到底是固定还是随机？
2018-Apr-27更新
Xu SZ. Advanced Statistical Methods for Estimating Genetic Variances in Plants. in Plant breeding review vol. 22 2003
Cockerham (1980) further clarified the difference between a fixed effect model and a random effect model. When the founders are not randomly sampled, the genetic effects (first moments) are considered to be the parameters of interest and the model is a fixed model. Under the fixed effect model, researchers are primarily interested in the genetic differences of the founders under investigation and have no desire to infer the genetic variance of the population from which the founders are sampled. On the other hand, if the founders are randomly sampled from a population, the genetic effects are considered as random variables. In this case, the purpose of the genetic analysis is to infer the genetic variance of the population from which the founders are drawn, leading to a random model.
Cockerham原文中是这样说的：
It is for estimation and hypothesis testing concerning gene action that I wish to review and compare some of the random and fixed entry approaches. Sometimes the breeder is working with populations such as varieties which are near-equilibrium populations. In this case many forms of breeding lead to individuals which can be considered to be random members of the population. The population then serves as a reference base with parameters for random members, and thus, the model for the individual with random gene effects. On the other hand, the breeder often has selected sets of material such as screened inbred lines or varieties, or such a varied collection of these, that it is hard to imagine that they could have any connection with some equilibrium population. Consequently, he tends to view his collection as a fixed set. Moreover, he may be interested only in possible derivatives of his material, and thus he has all of the genes of interest constituted in the material at hand, but of course not necessarily constituted in the best combinations.
一个效应到底应该当做固定还是随机通常令人困惑。如果已有惯例，例如父本、家系效应一般当做随机，而重复、性别当做固定，照搬就是。相反，对另外一些效应的处理如果没有多少文献支撑，就有点让人模棱两可。总不能没有规则地按照自己的喜好吧？Smith（2001）给了一个明确的信息，即在需要预测一个效应的未来表现时要随机，否则要固定，并举例说要预测品种（variety）的未来表现，而不希望预测环境效应。这样这个问题就很明确了。原文如下：
Smith A, Cullis B, Gilmour A. 2001. The Analysis of Crop Variety Evaluation Data in Australia. Australian & New Zealand Journal of Statistics, 43(2): 129–145.
One possibly contentious issue is the choice between fixed and random effects in the analysis. The standard text-book notion of effects being random if they have been sampled from a population and fixed if attention is confined only to those effects in the model (see Searle, 1971, for example) is unhelpful and can lead to a circular argument. In our opinion the choice depends on the aim of the analysis. In terms of variety effects our aim is to predict future performance. This is best achieved by assuming the effects to be random. We do not wish to predict environment effects. The effects could be assumed random in order to recover information on varieties, but the variance component for environments is usually so large that very little information is recovered. The magnitude of the component also means there is very little shrinkage of environment effects, with the result that BLUPs and BLUEs are almost identical. We therefore assume that environment effects are fixed.
