, we propose a modelling framework that combines identity splines with LASSO regression to support scenario-based analysis of social inequalities. The identity spline is a specialised spline function that enables controlled perturbations of a variable by adjusting its nodal coefficients. When used to represent the response variable-here an indicator of social inequalities-this construction allows for structured and interpretable modifications, facilitating the exploration of alternative policy scenarios. The LASSO regression model (Least Absolute Shrinkage and Selection Operator) is a widely used penalised regression technique that performs simultaneous variable selection and regularisation, making it well-suited for high-dimensional or multicollinear settings commonly encountered in socio-economic data. Building on this, we introduce a functional-scalar LASSO regression model, in which the response variable is transformed into a functional object via the identity spline. This formulation enables the response to be perturbed in a structured manner, allowing statisticians to investigate the sensitivity of outcomes to hypothetical interventions. The proposed model thus offers a principled statistical framework for scenario-based policy evaluation in the presence of complex predictor structures and uncertain outcomes.