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We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects\u2019 wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00539.x","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T15:10:01Z","timestamp":1141398601000},"page":"179-199","source":"Crossref","is-referenced-by-count":280,"title":["Wavelet-based Functional Mixed Models"],"prefix":"10.1093","volume":"68","author":[{"given":"Jeffrey S.","family":"Morris","sequence":"first","affiliation":[{"name":"University of Texas MD Anderson Cancer Center , Houston , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raymond J.","family":"Carroll","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,3,3]]},"reference":[{"key":"2023040707474209700_","volume-title":"Technical Report RP SOR-03-03","author":"Abramovich","year":"2003"},{"key":"2023040707474209700_","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1111\/1467-9868.00151","article-title":"Wavelet thresholding via a Bayesian approach","volume":"60","author":"Abramovich","year":"1998","journal-title":"J. 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