Optimal well-being is a new multi-dimensional construct, which incorporates the well-known preexisting notions of subjective and psychological well-being. Classical models for describing the predictors of optimal well-being binary response variable are generalized linear models (GLM), such as logistic regression model. Since the number of predictors might be relatively large in these models, we devise a sparse optimization method for the regression problem based on subsequent iterations of a suitable sparse quadratic approximant problem, so that the resulting parameter vector estimate is sparse and indicates few significant predictors. We conduct empirical assessments using data of the European Social Survey (ESS), in order to identify the set of determinants which better predict optimal well-being by means of the proposed sparse regression method. ESS data analysis confirms that few selected predictors provide good data interpretation and no loss of information in the frequency of correct classification for people meeting the criteria of optimal well-being. Moreover, simulations with different structural parameter values indicate that sparse logistic model performs better in terms of the estimation of the true vector of parameters in a more parsimonious setting compared to classical logistic regression. The benefits increase as the structural sparsity of the optimization problem becomes stronger.

中文翻译：

---

最优幸福感决定因素的稀疏逻辑最大似然估计

最佳幸福感是一种新的多维结构，它结合了众所周知的主观幸福感和心理幸福感。用于描述最佳幸福感二元响应变量预测变量的经典模型是广义线性模型 (GLM)，例如逻辑回归模型。由于这些模型中预测变量的数量可能相对较大，因此我们为回归问题设计了一种基于合适的稀疏二次逼近问题的后续迭代的稀疏优化方法，从而使生成的参数向量估计是稀疏的，并且表明很少有重要的预测变量。我们使用欧洲社会调查 (ESS) 的数据进行实证评估，以便通过提议的稀疏回归方法确定一组可以更好地预测最佳幸福感的决定因素。ESS 数据分析证实，很少有选定的预测变量能够提供良好的数据解释，并且对于满足最佳幸福感标准的人来说，正确分类的频率不会丢失信息。此外，具有不同结构参数值的模拟表明，与经典逻辑回归相比，稀疏逻辑模型在更简约的设置中在参数真实向量的估计方面表现更好。随着优化问题的结构稀疏性变得更强，收益也会增加。具有不同结构参数值的模拟表明，与经典逻辑回归相比，稀疏逻辑模型在更简约的设置中在估计参数的真实向量方面表现更好。随着优化问题的结构稀疏性变得更强，收益也会增加。具有不同结构参数值的模拟表明，与经典逻辑回归相比，稀疏逻辑模型在更简约的设置中在估计参数的真实向量方面表现更好。随着优化问题的结构稀疏性变得更强，收益也会增加。