David A. Kenny
November 17, 1997

Illustration of Deriving Correlations in terms of Path Coefficients
Study
                                
  Rohner, R. P., Kean, K. J., & Cournoyer, D. E.  (1991).  Effects
     of corporal punishment, perceived caretaker warmth, and
     cultural beliefs on the psychological adjustment of children
     in St. Kitts, West Indies.  Journal of Marriage and the
     Family, 53, 681-693.
                                
Variables

     PP -- physical punishment
     CR -- caretaker rejection
     CB -- child beliefs
     PA -- psychological adjustment


Structural Equations

CR = .470PP + .883U
CB = .023PP + 1.000V
PA = .752CR + .172PP + .240CB + .610W
rUV = -.477

Tracing Rule

rCR,PP = .470
rCB,PP = .023
rCR,CB = (.470)(.023) + (.883)(1.000)(-.477) = -.410
rPA,PP = (.470)(.752) + (.023)(.240) + .172 = .531
rPA,CR = .752 + (.470)(.172) + (.023)(.470)(.240) +
                           (.883)(1.000)(.477)(.240) = .734
rCB,PA = .240 + (.023)(.172) + (.023)(.470)(.752) +
                          (.883)(1.000)(-.477)(.752) = -.065

First Law

rCR,PP = .470
rCB,PP = .023
rCR,CB = (.470)(.023) + (.883)(-.477)(1.000)  = -.410
rPA,PP = (.470)(.752) + (.023)(.240) + .172 = .531
rPA,CR = .752 + (.172)(.470) + (.240)(-.410) = .734
rCB,PA = .240 + (.752)(-.410) + (.172)(.023) = -.064


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