Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models

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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Latent Variable and Structural Equation Models for Multivariate Data

Bayesian Statistical Modelling - Wiley Series in Probability and Statistics ◽

10.1002/9780470035948.ch12 ◽

2007 ◽

pp. 425-455 ◽

Cited By ~ 1

Keyword(s):

Latent Variable ◽

Structural Equation ◽

Structural Equation Models ◽

Multivariate Data

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Products of Variables in Structural Equation Models: Multiplicative Reticular Action Models

10.31234/osf.io/36y9n ◽

2019 ◽

Author(s):

Steven M. Boker ◽

Timo von Oertzen ◽

Andreas Markus Brandmaier

Keyword(s):

Latent Variables ◽

Latent Variable ◽

Structural Equation ◽

Structural Equation Models ◽

Equation Model ◽

Random Coefficients ◽

Action Model ◽

Action Models ◽

Special Case ◽

General Method

A general method is introduced in which variables that are products of other variables in the context of a structural equation model (SEM) can be decomposed into the sources of variance due to the multiplicands. The result is a new category of SEM which we call a Multiplicative Reticular Action Model (XRAM). XRAM can include interactions between latent variables, multilevel random coefficients, latent variable moderators, and novel constructs such as factors of paths and twin genetic decomposition of multilevel random coefficients. The method relies on an assumption that all variance sources in a model can be decomposed into linear combinations of independent normal standardized variables. Although the distribution of a variable that is an outcome of multiplication between other variables is not normal, the assumption is that it can be decomposed into sources that are normal if one takes into account the non-normality induced by the multiplication. The method is applied to an example to show how in a special case it is equivalent to known unbiased and efficient estimators in the statistical literature. Two simulations are presented that demonstrate the precision of the approximation and implement the method to estimate parameters in a multilevel autoregressive framework.

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