title: Circular piecewise regression with applications to cell-cycle data.
abstract: Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell-cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology.
authors.affiliation: Departamento de Estadística e I.O., Universidad de Valladolid, 47011 Valladolid, Spain.
authors.forename: Cristina
authors.initials: C
authors.lastname: Rueda
authors.affiliation: Departamento de Estadística e I.O., Universidad de Valladolid, 47011 Valladolid, Spain.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Fernández
authors.affiliation: Departamento de Estadística e I.O., Universidad de Valladolid, 47011 Valladolid, Spain.
authors.forename: Sandra
authors.initials: S
authors.lastname: Barragán
authors.affiliation: Department of Statistics, University of Oxford, Oxford, U.K., and Department of Statistics, University of Leeds, Leeds, U.K.
authors.forename: Kanti V
authors.initials: KV
authors.lastname: Mardia
authors.affiliation: Biostatistics and Computational Biology Branch NIEHS (NIH), Research Triangle Park, NC, U.S.A.
authors.forename: Shyamal D
authors.initials: SD
authors.lastname: Peddada
mesh_terms: D001683:Biological Clocks; D002453:Cell Cycle / Q000235:genetics; D003198:Computer Simulation; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D012044:Regression Analysis; D012440:Saccharomyces / Q000166:cytology / Q000235:genetics
keywords: Change points; Circular data; Circular-circular regression; Gene expression; Generalized AIC; Von Mises distribution