Biometrics Unit Technical Reports: Number BU-1560-M: Self-Modeling Regression with Random Effects (original) (raw)

In many longitudinal studies, the response can be modeled as a (discretely sampled) curve over time for each subject. Often these curves have a common shape function and individual subjects differ from the common shape by a transformation ofthe time and response scales. Lindstrom (1995) represented the common shape by a free-knot regression spline, and used a parametric random effects model to represent the differences between curves. We extend Lindstrom's work by representing the common shape by a penalized regression spline, and use a parametric random effects model to represent the differences between curves. The use of penalized regression splines allows for a generalization in the modeling, estimation, and testing of parameters and is easily implemented. An iterative two-step algorithm is proposed for fitting the model. Conditional on the fitted common shape model, it is possible to fit and test nonlinear mixed effects using standard methods. While the sieve parametric form of the model suggests that a conditional likelihood ratio test should be available for testing whether the shape varies with a time invariant covariate, the null distribution of the likelihood ratio test may not be chisquared.