A comparison of methods for estimating quadratic effects in nonlinear structural equation models.

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

doi:10.1037/a0027539

Cited by 52 publications

(53 citation statements)

References 67 publications

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“…Furthermore, [20] puts forth a hierarchical Bayesian nonlinear modeling approach in which unknown random parameters capture the strength and directions of causal links among variables. Several other studies adopt polynomial SEMs, which offer an immediate extension to classical linear SEMs; see e.g., [18], [21], [23], [39]. In all these contemporary approaches, it is assumed that the network connectivity structure is known a priori, and developed arXiv:1610.06551v1 [stat.AP] 20 Oct 2016 algorithms only estimate the unknown edge weights.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Structural Vector Autoregressive Models With Application to Directed Brain Networks

Shen

Giannakis

Baingana³

2019

IEEE Trans. Signal Process.

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Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that causal dependencies arise due to contemporaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that leverage both contemporaneous and time-lagged nodal data have recently been put forth. Albeit simple and tractable, linear SVARMs are quite limited since they are incapable of modeling nonlinear dependencies between neuronal time series. To this end, the overarching goal of the present paper is to considerably broaden the span of linear SVARMs by capturing nonlinearities through kernels, which have recently emerged as a powerful nonlinear modeling framework in canonical machine learning tasks, e.g., regression, classification, and dimensionality reduction. The merits of kernel-based methods are extended here to the task of learning the effective brain connectivity, and an efficient regularized estimator is put forth to leverage the edge sparsity inherent to real-world complex networks. Judicious kernel choice from a preselected dictionary of kernels is also addressed using a data-driven approach. Extensive numerical tests on ECoG data captured through a study on epileptic seizures demonstrate that it is possible to unveil previously unknown causal links between brain regions of interest.Index Terms-Network topology inference, structural vector autoregressive models, nonlinear models †

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Section: Introductionmentioning

confidence: 99%

Nonlinear Structural Vector Autoregressive Models With Application to Directed Brain Networks

Shen

Giannakis

Baingana³

2019

IEEE Trans. Signal Process.

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“…Recognizing that summands in the regularization term of (14) can be written as (14) is a convex problem admitting a globally-optimal solution. Exploiting the structure inherent to (14), the next section develops inference algorithms for unveiling the unknown network topology.…”

Section: Kernel-based Topology Estimationmentioning

confidence: 99%

“…Since the decoupled convex cost in (14) reduces to a weighted version of the group Lasso solver, it is prudent to first define the change of variables ζ ij := K…”

Section: B Proximal Gradient Iterationsmentioning

confidence: 99%

Kernel-Based Structural Equation Models for Topology Identification of Directed Networks

Shen

Baingana

Giannakis

2017

IEEE Trans. Signal Process.

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Abstract-Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or rumors propagate. The appeal of SEMs in these settings stems from their simplicity and tractability, since they typically assume linear dependencies among observable variables. Acknowledging the limitations inherent to adopting linear models, the present paper advocates nonlinear SEMs, which account for (possible) nonlinear dependencies among network nodes. The advocated approach leverages kernels as a powerful encompassing framework for nonlinear modeling, and an efficient estimator with affordable tradeoffs is put forth. Interestingly, pursuit of the novel kernel-based approach yields a convex regularized estimator that promotes edge sparsity, and is amenable to proximal-splitting optimization methods. To this end, solvers with complementary merits are developed by leveraging the alternating direction method of multipliers, and proximal gradient iterations. Experiments conducted on simulated data demonstrate that the novel approach outperforms linear SEMs with respect to edge detection errors. Furthermore, tests on a real gene expression dataset unveil interesting new edges that were not revealed by linear SEMs, which could shed more light on regulatory behavior of human genes.

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“…We have used indicator reliability because of it has been shown to affect power to detect interaction effect in a latent variable interaction model (Harring et al, 2012). We chose the indicator reliabilities to be equal across the 12 indicator variables.…”

Section: Simulation Designmentioning

confidence: 99%

Estimating Three-way Latent Interaction Effects in Structural Equation Modeling

Urge

Makambi

Wanjoya

2016

IJSP

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A Monte Carlo simulation was performed for estimating and testing hypotheses of three-way interaction effect in latent variable regression models. A considerable amount of research has been done on estimation of simple interaction and quadratic effect in nonlinear structural equation. The present study extended to three-way continuous latent interaction in structural equation model. The latent moderated structural equation (LMS) approach was used to estimate the parameters of the three-way interaction in structural equation model and investigate the properties of the method under different conditions though simulations. The approach showed least bias, standard error,and root mean square error as indicator reliability and sample size increased. The power to detect interaction effect and type I error control were also manipulated showing that power increased as interaction effect size, sample size and latent covariance increased.

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A comparison of methods for estimating quadratic effects in nonlinear structural equation models.

Cited by 52 publications

References 67 publications

Nonlinear Structural Vector Autoregressive Models With Application to Directed Brain Networks

Nonlinear Structural Vector Autoregressive Models With Application to Directed Brain Networks

Kernel-Based Structural Equation Models for Topology Identification of Directed Networks

Estimating Three-way Latent Interaction Effects in Structural Equation Modeling

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