Factor structure and measurement invariance of conceptions of happiness in Korea and Canada: an application of penalized structural equation modeling in Mplus

This study aimed to illustrate how penalization (also known as regularization) can be used within the framework of structural equation modeling to examine the factor structure and measurement invariance for complex multi-dimensional constructs. The study examined the factor structure and measurement invariance of 36 items measuring seven conceptions of happiness in Korea and Canada. Penalized factor analysis was used to shrink the cross-loadings in factor analysis and predictive paths in a MIMIC model toward zero. The findings supported the hypothesized factor structure, with seven latent variables accounting for the inter-relationships between the 36 items. Target loadings were generally substantial. Although a small number of non-trivial cross-loadings were observed, the majority of non-target loadings were trivial, affirming a factor structure aligned with the theoretical framework. Measurement invariance analysis revealed a large number of non-invariant items across cultures. Penalized structural equation modeling proved effective in handling complex measurement and MIMIC models and allowed for the identification of otherwise unidentifiable models. Overall, the findings empirically validate the proposed seven-dimensional factor model of happiness conceptions, while emphasizing the importance of addressing measurement non-invariance across cultures. Furthermore, this study suggests potential areas for improvement, particularly in relation to the valuing happiness scale.