Comparing linear and nonlinear mixed model approaches to cosinor analysis
Comparing linear and nonlinear mixed model approaches to cosinor analysis
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DOI：
10.1002/sim.1560
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发表时间：
2003-10-30
影响因子：
2
通讯作者：
Crowley, TJ
中科院分区：
文献类型：
--
作者：
Mikulich, SK;Zerbe, GO;Crowley, TJ
余弦模型，用于由昼夜节律和其他生物节律控制的变量，是振幅和acrophase参数的非线性模型，其在变换时具有线性表示。利用线性余弦分析，每个谐波的幅度和顶相可以被计算为估计的线性回归系数的非线性函数。在这里，一个灵活的混合模型方法余弦分析被认为是，其中固定效应参数可以进入非线性作为acrophase和振幅为每个谐波或线性后，转换为回归系数。此外，随机效应可以非线性地作为受试者特异性与顶相和振幅的偏差进入，或者线性地作为受试者特异性与回归系数的偏差进入。固定效应也可能非线性进入，而随机效应线性进入。此外，我们评估是否包括高阶线性调和项作为随机效应，即Rao-Khatri“协方差调整”，提高精度。将delta方法应用于线性混合余弦模型参数的非线性函数以获得近似方差，产生的结果通常与非线性混合模型的结果相同。因此，传统的线性余弦分析通常可以用来估计和比较感兴趣的非线性参数，即幅度和acrophase，通过delta方法。这是有利的，因为非线性混合模型对于更复杂的模型可能具有收敛困难。然而，对于某些多组分析，不应使用线性余弦变换，我们澄清了这两种方法何时等效，何时不同。版权所有（C）2003约翰威利父子有限公司。
The cosinor model, used for variables governed by circadian and other biological rhythms, is a nonlinear model in the amplitude and acrophase parameters that has a linear representation upon transformation. With linear cosinor analysis, amplitude and acrophase for each harmonic can be computed as nonlinear functions of the estimated linear regression coefficients. Here a flexible mixed model approach to cosinor analysis is considered, where the fixed effect parameters may enter nonlinearly as acrophase and amplitude for each harmonic or linearly after transformation to regression coefficients. In addition, the random effects may enter nonlinearly as subject-specific deviations from the acrophases and amplitudes or linearly as subject-specific deviations from the regression coefficients. It is also possible for the fixed effects to enter nonlinearly while the random effects enter linearly. Additionally, we evaluate whether including higher order linear harmonic terms as random effects, that is, Rao-Khatri 'covariance adjustment', improves precision. Applying the delta method to nonlinear functions of the parameters from linear mixed cosinor models to obtain approximate variances produces results that are often identical to results from nonlinear mixed models. Consequently, traditional linear cosinor analysis can often be used to estimate and compare the nonlinear parameters of interest, that is, amplitudes and acrophases, via the delta method. This is advantageous since the nonlinear mixed model may have convergence difficulties for more complex models. However, for some multiple-group analyses, the linear cosinor transformation should not be used and we clarify when the two methods are equivalent and when they differ. Copyright (C) 2003 John Wiley Sons, Ltd.