Dynamic GSCA (Generalized Structured Component Analysis) with Applications to the Analysis of Effective Connectivity in Functional Neuroimaging Data
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We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also incorporates direct and modulating effects of input variables on specific latent variables and on connections between latent variables, respectively. An alternating least square (ALS) algorithm is developed for parameter estimation. An improved bootstrap method called a modified moving block bootstrap method is used to assess reliability of parameter estimates, which deals with time dependence between consecutive observations effectively. We analyze synthetic and real data to illustrate the feasibility of the proposed method.
Key wordsgeneralized structured component analysis (GSCA) structural equation modeling (SEM) longitudinal and time series data alternating least squares (ALS) algorithm a modified moving block bootstrap method functional neuroimaging effective connectivity
The work reported in this paper has been supported by a postdoctoral fellowship from the Mind Foundation of British Columbia to the first author, the Social Sciences and Humanities Research Council of Canada (SSHRC) grant 36952 and the Natural Sciences and Engineering Research Council of Canada (NSERC) discovery grant 10630 to the second author, and salary awards from the Canadian Institutes of Health Research (CIHR) and the Michael Smith Foundation for Health Research (MSFHR) to the fourth author. We are thankful to Dr. Henk Kiers for providing a Matlab routine for the ten Berge and Nevels algorithm used to update w’s. We are also grateful to Dr. Liang Wang for providing the memory data and his practical advice. Matlab programs that carried out the computations reported in the paper are available upon request.
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