A structural equation model (SEM) for analyzing effective connectivity in brain

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A structural equation model (SEM) for analyzing
effective connectivity in brain

• Yoshio Takane
• McGill University
• with contributions by Kwanghee Jung and Heungsun
  Hwang

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Structural equation models (SEMs)

• Methods for investigating if hypothesized
  relationships among observed variables are
  consistent with data
• path analysis (sociology)
• simultaneous equation models
  
• 
  (econometrics)
• Latent variables to simplify the relationships
  among observed variables (psychometrics)

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A diagram of SEM
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SEM
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Fitting models

• Estimate model parameters in such a way as to
  minimize the sum of squared residuals under some
  side conditions

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Estimated regression coefficients
Coeff. Path Estimate S.E.
p-value a1 V5-gtV1 0.347 0.034
0 a2 SPC-gtV1 0.146 0.037
0 a3 V1-gtV5 0.601 0.058
0 a4 SPC-gtV5 0.307 0.047 0
a5 V1-gtSPC 0.335 0.069 0 a6
V5-gtSPC 0.404 0.062 0 a7
V1-gtV1 0.329 0.034 0 a8
V5-gtV5 -0.044 0.055 0.176 a9
SPC-gtSPC 0.052 0.045 0.136 d1
V1 0.267 0.032 0 m1
V1-gtV5 -0.028 0.043 0.180 m2
SPC-gtV5 0.018 0.047 0.288
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Further work

• Simultaneous analysis of multiple subjects
  multiple-group analysis, multilevel analysis
• More than one latent variable per ROI
• Differential weightings of measurement and
  structural equations
• Handling excess serial correlations
• User-friendly software

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