A Multivariate Multilevel Longitudinal Functional Model for Repeatedly Observed Human Movement Data

Edward Gunning; Steven Golovkine; Andrew J. Simpkin; Aoife Burke; Sarah Dillon; Shane Gore; Kieran Moran; Siobhan O'Connor; Enda Whyte; Norma Bargary

arXiv · 2408.08481

A Multivariate Multilevel Longitudinal Functional Model for Repeatedly Observed Human Movement Data

Edward Gunning·Steven Golovkine·Andrew J. Simpkin·Aoife Burke·Sarah Dillon·Shane Gore·Kieran Moran·Siobhan O'Connor·Enda Whyte·Norma Bargary

View original source ↗Read source document ↗Export metadata ↓

Abstract

Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to functional data analysis. It is now increasingly common to record the same movement repeatedly for each individual, resulting in curves that are serially correlated and can be viewed as longitudinal functional data. We present a new approach for modelling multivariate multilevel longitudinal functional data, with application to kinematic data from recreational runners collected during a treadmill run. For each stride, the runners' hip, knee and ankle angles are modelled jointly as smooth multivariate functions that depend on subject-specific covariates. Longitudinally varying multivariate functional random effects are used to capture the dependence among adjacent strides and changes in the multivariate functions over the course of the treadmill run. A basis modelling approach is adopted to fit the model -- we represent each observation using a multivariate functional principal components basis and model the basis coefficients using scalar longitudinal mixed effects models. The predicted random effects are used to understand and visualise changes in the multivariate functional data over the course of the treadmill run. In our application, our method quantifies the effects of scalar covariates on the multivariate functional data, revealing a statistically significant effect of running speed at the hip, knee and ankle joints. Analysis of the predicted random effects reveals that individuals' kinematics are generally stable but certain individuals who exhibit strong changes during the run can also be identified. A simulation study is presented to demonstrate the efficacy of the proposed methodology under realistic data-generating scenarios.

Explore related subjects

stat.ME stat.AP

Keep this discovery

BibTeX RIS

Edward Gunning, Steven Golovkine, Andrew J. Simpkin, Aoife Burke, Sarah Dillon, Shane Gore, Kieran Moran, Siobhan O'Connor, Enda Whyte, Norma Bargary. 2024-08-16. A Multivariate Multilevel Longitudinal Functional Model for Repeatedly Observed Human Movement Data. https://arxiv.org/abs/2408.08481

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗

arXiv2026

Generalized Ridge Refitting for the Lasso and Prediction Improvement Bounds

We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.

stat.ME↗

arXiv2026

Discretization in covariate-adaptive randomization: gains and losses

Covariate-adaptive randomization(CAR) is widely implemented in clinical trials to balance prognostic covariates across treatment arms. Continuous covariates are often discretized into strata in practice, yet their consequences are not clearly understood. This paper provides a comprehensive study of the impact of discretization on both the CAR design process and the inferential results thereafter. We establish the asymptotic properties of both imbalance measures and treatment effect estimators under discretized and non-discretized settings. Practical recommendations are given on when and how discretization should be employed. We show that discretization in design is generally recommended, as it enhances robustness against model misspecification. However, if the true model is known, the most efficient strategy is to balance covariates according to that model in the design. The theoretical results are corroborated by extensive simulation studies and an empirical application to a diabetes trial dataset. Together, the results clarify the gains and losses of discretization in CAR and pave the way for learning impact of discretization to other designs and beyond.

stat.ME↗