12.1 In Example 12.1 estimate the six equations of the measurement model with scale mixing

(equivalent to Student t sampling) and degrees of freedom in each equation as additional unknowns in the model. Thus for the first measurement equation one would have yi1 ∼ N(αy1 + λ11Fi1, σ2 1 /ζi ),

ζi ∼ Gamma(0.5ν1, 0.5ν1).

with ν1 unknown. How does adopting this approach affect the posterior estimates for the structural coefficients {β, γ1, γ2}? Apply a posterior predictive check to the measurement model based on the classical SEM test statistic comparing actual and model covariance matrices.