Using IRT parameters as informative priors in second-order Bayesian latent growth modeling

In education, a wide variety of statistical methodologies are available to study change over time. For example, second-order latent growth models correct for item characteristics while estimating student-level growth. However, second-order latent growth models are difficult to estimate, with low convergence rates and high bias (Murphy, Beretvas, and Pituch, 2011). In attempting to correct this, I proposed and evaluated a new estimation method using the Kalman filter and informative priors for item parameters. This fully Bayesian estimation method was theoretically guaranteed to converge eventually, while informative parameters, theoretically justified within Item Response Theory, were hypothesized to reduce the mean squared error of parameter estimates. However, a simulation study found several scaling problems with the estimation method, and estimation using a real data set failed to converge. Discussion provides a few recommendations to correct these scaling problems.