Studying the relationship between change and initial value in longitudinal studies

Blomqvist's problem of studying the relationship between change and initial value in a linear growth curve setting is reformulated from a random effects model perspective. First, a maximum likelihood estimate of the between-individual covariance matrix for a simple linear regression model with stochastic parameters is obtained via an EM algorithm as discussed by Laird and Ware. Second, the regression coefficient of the individual-specific slopes on the individual-specific intercepts is estimated as a ratio of elements of the between-individual covariance matrix as discussed by Zucker et al. Then a Fieller's type confidence interval for this ratio is proposed. Discussion is facilitated by recognizing the Laird-Ware model as a special case of a more general model discussed by Hocking.