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Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The parametric components of the single-index models are estimated via quasi-score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit-flies (medflies).<\/jats:p>","DOI":"10.1111\/1467-9868.00393","type":"journal-article","created":{"date-parts":[[2004,12,28]],"date-time":"2004-12-28T19:38:40Z","timestamp":1104262720000},"page":"405-423","source":"Crossref","is-referenced-by-count":67,"title":["Functional Quasi-Likelihood Regression Models with Smooth Random Effects"],"prefix":"10.1093","volume":"65","author":[{"given":"Jeng-Min","family":"Chiou","sequence":"first","affiliation":[{"name":"National Health Research Institutes , Taipei , Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hans-Georg","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"University of California , Davis , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jane-Ling","family":"Wang","sequence":"additional","affiliation":[{"name":"University of California , Davis , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,4,25]]},"reference":[{"key":"2023033000105506100_","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1080\/01621459.1998.10473755","article-title":"Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion)","volume":"93","author":"Brumback","year":"1998","journal-title":"J. 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