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Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non‐normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.
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Bond Breaking Kinetics in Mechanically Controlled Break Junction Experiments: A Bayesian Approach
Break junction experiments allow investigating electronic and spintronic properties at the atomic and molecular scale. These experiments generate by their very nature broad and asymmetric distributions of the observables of interest, and thus, a full statistical interpretation is warranted. We show here that understanding the complete lifetime distribution is essential for obtaining reliable estimates. We demonstrate this for Au atomic point contacts by adopting Bayesian reasoning to make maximal use of all measured data to reliably estimate the distance to the transition state, x‡, the associated free energy barrier, ΔG‡, and the curvature, v, of the free energy surface. Obtaining robust estimates requires less experimental effort than with previous methods and fewer assumptions and thus leads to a significant reassessment of the kinetic parameters in this paradigmatic atomic-scale structure. Our proposed Bayesian reasoning offers a powerful and general approach when interpreting inherently stochastic data that yield broad, asymmetric distributions for which analytical models of the distribution may be developed.
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- Award ID(s):
- 2225369
- PAR ID:
- 10484004
- Publisher / Repository:
- ACS
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry Letters
- Volume:
- 14
- Issue:
- 49
- ISSN:
- 1948-7185
- Page Range / eLocation ID:
- 10935 to 10942
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acs.jpclett.3c02643
