Biomaterial Database

Penalized Least Squares for Structural Equation Modeling with Ordinal Responses. 2022

Po-Hsien Huang

Department of Psychology, National Cheng Kung University.

Statistical modeling with sparsity has become an active research topic in the fields of statistics and machine learning. Because the true sparsity pattern of a model is generally unknown aforehand, it is often explored by a sparse estimation procedure, like least absolute shrinkage and selection operator (lasso). In this study, a penalized least squares (PLS) method for structural equation modeling (SEM) with ordinal data is developed. PLS describes data generation by an underlying response approach, and uses a least squares (LS) fitting function to construct a penalized estimation criterion. A numerical simulation was used to compare PLS with existing penalized likelihood (PL) in terms of averaged mean square error, absolute bias, and the correctness of the model. Based on these empirical findings, a hybrid PLS was also proposed to improve both PL and PLS. The hybrid PLS first chooses an optimal sparsity pattern by PL, then estimates model parameters by an unpenalized LS under the model selected by PL. We also extended PLS to cases of mixed type data and multi-group analysis. All proposed methods could be realized in the R package lslx.

UI	MeSH Term	Description	Entries
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D000077272	Latent Class Analysis	A statistical algorithm used to analyze clusters of observed variables by constructing categorical unobserved or latent segment based on weighted analysis and the average probabilities. Such latent classes are used to infer variables whose relationships are not directly observed. In biomedical research, it is often used to categorize data that allows the determination of symptom clusters.	Latent Class Model,Latent Variable Modeling,Probabilistic Latent Semantic Analysis,Structural Equation Modeling,Latent Class Analyses,Latent Class Models,Latent Variable Modelings,Model, Latent Class,Modeling, Latent Variable,Modeling, Structural Equation,Structural Equation Modelings,Variable Modeling, Latent
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D016018	Least-Squares Analysis	A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model.	Rietveld Refinement,Analysis, Least-Squares,Least Squares,Analyses, Least-Squares,Analysis, Least Squares,Least Squares Analysis,Least-Squares Analyses,Refinement, Rietveld