Extension to the PATHMOX Approach to Detect Which Constructs Differentiate Segments and to Test Factor Invariance: Application to Mental Health Data

In most cases, path modeling data come from surveys or researches that contain more information (i.e., observed heterogeneity) than is used for the path models definition. For instance, in many marketing studies like those of consumer satisfaction, it is usual to collect socio-demographic variables and psycho-demographic variables such as age, gender, social-status, or consumers’ habits that take no part in the path model but that can be extremely useful for segmentation purposes. In 2009, Gastón Sánchez introduced the PATHMOX methodology to incorporate the available external variables to identify different segments. The algorithm solves this problem by building a binary tree to detect those segments present in the population that cause the heterogeneity. The F-global test, based on the Fisher’s F for testing the equality of two regression models, is adapted and used, as a splitting criterion, to discover whether two structural models calibrated from two different segments (i.e., two successors of a node), can be considered to be different. However PATHMOX does not identify which of the block or variables indicators are responsible for the heterogeneity. In this article we propose to extend the PATHMOX methodology to test the equality of every endogenous equation of the structural model in order to compare all path coefficients of the structural model estimated in two segments.