非独立试验数据的一般线性混合模型分析

Analysis of Dependent Data Based on General Linear Mixed Model

传统方差分析模型的假设条件之一是试验数据相互独立,实际的试验数据未必能满足其条件,这使方差分析的应用范围和分析的效果受到限制。近年来,一般线性混合模型得到发展,为分析非独立试验数据提供了新途径。本文讨论了一般线性混合模型分析非独立试验数据的方法及其在SAS软件的实现,对小麦品比和玉米灌溉2个不同试验的非独立数据进行了一般线性混合模型与方差分析模型的对比分析。结果表明,与传统方差分析法相比,一般线性混合模型数据拟合效果好,在小麦品比试验使小麦品系效应比较的平均标准误降低18.4%,平均分析相对效率为1.5,而在玉米灌溉试验使灌溉效应比较和品种×灌溉交互效应比较的平均标准误降低9.1%￣10.8%,平均分析相对效率均约为1.2。因此,对非独立试验数据,一般线性混合模型分析的准确性和效率要比传统方差分析模型高。

One assumption of the models of traditional analysis of variance is that data are independent, which limits the application and power of the analysis of variance. Recently, general linear mixed models accounting for the dependence of data have been developed. The theory of general linear mixed model for analyzing dependent data and its implementation using software SAS were discussed in this paper, and the performance of general linear mixed model with the analysis of variance based on analyzing 2 data sets from a wheat line trial and a maize-irrigation trial were compared. The result showed that in comparison with the analysis of variance, the general linear mixed model fitted the data sets better, reduced standard error for wheat line effect contrast averagely by 18.4%, average relative efficiency was 1.5, and reduced standard error for irrigation effect contrast and variety-irrigation interaction contrast averagely by 9.1%- 10.8 %, average relative efficiency was 1.2. Hence, the general linear model is more efficient than the analysis of variance for analysis of dependent data.