[1 point] What are the number of parameters to be estimated of each
type (path coefficients/direct effects, variances, covariances)?
Direct Effects: 8
Variances: 6
Covariances: 1
[1 point] What is the model degree of freedom?
Data Observed p= 6*(6+1)/2 = 21
Estimated Parameters q = 8 + 6 + 1 = 15
Model degree of freedom 21-15 = 6
[1.5 point] What is the total effect of variable ‘C’ on variable ‘D’ in terms of path coefficients? You can assume that the direct effect (or path coefficient) of variable 𝑖 on variable 𝑗 is 𝛽𝑖𝑗 (e.g., the direct effect of ‘C’ on ‘D’ can be represented by 𝛽𝐶𝐷).
Total effect = \(B_{cd}\) + (\(B_{ce}\) x \(B_{ed}\)) + (\(B_{cb}\) x \(B_{bd}\))
[1.5 point] What is the total effect of variable ‘A’ on variable ‘D’ in terms of path coefficients?
Total effect = (\(B_{ab}\) + \(B_{af}\) + \(B_{fb}\)) x \(B_{bd}\)
[Bonus* 2 points] Write the path model in the equation form. You can use any notation (e.g., LISREL) as long as you explain what each variable denotes. Start by identifying the number of exogenous and endogenous variables.
Exogenous: 2 Endogenous: 4
\(Y_1\) = \(Y_{11}\) \(Y_{12}\) \(Y_{13}\) \(X_1\) + \(\beta_{14}\) \(Y_1\) + \(\epsilon_1\) \(\epsilon_2\)
\(Y_2\) = \(Y_{21}\) \(Y_{22}\) \(Y_{23}\) \(X_2\) + \(\beta_{24}\) \(Y_2\) + \(\epsilon_3\) \(\epsilon_4\)