Tudying 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.