Modern Multiple Imputation with Functional Data

TL;DR

This paper introduces a novel multiple imputation approach for sparsely sampled functional data, improving estimation accuracy for complex non-linear models and demonstrating effectiveness through simulations and a health study application.

Contribution

It proposes a new imputation method combining MissForest and Local Linear Forest, addressing limitations of existing methods for irregularly sampled functional data.

Findings

Modified imputation approach yields better estimates than traditional methods.

The new method performs well across various sparsity levels in simulations.

Application to health data reveals meaningful relationships between variables.

Abstract

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.