NONLINEAR ESTIMATION AND STATISTICAL TESTING OF PERIODS IN NONSINUSOIDAL LONGITUDINAL TIME SERIES WITH UNEQUIDISTANT OBSERVATIONS

Abstract

The analysis of multiple components is often used to modelbiological variables that show nonsinusoidal predictable changes of knownperiods. In general, to anticipate the periods is not easy, and even in caseswhen we have some a priori information, it is advisable to have a statisticaltool to test the chosen periods. In this work, we introduce a statisticalprocedure to estimate periods of longitudinal series by applying nonlinearregression techniques to the multiple sinusoidal model, as well as to thegeneral linear model. Approximate inferences about the parameters of the modelare carried out under the usual hypothesis of normality, independence, andconstant variance of the errors. Confidence intervals (CIs) for each individualparameter, as well as for the amplitude-acrophase pair or for any other subgroupof parameters of interest, can be computed. As in the linear analysis of multiplecomponents, it is possible to check the existence of rhythm by means of azero-amplitude test. The method also allows statistical testing of severalhypotheses related to the periods. For example, it is possible to test ifthe periods are equal to certain values of chronobiologic interest and tocheck if some components included in the model are harmonically related. Onthe other hand, when the fitted components have proximal periods, the methodallows one to verify if they are modeling the same or different spectral peaks.The method, which was validated by a simulation study for a model of two componentsand is illustrated by an example of modeling the diastolic blood pressureof two subjects, represents a new step in the development of statistical proceduresin chronobiology. (Chronobiology International, 18(2),285–308, 2001)

• Analysis of multiple components
• Longitudinaldata
• Nonlinear regression
• Period estimation
• Time series statistical methods