Multilevel functional principal components analysis in the case of unbalanced design and small number of subjects
Abstract
Multilevel Functional Principal Component Analysis (MFPCA) distinguishes two types of variability present in the
functional data with repeated measurements - the variability between subjects and the variability within subjects.
This technique is appropriate for detection of a subject-specic pattern and the
differences between functional data obtained from different sessions of the same
subject.
In the original article only balanced design is considered - for each subject
the same number of measurements is available. On the other hand the authors
claim, that the assumption of a balanced design is not restrictive and the method
itself is also able to deal with unbalanced data.
However, the MFPCA algorithm faces problems when i) the number of subjects is small, ii)
the variability within subjects is close to zero because their
observations are almost identical for all sessions, and iii) unbalanced design is
considered, where for some subjects the number of observations is significantly lower in
comparison to the remaining part of the dataset. In all such cases, MFPCA is not able to properly detect subject-specific profiles and a part of
the between subjects variability is mixed with within{subjects variability.
In this study we implement the algorithm which deals with the problem and
we validate the approach on an artificial and real dataset.
Go back