  This work presents a new approach, called MISFIT, for fitting generalized
functional linear regression models with sparsely and irregularly sampled data.
Current methods do not allow for consistent estimation unless one assumes that
the number of observed points per curve grows sufficiently quickly with the
sample size. In contrast, MISFIT is based on a multiple imputation framework,
which has the potential to produce consistent estimates without such an
assumption. Just as importantly, it propagates the uncertainty of not having
completely observed curves, allowing for a more accurate assessment of the
uncertainty of parameter estimates, something that most methods currently
cannot accomplish. This work is motivated by a longitudinal study on
macrocephaly, or atypically large head size, in which electronic medical
records allow for the collection of a great deal of data. However, the sampling
is highly variable from child to child. Using MISFIT we are able to clearly
demonstrate that the development of pathologic conditions related to
macrocephaly is associated with both the overall head circumference of the
children as well as the velocity of their head growth.
