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\(L\) models and multiple regressions designs. (English) Zbl 1247.62173

Summary: Given an orthogonal model \(\lambda=\sum_{i=1}^m X_i\alpha_i\), an \(L\) model \(y=L(\sum_{i=1}^{m}X_{i}\alpha_{i})+e\) is obtained, and the only restriction is the linear independence of the column vectors of matrix \(L\). Special cases of the \(L\) models correspond to blockwise diagonal matrices \(L = D(L_{1},\dots, L_{ c })\). In multiple regression designs this matrix will be of the form \(L=D(\hat{X}_{1},\dots,\hat{X}_{c}\)) with \(\hat{X}_{j}\), \(j=1,\dots,c\) the model matrices of the individual regressions, while the original model will have fixed effects. In this way, we overcome the usual restriction of requiring all regressions to have the same model matrix.

MSC:

62J05 Linear regression; mixed models
15A99 Basic linear algebra
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