"Modeling Longitudinal Fecundity Data through a Semiparametric Random
Effects Model"

Jeng-Min Chiou, National Health Research Institute, Tawiwan, R.O.C.
Hans-Georg Mueller and Jane-Ling Wang*, University of California at Davis,


Data on daily egg-laying for 1,000 female Mediterranean fruit flies were
collected throughout the lifetime of each fly.  This resulted in 1,000
fecundity curves recording the entire reproductive history and lifetime of
each fly. The goal is to explore reproductive patterns and their
connections to lifetime reproduction and longevity.

Since the data are fairly unstructured, we propose a class of
semiparametric regression models to describe the influence of covariates
on a longitudinal (or functional) response. The model includes indices,
which are linear functions of the covariates, unknown random functions of
the indices, and unknown variance functions. Several submodels of these
semiparametric random effects models are of particular interest. The
parametric components of the indices are estimated via quasi-score
estimating equations, and the unknown smooth random and variance functions
are estimated nonparametrically.  The procedure is illustrated with the
medfly fecundity data.