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.
Zerbe
G O
GO
Division of Biometrics, University of Colorado Health Sciences Center, Denver 820262.
Wu
M C
MC
Zucker
D M
DM
D000465:Algorithms; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D015233:Models, Statistical; D012044:Regression Analysis