Nonlinear redundancy analysis and canonical correspondence analysis based on polynomial regression
Nonlinear redundancy analysis and canonical correspondence analysis based on polynomial regression
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DOI：
10.2307/3071920
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发表时间：
2002-04-01
期刊：
影响因子：
4.8
通讯作者：
Legendre, P
中科院分区：
文献类型：
--
作者：
Makarenkov, V;Legendre, P
在统计文献中可用的各种形式的典型分析中，RDA（冗余分析）和CCA（典型对应分析）已成为生态研究的首选工具，因为它们认识到解释性和响应数据表的不同作用。数据表Y包含响应变量（例如，物种数据），而数据表X包含解释变量。RDA是多元线性回归的扩展;它使用X和Y中变量之间关系的线性模型。在CCA中，响应变量作为初始步骤进行卡方变换，但变换后的响应数据与X中的解释变量之间的关系仍然假设为线性。自然界中物种组合的变化与环境变量的变化呈线性关系，这并没有什么特别的原因。在模拟生态过程时，假设线性在大多数情况下是不现实的，只是因为没有更合适的分析方法。我们提出了两种基于多项式回归的典型分析的经验方法，以消除在对X和Y中的变量之间的关系建模时的线性假设。它们分别被称为多项式RDA和多项式CCA。并且可以被视为经典线性RDA和CCA的替代方案。由于分析使用解释变量的非线性函数，因此开发了在双标图中表示这些变量的新方法。这些方法的使用证明了对真实的数据集和使用模拟。在示例中，与标准线性RDA和CCA相比，新技术产生了由模型解释的Y的变化量的显著增加。进行新分析的免费软件可在欧空局的电子数据档案、生态档案中获得。
Among the various forms of canonical analysis available in the statistical literature, RDA (redundancy analysis) and CCA (canonical correspondence analysis) have become instruments of choice for ecological research because they recognize different roles for the explanatory and response data tables. Data table Y contains the response variables (e.g., species data) while data table X contains the explanatory variables. RDA is an extension of multiple linear regression; it uses a linear model of relationship between the variables in X and Y. In CCA, the response variables are chi-square transformed as the initial step, but the relationship between the transformed response data and the explanatory variables in X is still assumed to be linear. There is no special reason why nature should linearly relate changes in species assemblages to changes in environmental variables, When modeling ecological processes, to assume linearity is unrealistic in most instances and is only done because more appropriate methods of analysis are not available. We propose two empirical methods of canonical analysis based on polynomial regression to do away with the assumption of linearity in modeling the relationships between the variables in X and Y. They are called polynomial RDA and polynomial CCA, respectively. and may be viewed as alternatives to classical linear RDA and CCA. Because the analysis uses nonlinear functions of the explanatory variables, new ways of representing these variables in biplot diagrams have been developed. The use of these methods is demonstrated on real data sets and using simulations. In the examples, the new techniques produced a noticeable increase in the amount of variation of Y accounted for by the model, compared to standard linear RDA and CCA. Freeware to carry out the new analyses is available in ESA's Electronic Data Archive, Ecological Archives.