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However, estimations of model parameters, including the learning rate, require a demanding computational burden, especially when the data are collected over a long period. To overcome computational difficulty, we utilize an efficient sequential Monte Carlo method, dynamically weighted particle filter, in the estimations of model parameters. Alternatively, we consider a functional data analysis for the learning rates and the effect of the incentivization. Two approaches have led to reasonable estimations of learning rates. We present the estimated learning rates and the effect of incentivization on the learning rates from two approaches, as well as the comparisons of their results.<\/jats:p>","DOI":"10.1371\/journal.pone.0329940","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T17:48:57Z","timestamp":1756489737000},"page":"e0329940","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Comparison of sequential data analysis and functional data analysis for locomotor adaptation"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5045-1948","authenticated-orcid":true,"given":"Torin","family":"Quinlivan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kacy","family":"Kane","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher M.","family":"Hill","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Duchwan","family":"Ryu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"issue":"20","key":"pone.0329940.ref001","doi-asserted-by":"crossref","first-page":"2707","DOI":"10.1016\/j.cub.2016.08.012","article-title":"Seeing the errors you feel enhances locomotor performance but not learning","volume":"26","author":"RT Roemmich","year":"2016","journal-title":"Curr Biol"},{"issue":"10","key":"pone.0329940.ref002","doi-asserted-by":"crossref","first-page":"3519","DOI":"10.1152\/jn.00965.2014","article-title":"Two ways to save a newly learned motor pattern","volume":"113","author":"RT Roemmich","year":"2015","journal-title":"J Neurophysiol"},{"key":"pone.0329940.ref003","doi-asserted-by":"crossref","first-page":"459","DOI":"10.3389\/fnhum.2015.00459","article-title":"A reinforcement learning approach to gait training improves retention","volume":"9","author":"CJ Hasson","year":"2015","journal-title":"Front Hum Neurosci"},{"issue":"14","key":"pone.0329940.ref004","doi-asserted-by":"crossref","first-page":"4845","DOI":"10.1523\/JNEUROSCI.4390-13.2014","article-title":"Does the processing of sensory and reward-prediction errors involve common neural resources? 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