Consumer engagement (CE) refers to the interaction between a customer and an organization, such as company or brand, through various online or offline channels. Our study concerned the interplay among CEs with multiple objects in a fashion consumption context. In our qualitative research, CE was defined as Cognitive, Emotional and Behavioral investments made by consumers in fashion-related interactions. We identified the focal objects of CE, such as Fashion, Brand and Sales assistant. Moreover, we investigate the effect of involvement on CE. The involvement is focused on the commitment to the same three objects as CE. Then, we develop conceptual models associated with CEs and involvements and employ structural equation modeling (SEM) to examine their interplay. The quantitative research collected data for measuring CEs and involvements with Likert scale. When observed Likert scale data are not approximately normally distributed, we propose quantifying the data. Nonlinear principal component analysis (NPCA) obtains optimally scaled data by quantifying Likert scale data and computes principal component scores of the optimally scaled data. SEM combined with NPCA is referred to as NPCA-SEM. In the analysis of our research data, we compare the goodness of fit of conceptual models obtained from NPCA-SEM with that from ordinal SEM and examine the performance of NPCA-SEM.
