The Linear Model
The Linear Model
复制标题
线性模型
DOI：
10.1007/978-1-4612-5752-3_2
复制
发表时间：
1982
影响因子：
3
通讯作者：
A. Mclntosh
中科院分区：
文献类型：
--
作者：
A. Mclntosh
假设我们要分析 n 个测量值或观察值 y i 来了解它们如何依赖于 q 个其他测量值或观察值 Fl … F q 如果 F j 被认为是定量的，我们将其称为变量。如果 F j 被认为是定性的，我们将其称为因子，并使用符号 n j 来表示 F j 的级别数。 （换句话说，n j 是 F j 将 n 个测量值 y 分成的类数。）在本报告的其余部分中，我们将几乎专门处理方差模型的分析，即所有 F j 都是因子的模型。其中一些 F j 是变量的模型将被称为协方差模型的分析。我们将使用“因子设计”一词来描述所有（或几乎所有）因子 Fl … F q 的组合都令人感兴趣的实验。根据因素或设计的性质，嵌套模型很可能适合此类设计。
Suppose that we are to analyze n measurements or observations y i to see how they depend upon q other sets of measurements or observations Fl … F q If F j is considered quantitative, we will refer to it as a variate. If F j is considered qualitative, we will refer to it as a factor, and use the notation n j to denote the number of levels of F j . (In other words, n j is the number of classes into which F j divides the n measurements y.) In the balance of this report, we will deal almost exclusively with analysis of variance models, that is, models in which all the F j are factors. Models in which some of the F j are variates will be referred to as analysis of covariance models. We will use the phrase factorial design to describe any experiment in which all (or nearly all) of the combinations of the factors Fl … F q are of interest. Depending on the nature of the factors or the design, a nested model might well be appropriate in such a design.