The Pathmox approach for PLS path modeling segmentation

Abstract

Modeling has very often failed to live up to expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics, psychographics or consumption constitute potential sources of heterogeneity. In such cases, the assumption of "one model fits all" is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub-populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in Partial Least Squares Path Modeling (PLS-PM). The idea behind Pathmox is to build a tree of path models that have look-alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an F statistic comparing two structural models, which test the identity of two regression models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured Satisfaction among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting PLS-PM heterogeneity. Keywords: Heterogeneity, Partial Least Squares Path Modeling, Segmentation, Model Comparison, Segmentation Trees. IntroductionIn survey research, it is very often taken for granted that a single model will represent the whole population that is, homogeneity is presumed for all the individuals. However, it is sometimes reasonable to cast doubt on such supposed homogeneity, and it is even logical to assume that groups have different behaviors. This is especially true of market research studies, where different customers/users may have different needs ([1], [2], [3] and [4]). If we do not consider the possible existence of segments in our population, the one-size-fits-all solution might be inappropriate and may generate inaccurate and/or inadequate results. This is particularly the case of Structural Equation Modeling (SEM) studies, where variables of socio-demographics, psychographics or consumption may stem from potential sources of heterogeneity. As [3] pointed out SEM has become a quasi-standard in marketing research. Its main advantages are: it allows to model latent concepts together with observed variables; researchers can test their current knowledge of phenomena using information gathered from the data; and they can validate theories, establish the main drivers of a phenomenon, measure intangibles, and advance new hypotheses. Regarding the problem of customer satisfaction, Partial Least Squares Path Modeling (PLS-PM) has become a reference methodology ([5] [13]). PLS-PM is based on an iterat...

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