Heungsun Hwang

Generalized Structured Component Analysis.

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.

A comparative study on parameter recovery of three approaches to structural equation modeling

Traditionally, two approaches have been employed for structural equation modeling: covariance structure analysis and partial least squares. A third alternative, generalized structured component analysis, was introduced recently in the psychometric literature. The authors conduct a simulation study to evaluate the relative performance of these three approaches in terms of parameter recovery under different experimental conditions of sample size, data distribution, and model specification. In this study, model specification is the only meaningful condition in differentiating the performance of the three approaches in parameter recovery. Specifically, when the model is correctly specified, covariance structure analysis tends to recover parameters better than the other two approaches. Conversely, when the model is misspecified, generalized structured component analysis tends to recover parameters better. Finally, partial least squares exhibits inferior performance in parameter recovery compared with the other approaches. In particular, this tendency is salient when the model involves cross-loadings. Thus, generalized structured component analysis may be a good alternative to partial least squares for structural equation modeling and is recommended over covariance structure analysis unless correct model specification is ensured.

Generalized Constrained Canonical Correlation Analysis.

A method for generalized constrained canonical correlation analysis (GCCANO) is proposed that incorporates external information on both rows and columns of data matrices. In this method each set of variables is first decomposed into the sum of several submatrices according to the external information, and then canonical correlation analysis is applied to pairs of derived submatrices, one from each set, to explore linear relationships between them. Technically, the former amounts to projections of the data matrix onto the spaces spanned by matrices of external information, while the latter involves the generalized singular value decomposition of a matrix with certain metric matrices. GCCANO subsumes a number of existing methods as special cases. It generalizes various kinds of linearly constrained correspondence analysis as well as multivariate analysis of variance/canonical discriminant analysis. Permutation tests are applied to test the significance of canonical correlations obtained from GCCANO. Examples are given to illustrate the proposed method.

Symptom Dimensions of the Psychotic Symptom Rating Scales in Psychosis: A Multisite Study

The Psychotic Symptom Rating Scales (PSYRATS) is an instrument designed to quantify the severity of delusions and hallucinations and is typically used in research studies and clinical settings focusing on people with psychosis and schizophrenia. It is comprised of the auditory hallucinations (AHS) and delusions subscales (DS), but these subscales do not necessarily reflect the psychological constructs causing intercorrelation between clusters of scale items. Identification of these constructs is important in some clinical and research contexts because item clustering may be caused by underlying etiological processes of interest. Previous attempts to identify these constructs have produced conflicting results. In this study, we compiled PSYRATS data from 12 sites in 7 countries, comprising 711 participants for AHS and 520 for DS. We compared previously proposed and novel models of underlying constructs using structural equation modeling. For the AHS, a novel 4-dimensional model provided the best fit, with latent variables labeled Distress (negative content, distress, and control), Frequency (frequency, duration, and disruption), Attribution (location and origin of voices), and Loudness (loudness item only). For the DS, a 2-dimensional solution was confirmed, with latent variables labeled Distress (amount/intensity) and Frequency (preoccupation, conviction, and disruption). The within-AHS and within-DS dimension intercorrelations were higher than those between subscales, with the exception of the AHS and DS Distress dimensions, which produced a correlation that approached the range of the within-scale correlations. Recommendations are provided for integrating these underlying constructs into research and clinical applications of the PSYRATS.

An improved method for generalized constrained canonical correlation analysis

An improved method for generalized constrained canonical correlation analysis (GCCANO) is proposed. In the original GCCANO, data matrices were first decomposed into the sum of several matrices according to some external information on rows and columns of the data matrices. Decomposed matrices were then subjected to canonical correlation analysis (CANO). However, orthogonal decompositions of data matrices do not necessarily entail orthogonal decompositions of projectors defined by the data matrices. This latter property is crucial in additive partitionings of the total association between two sets of variables. Consequently, no additive partitionings of the total association was possible in the original GCCANO. In this paper two orthogonal decompositions of projectors were proposed that allow additive partitionings of the total association. Terms in the decompositions have straightforward interpretations. An improved method for GCCANO is developed based on the decompositions, while preserving the most important features of the original method. An example is given to illustrate the proposed method.

Regularized Linear and Kernel Redundancy Analysis

Redundancy analysis (RA) is a versatile technique used to predict multivariate criterion variables from multivariate predictor variables. The reduced-rank feature of RA captures redundant information in the criterion variables in a most parsimonious way. A ridge type of regularization was introduced in RA to deal with the multicollinearity problem among the predictor variables. The regularized linear RA was extended to nonlinear RA using a kernel method to enhance the predictability. The usefulness of the proposed procedures was demonstrated by a Monte Carlo study and through the analysis of two real data sets.

