Multivariate statistical analysis of data from the PERMA+4 questionnaire “Subjective well-being of an organization’s employees”: Application of dimension reduction and clustering methods

The development of machine learning methods opens new opportunities for analyzing multidimensional psychological constructs traditionally studied via classical statistical approaches. This study presents a comprehensive multidimensional statistical analysis of data on the employee's subjective well-being obtained via PERMA+4 questionnaire. This study used contemporary methods of dimensionality reduction (PCA, t-SNE, UMAP, Isomap, MDS) and clustering (K-means, DBSCAN, agglomerative clustering) to reveal the latent structure of wellbeing data. The quality of the solutions was assessed via a set of validated metrics: the silhouette score, the Kalinski–Harabasz score, and the Davies–Bouldin score. The sample consisted of 325 respondents. Measurements were taken across nine employee well-being indicators included in the PERMA+4 model. This study revealed the exceptionally high effectiveness of UMAP in combination with K-means clustering (silhouette coefficient = 0.942). A stable 2-cluster data structure was identified, reflecting a qualitative difference between groups of employees with moderate (78%) and high (22%) levels of well-being. All measures used showed statistically significant differences between clusters (p<0.001, effect sizes r=0.405-0.672). Correlation analysis of the UMAP space revealed the dominance of a general wellbeing factor (first axis) with a specific role for Economic security as a partially independent measure (second axis). The results obtained not only make a significant contribution to understanding the interaction of the components of subjective employee well-being, confirm its systemic nature, and provide empirical grounds for developing differentiated strategies to improve well-being but also demonstrate the high applicability of nonlinear dimension reduction methods for analyzing the structure of psychometric data.