Abstract
Functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations. However, there is no formal testing procedure to determine if functional methods are actually necessary. We propose a goodness‐of‐fit test for comparing parametric covariance functions against general nonparametric alternatives for both irregularly observed longitudinal data and densely observed functional data. We consider a smoothing‐based test statistic and approximate its null distribution using a bootstrap procedure. We focus on testing a quadratic polynomial covariance induced by a linear mixed effects model and the method can be used to test any smooth parametric covariance function. Performance and versatility of the proposed test is illustrated through a simulation study and three data applications.
Highlights
Functional data have become increasingly common in fields such as medicine, agriculture, and economics
We consider the case of testing if a simple linear mixed effects model is sufficient for longitudinal data or if a more complex functional data model is required
We first consider a dataset of diffusion tensor imaging (DTI) of intracranial white matter microstructure with dense, common sampling design for a group of normal and multiple sclerosis patients
Summary
Functional data have become increasingly common in fields such as medicine, agriculture, and economics. Zhong et al (2017) developed a general goodness-of-fit test that can be applied to many common parametric covariances These methods are ill-suited for the comparison between functional and longitudinal data models because they (a) fail to account for the underlying smoothness of the process and (b) require data observed at fixed time points for all subjects, i.e., a (fixed) common design The CD4 dataset has an irregular design where time points differ for each subject, so cannot be tested with these approaches. The objective of this article is to develop a testing procedure for comparing parametric longitudinal versus nonparametric functional data covariance models applied to repeated measured data with irregular and/or highly frequent sampling design.
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