Component-Based Structural Equation Modeling
Symposium organised by Heungsun Hwang, Department of Psychology,
Chair: Heungsun Hwang, Thursday 23rd July, 14.55 - 16.15, Palmeston Lecture Theatre, Fisher Building.
Michel Tenenhaus, HEC Paris, France. A Criterion Based PLS Approach to Structural Equation Modelling.
Yoshio Takane, Department of Psychology, McGill University, Montreal, Canada. Symbolic Computation in Generalized Structured Component Analysis.
Irene R. R. Lu, Roland D. Thomas, and Ernest Kwan, Sprott
Heungsun Hwang, Department of Psychology,
ABSTRACTS
A Criterion Based PLS Approach to Structural Equation Modelling
Michel Tenenhaus
For more than two blocks, the properties of the Wold’s PLS algorithm for SEM have long remained unknown. We propose a more general approach based on a continuum going from a new mode A to the usual mode B. When a structural equation model based on J blocks X1,…, XJ of manifest variables is considered, we consider an optimization problem. Based on cancelling the derivatives of the Lagrangian functions related to these maximisation problems, an iterative algorithm is proposed. The convergence of the algorithm is proven when the Wold’s iterative procedure is used. That means that the bounded criterion to be maximized is increasing at each step of the procedure. When g is the absolute or squared value and ti = 0 for all i, PLS mode B + centroid or factorial scheme is found again. Our approach generalizes results of Hanafi on PLS mode B and of Krämer on PLS mode A.
Symbolic Computation in Generalized Structured Component Analysis
Yoshio Takane
Generalized structured component analysis (GSCA) has been proposed for path analysis with latent variables defined as exact linear combinations of observed variables. In contrast with the partial least squares (PLS) approach, GSCA systematically minimizes a single global loss function by an alternating least squares algorithm. Most often, simple analytic forms of updating equations, which significantly cut down the computation time, can be derived through symbolic manipulations of the loss function. However, updating equations typically depend on particular path models being fitted. To automate this process, we may use SUMOPack, a Mathematica based symbolic matrix manipulation tool developed by Shin-ichi Mayekawa. In this paper, we demonstrate possible uses of this package to develop an efficient computer program for GSCA. Examples are given to illustrate the method.
The Comparison of Component- and Covariance-Based Structural Equation Modeling Approaches: Bias and Confidence Interval Coverage
Irene R. R. Lu, Roland D. Thomas, and Ernest Kwan
Extant simulation studies of component- and covariance-based structural equation modeling approaches have largely downplayed the roles of parameter estimation bias and confidence interval coverage in statistical inference.
Through a series of
Based on the simulation results we provide some recommendations on choosing methods for latent variable modeling.
Regularized Generalized Structured Component Analysis
Heungsun Hwang
Generalized structured component analysis (GSCA) has been proposed as a component-based approach to structural equation modeling. In practice, GSCA may suffer from multicollinearity, i.e., high correlations among exogenous variables. GSCA has yet no remedy for this problem. Thus, a regularized extension of GSCA is proposed that integrates a ridge type of regularization into GSCA in a unified framework, thereby enabling to handle multicollinearity problems effectively. An alternating regularized least squares algorithm is developed for parameter estimation. An empirical application concerning customer satisfaction is presented to demonstrate the empirical usefulness of the proposed method. (60)