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We investigate the estimation of parameters in the random coefficient autoregressive model. We consider a nonstationary RCA process and show that the innovation variance parameter cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for the remaining model parameters is proven so the unit root problem does not exist in the random coefficient autoregressive model.

We investigate the estimation of parameters in the random coefficient autoregressive model. We consider a nonstationary RCA process and show that the innovation variance parameter cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for the remaining model parameters is proven so the unit root problem does not exist in the random coefficient autoregressive model.

Literature addressing missing data handling for random coefficient models is particularly scant, and the few studies to date have focused on the fully conditional specification framework and "reverse random coefficient" imputation. Although it has not received much attention in the literature, a joint modeling strategy that uses random within-cluster covariance matrices to preserve cluster-specific associations (Yucel, 2011) is a promising alternative for random coefficient analyses. This study is apparently the first to directly compare these procedures. Analytic results suggest that both imputation procedures can introduce bias-inducing incompatibilities with a random coefficient analysis model. Problems with fully conditional specification result from an incorrect distributional assumption, whereas joint imputation uses an underparameterized model that assumes uncorrelated intercepts and slopes. Monte Carlo simulations suggest that biases from these issues are tolerable if the missing data rate is 10% or lower and the sample is comprised of at least 30 clusters with 15 observations per group. Further, fully conditional specification tends to be superior with intraclass correlations that are typical of cross-sectional data (e.g., ICC = 0.10), whereas the joint model is preferable with high values typical of longitudinal designs (e.g., ICC = 0.50). [This paper was published in "Multivariate Behavioral Research" v53 n5 p695-713 2018.]

Literature addressing missing data handling for random coefficient models is particularly scant, and the few studies to date have focused on the fully conditional specification framework and "reverse random coefficient" imputation. Although it has not received much attention in the literature, a joint modeling strategy that uses random within-cluster covariance matrices to preserve cluster-specific associations (Yucel, 2011) is a promising alternative for random coefficient analyses. This study is apparently the first to directly compare these procedures. Analytic results suggest that both imputation procedures can introduce bias-inducing incompatibilities with a random coefficient analysis model. Problems with fully conditional specification result from an incorrect distributional assumption, whereas joint imputation uses an underparameterized model that assumes uncorrelated intercepts and slopes. Monte Carlo simulations suggest that biases from these issues are tolerable if the missing data rate is 10% or lower and the sample is comprised of at least 30 clusters with 15 observations per group. Further, fully conditional specification tends to be superior with intraclass correlations that are typical of cross-sectional data (e.g., ICC = 0.10), whereas the joint model is preferable with high values typical of longitudinal designs (e.g., ICC = 0.50). [This paper was published in "Multivariate Behavioral Research" v53 n5 p695-713 2018.]