An extended redundancy analysis and its applications to two practical examples

An extension of redundancy analysis is proposed that allows analyzing a variety of directional relationships among multiple sets of variables. The proposed method subsumes an existing redundancy analysis method as a special case. It is also extended further to analyze more complex relationships among variables such as direct effects of observed exogenous variables, higher-order components and multi-sample comparisons. An alternating least-squares algorithm is developed for parameter estimation. A small simulation study is conducted to investigate the performance of the proposed method. Two real examples are given to illustrate the empirical use of the proposed method.

Generalized Constrained Multiple Correspondence Analysis.

A comprehensive approach for imposing both row and column constraints on multivariate discrete data is proposed that may be called generalized constrained multiple correspondence analysis (GCMCA). In this method each set of discrete data is first decomposed into several submatrices according to its row and column constraints, and then multiple correspondence analysis (MCA) is applied to the decomposed submatrices to explore relationships among them. This method subsumes existing constrained and unconstrained MCA methods as special cases and also generalizes various kinds of linearly constrained correspondence analysis methods. An example is given to illustrate the proposed method.

A functional analysis of deception detection of a mock crime using infrared thermal imaging and the Concealed Information Test

The purpose of this study was to utilize thermal imaging and the Concealed Information Test to detect deception in participants who committed a mock crime. A functional analysis using a functional ANOVA and a functional discriminant analysis was conducted to decrease the variation in the physiological data collected through the thermal imaging camera. Participants chose between a non-crime mission (Innocent Condition: IC), or a mock crime (Guilty Condition: GC) of stealing a wallet in a computer lab. Temperature in the periorbital region of the face was measured while questioning participants regarding mock crime details. Results revealed that the GC showed significantly higher temperatures when responding to crime relevant items compared to irrelevant items, while the IC did not. The functional ANOVA supported the initial results that facial temperatures of the GC elevated when responding to crime relevant items, demonstrating an interaction between group (guilty/innocent) and relevance (relevant/irrelevant). The functional discriminant analysis revealed that answering crime relevant items can be used to discriminate guilty from innocent participants. These results suggest that measuring facial temperatures in the periorbital region while conducting the Concealed Information Test is able to differentiate the GC from the IC.

Generalized structured component analysis : a component-based approach to structural equation modeling

Introduction Structural Equation Modeling Traditional Approaches to Structural Equation Modeling Why Generalized Structured Component Analysis? Generalized Structured Component Analysis Model Specification Estimation of Model Parameters Model Evaluation Example Other Related Component-Based Methods Appendix The Alternating Least-Squares Algorithm for Generalized Structured Component Analysis Appendix Extensions of the Least-Squares Criterion for Generalized Structured Component Analysis Appendix A Partial Least Squares Path Modeling Algorithm Basic Extensions of Generalized Structured Component Analysis Constrained Analysis Higher-Order Latent Variables Multiple Group Analysis Total and Indirect Effects Missing Data Summary Appendix The Imputation Phase of the Alternating Least-Squares Algorithm for Estimating Missing Observations Fuzzy Clusterwise Generalized Structured Component Analysis Fuzzy Clustering Fuzzy Clusterwise Generalized Structured Component Analysis Example: Clusterwise Latent Growth Curve Modeling of Alcohol Use among Adolescents Summary Appendix The Alternating Least-Squares Algorithm for Fuzzy Clusterwise Generalized Structured Component Analysis Appendix Regularized Fuzzy Clusterwise Generalized Structured Component Analysis Nonlinear Generalized Structured Component Analysis Introduction Nonlinear Generalized Structured Component Analysis Examples Summary Appendix Algorithms for Kruskals (1964a, b) Least-Squares Monotonic Transformations Generalized Structured Component Analysis with Latent Interactions Generalized Structured Component Analysis with Latent Interactions Probing of Latent Interaction Effects Testing Latent Interaction Effects in Partial Least Squares Path Modeling Example Summary Appendix The Alternating Least-Squares Algorithm for Generalized Structured Component Analysis with Latent Interactions Multilevel Generalized Structured Component Analysis Model Specification Parameter Estimation Example: The ACSI Data Summary Appendix The Alternating Least-Squares Algorithm for Two-Level Multilevel Generalized Structured Component Analysis Appendix The Three-Level Generalized Structured Component Analysis Model Regularized Generalized Structured Component Analysis Ridge Regression Regularized Generalized Structured Component Analysis Example Summary Appendix The Alternating Regularized Least-Squares Algorithm for Regularized Generalized Structured Component Analysis Lasso Generalized Structured Component Analysis Lasso Regression Lasso Generalized Structured Component Analysis Example: The Company-Level ACSI Data Summary Appendix The Alternating Coordinate-Descent Algorithm for Lasso Generalized Structured Component Analysis Dynamic Generalized Structured Component Analysis Introduction The Method Examples of Application to Real Functional Neuroimaging Data Summary and Discussion Appendix Algorithm for Dynamic Generalized Structured Component Analysis Functional Generalized Structured Component Analysis Functional Generalized Structured Component Analysis A Related Method: Functional Extended Redundancy Analysis Examples Summary Appendix The Alternating Regularized Least-Squares Algorithm for Functional Generalized Structured Component Analysis References Index