Measuring individual differences in reaction norms in field and experimental studies: a power analysis of random regression models
Measuring individual differences in reaction norms in field and experimental studies: a power analysis of random regression models
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DOI：
10.1111/j.2041-210x.2010.00084.x
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发表时间：
2011-08-01
影响因子：
6.6
通讯作者：
Reale, Denis
中科院分区：
文献类型：
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作者：
Martin, Julien G. A.;Nussey, Daniel H.;Reale, Denis
1. 过去几年，在进化和生态学领域，人们对使用混合效应（更具体地说，随机回归模型）测量反应规范的个体差异的兴趣迅速增长。然而，这些都是需要大量数据的方法，迄今为止，我们还没有投入多少精力来了解我们需要收集多少数据以及收集哪些类型的数据，以便有效、可靠地应用这些模型。2．我们进行模拟来解决三个核心问题。首先，收集足够数据以使用随机回归模型测试个体变异的最佳抽样策略是什么？其次，在精度难以评估的情况下，我们是否可以确信，未能使用随机回归检测可塑性的显着方差代表了生物学现实，而不是缺乏统计能力？最后，用一项或少数重复测量来审查个体的常见做法是否会提高或降低随机回归中估计个体变异的能力？3。我们还在 R 的“pamm”统计软件包中开发了一系列易于使用的函数，该软件包是免费提供的，这将使研究人员能够根据自己的数据进行更具体的类似功效分析。4。我们的结果揭示了潜在有用的经验法则：需要大数据集（N > 200）来评估个体特定斜率的方差；大约 0.5 的个体数量/每个个体的观察数量比率始终产生检测随机效应的最高功效；具有一次或少量观察结果的个人通常不应受到审查，因为这会降低检测可塑性差异的能力。5。我们讨论了这些模拟和剩余挑战的更广泛影响，并提出了一种标准化结果的新方法，以更好地促进实证研究结果的比较。
1. Interest in measuring individual variation in reaction norms using mixed-effects and, more specifically, random regression models have grown apace in the last few years within evolution and ecology. However, these are data hungry methods, and little effort to date has been put into understanding how much and what kind of data we need to collect in order to apply these models usefully and reliably.2. We conducted simulations to address three central questions. First, what is the best sampling strategy to collect sufficient data to test for individual variation using random regression models? Second, on occasions when precision is difficult to assess, can we be confident that a failure to detect significant variance in plasticity using random regression represents a biological reality rather than a lack of statistical power? Finally, does the common practice of censoring individuals with one or few repeated measures improve or reduce power to estimate individual variation in random regressions?3. We have also developed a series of easy-to-use functions in the 'pamm' statistical package for R, which is freely available, that will allow researchers to conduct similar power analyses tailored more specifically to their own data.4. Our results reveal potentially useful rules of thumb: large data sets (N > 200) are needed to evaluate the variance of individual-specific slopes; a number of individuals/number of observations per individual ratio of approximately 0.5 consistently yielded the highest power to detect random effects; individuals with one or few observations should not generally be censored as this reduces power to detect variance in plasticity.5. We discuss the wider implications of these simulations and remaining challenges and suggest a new way to standardize results that would better facilitate the comparison of findings across empirical studies.