  This work considers the problem of fitting functional models with sparsely
and irregularly sampled functional data. It overcomes the limitations of the
state-of-the-art methods, which face major challenges in the fitting of more
complex non-linear models. Currently, many of these models cannot be
consistently estimated unless the number of observed points per curve grows
sufficiently quickly with the sample size, whereas, we show numerically that a
modified approach with more modern multiple imputation methods can produce
better estimates in general. We also propose a new imputation approach that
combines the ideas of {\it MissForest} with {\it Local Linear Forest} and
compare their performance with {\it PACE} and several other multivariate
multiple imputation methods. This work is motivated by a longitudinal study on
smoking cessation, in which the Electronic Health Records (EHR) from Penn State
PaTH to Health allow for the collection of a great deal of data, with highly
variable sampling. To illustrate our approach, we explore the relation between
relapse and diastolic blood pressure. We also consider a variety of simulation
schemes with varying levels of sparsity to validate our methods.
