Resumen de Pathmox approach: segmentation trees in partial least squares path modeling

Gastón Sánchez Trujillo

• Sometimes we must face the fact that the variables and concepts of interest in our models cannot be observed nor measured directly, In these cases we refer to them as theoretical constructs or latent variables. These variables are very common in social sciences. For instance, psychologists speak of satisfaction, sociologists refer to social status, and economists speak of economic development. When researchers work with theoretical concepts they usually conceive of expected relationships between two or more latent variables, they analyze the relationships, and propose theories and models. For such purposes structural equation modeling (SEM) is a statistical methodology with great flexibility and modeling power.

  Partial Least Squares Path Modeling (PLS-PM), also known as Structural Equation Modeling by PLS approach, is a methodology of multivariate data analysis that allows for modeling complex cause-effect relationships involving latent and observed variables. Developed by Herman Wold, PLS-PM was designed as a complementary technique to the covariance-based framework of SEM. Currently, typical applications of PLS-PM can be found within marketing and management studies especially those related with customer satisfaction and other types of intangibles measurement.

  Traditionally, SEM approaches assume homogeneity over the entire set of observations without considering any group structure. However, this assumption is unrealistic in many cases; for example, in consumer behavior research sources of heterogeneity can be due to customer age or gender.

  Analysts distinguish between two sources of heterogeneity: observed and unobserved. Heterogeneity is observed if it is possible to define segments based on an observed variable. Heterogeneity is unobserved when the variables that cause heterogeneity in the data are unknown beforehand. If population heterogeneity is not taken into account, conventional analysis may lead the analyst to inadequate results with a serious risk of drawing poor conclusions.

  In this dissertation we propose the PATHMOX approach which has been specifically designed to be used when observed sources of heterogeneity are available. Since much of the work on SEM depends on survey-based data, this type of studies usually provide sources of observed heterogeneity that can be used to detect different path models of segments in the population.

  Inspired by the segmentation scheme used in decision trees, PATHMOX produces a segmentation tree that has a similar structure to a binary decision tree. The main characteristic of the obtained tree is that each node corresponds to a different segment with its own particular path model. The aim of the algorithm is to select, among a set of segmentation variables (i.e. observed sources of heterogeneity), those having superior discriminant capacity in the sense that they separate the path models as much as possible. The split criterion in this case is used to decide whether two confronted structural models can be considered to be different. For this purpose, an F statistic-based test for assessing the equality of two regression models has been adapted for comparing two structural models by testing the equality of their path coefficients.

  In order to evaluate the sensitivity of the split criterion used in PATHMOX we have run a series of simulation studies. The goal is to assess the capabilities of the F-test when two path models are compared under different experimental conditions such as sample size, level of noise of disturbance terms, path coefficients, difference in variance of endogenous constructs, and data distributions. The results provide important evidence in favor of the adequate performance of the proposed F-test when it is applied for comparing two structural models in presence of non-normal data and skewed distributions. However, unbalanced segments and differences in the variance of the endogenous constructs may affect the sensitivity of the F-test.

  In regards to the practical aspect, two applications of PATHMOX with real data are described. The first application has to do with customer satisfaction.

  The second application involves a study on job satisfaction and motivation. We analyze the data using Visual Pathmox which is a program specifically designed to provide a graphical interface to calculate PLS path models and PATHMOX segmentation trees. Both analyses show the intuitive scheme, ease of interpretation, and meaningful description of PATHMOX with its potential to identify unexpected models for segments in the population.

  Keywords: Partial Least Squares Path Modeling, Structural Equation Modeling, Segmentation Trees, Pathmox Approach.