Residuals in the GMANOVA–MANOVA model with rank restrictions on the mean parameters is considered. The main objective is to define residuals useful for evaluating the reduced rank restriction model. We decompose linear spaces into four subspaces as it can be done for the Extended Growth Curve model with two “profiles”. The new residuals are defined by orthogonal projections on these subspaces. It is discussed how the new residuals can be used to test model assumptions.

中文翻译：

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GMANOVA-MANOVA 模型中具有参数秩限制的残差

考虑了 GMANOVA-MANOVA 模型中对平均参数有秩限制的残差。主要目标是定义对评估降阶限制模型有用的残差。我们将线性空间分解为四个子空间，因为它可以用于具有两个“轮廓”的扩展增长曲线模型。新残差由这些子空间上的正交投影定义。讨论了如何使用新残差来测试模型假设。