Convex formulation for regularized estimation of structural equation models

Abstract

Path analysis is a model class of structural equation modeling (SEM), which it describes causal relations among measured variables in the form of a multiple linear regression. This paper presents two estimation formulations, one each for confirmatory and exploratory SEM, where a zero pattern of the estimated path coefficient matrix can explain a causality structure of the variables. The original nonlinear equality constraints of the model parameters were relaxed to an inequality, allowing the transformation of the original problem into a convex framework. A regularized estimation formulation was then proposed for exploratory SEM using an l1-type penalty of the path coefficient matrix. Under a condition on problem parameters, our optimal solution is low rank and provides a useful solution to the original problem. Proximal algorithms were applied to solve our convex programs in a large-scale setting. The performance of this approach was demonstrated in both simulated and real data sets, and in comparison with an existing method. When applied to two real application results (learning causality among climate variables in Thailand and examining connectivity differences in autism patients using fMRI time series from ABIDE data sets) the findings could explain known relationships among environmental variables and discern known and new brain connectivity differences, respectively.

A Comparative Analysis of the Anxiety in Offenders of the Law Based on Structural Equational Models

“…Mathematically, these models are more complex to estimate what other multivariate models such as regression or exploratory factor analysis (Mclntosh & Gonzalez-Lima, 1994;Price, Laird, Fox, & Ingham, 2009). The great advantage of this type of models is that they allow to propose the type and direction of relationships that are expected to find among the various variables contained in it, for having to subsequently to estimate the parameters that are specified by the relations proposals at the theoretical level (Pruttiakaravanich & Songsiri, 2020). We analyzed the relationships between twenty-one constructs and two latent variables (physiological and cognitive).…”

Untitled

“…Structural equation modelling (SEM) is a class of multivariate models used for learning a causal relationship among variables (exploratory modelling) or for testing whether the model is best fit by given data (confirmatory modelling). A general SEM includes the observed and latent variables, while their relationships are explained by a linear model whose parameters explain the cause or influence from one variable to another (Pruttiakaravanich & Songsiri, 2020). SEM has been widely used in behavioral research, such as in psychology, sociology, business and medical research (Mclntosh & Gonzalez-Lima, 1994;Price, Laird, Fox, & Ingham, 2009).…”

Methods for Modeling and Evaluating Construction Disputes: A Critical Review

“…As discussed by [65], SEM represents a class of multivariate models that are utilized to determine a causal relationship between variables (exploratory modeling) or to investigate if a model is the most suitable for the data under study (confirmatory modeling).…”

“…SEM-based procedures have considerable benefits over second-generation regression methods, such as principal components analysis, factor analysis, discriminant analysis, or multiple regression [51], [52]. SEM procedures also give researchers more flexibility to work with both real and theoretical data [59], [68], [65]. See Table 4 for examples from the literature in which SEM was utilized in disputes and in construction-related studies.…”