Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis.

Neuroimaging data is being increasingly utilized to address questions of individual difference. When examined with task-related fMRI (t-fMRI), individual differences are typically investigated via correlations between the BOLD activation signal at every voxel and a particular behavioral measure. This can be problematic because: 1) correlational designs require evaluation of t-fMRI psychometric properties, yet these are not well understood; and 2) bivariate correlations are severely limited in modeling the complexities of brain-behavior relationships. Analytic tools from psychometric theory such as latent variable modeling (e.g., structural equation modeling) can help simultaneously address both concerns. This review explores the advantages gained from integrating psychometric theory and methods with cognitive neuroscience for the assessment and interpretation of individual differences. The first section provides background on classic and modern psychometric theories and analytics. The second section details current approaches to t-fMRI individual difference analyses and their psychometric limitations. The last section uses data from the Human Connectome Project to provide illustrative examples of how t-fMRI individual differences research can benefit by utilizing latent variable models.

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Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽

10.3390/en13174290 ◽

2020 ◽

Vol 13 (17) ◽

pp. 4290

Author(s):

Dongmei Zhang ◽

Yuyang Zhang ◽

Bohou Jiang ◽

Xinwei Jiang ◽

Zhijiang Kang

Keyword(s):

Sensitivity Analysis ◽

Gaussian Processes ◽

Latent Variable ◽

History Matching ◽

Latent Variable Models ◽

High Dimensional ◽

Model Parameters ◽

Variable Model ◽

Assisted History Matching ◽

Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

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Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure

Educational and Psychological Measurement ◽

10.1177/00131644211008643 ◽

2021 ◽

pp. 001316442110086

Author(s):

Tenko Raykov ◽

Natalja Menold ◽

Jane Leer

Keyword(s):

Latent Variable ◽

Large Scale ◽

Present Note ◽

Interval Estimation ◽

Psychological Research ◽

Latent Variable Modeling ◽

Model Choice ◽

Modeling Methodology ◽

Level 3 ◽

Level 2

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.

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