I employ a panel dataset (4,191 participants; 20,618 person-year observations) to model income dynamics. My model is as follows,
log(y_{it}) =X\beta + \lambda_t*\alpha_i+\delta_t (u_{it} +v_{it}) \\ u_{it} = \rho * u_{it-1} +\epsilon_{it}, \\ \alpha_i \sim N(0, \sigma^2_{\alpha}), \epsilon_{it} \sim N(0,\sigma^2_{\epsilon}), v_{it} \sim N(0,\sigma^2_{v})\\
y_{it} is annual earnings. X include age and its square. Both \lambda_t and \delta_t are loading factors. \alpha_i is permanent component, and u_{it} +v_{it} is transitory component.
How should I perform sensitivity analysis? Can I follow the methodology on pages 159-161 of Bayesian Data Analysis and compare the posterior predictive distributions of four test statistics—max(y), min(y), mean(y), and sd(y)—with the observed values of the test statistics?