L models and multiple regressions designs

Elsa Moreira; João Tiago Mexia; Miguel Fonseca; Roman Zmyślony

doi:10.1007/s00362-009-0255-3

L models and multiple regressions designs

Elsa Moreira, João Tiago Mexia, Miguel Fonseca, Roman Zmyślony

CMA - Centro de Matemática e Aplicações

Research output: Contribution to journal › Conference article › peer-review

9 Citations (Scopus)

Abstract

Given an orthogonal model an L model is obtained, and the only restriction is the linear independency of the column vectors of matrix L. Special cases of the L models correspond to blockwise diagonal matrices L = D(L₁,..., L_c). In multiple regression designs this matrix will be of the form L = D(X̌₁,..., X̌_c)with X̌_j, j = 1,...,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.

Original language	English
Pages (from-to)	869-885
Number of pages	17
Journal	Statistical Papers
Volume	50
Issue number	4
DOIs	https://doi.org/10.1007/s00362-009-0255-3
Publication status	Published - 5 Aug 2009
Event	International Conference on Trends and Perspectives in Linear Statistical Inference, LinStat'2008 - Bedlewo, Portugal Duration: 21 Apr 2008 → 25 Apr 2008

Keywords

Commutative Jordan algebras
Cross-nested models
L models
Multiple regression models
Orthogonal models

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10.1007/s00362-009-0255-3

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title = "L models and multiple regressions designs",

abstract = "Given an orthogonal model an L model is obtained, and the only restriction is the linear independency of the column vectors of matrix L. Special cases of the L models correspond to blockwise diagonal matrices L = D(L1,..., Lc). In multiple regression designs this matrix will be of the form L = D({\v X}1,..., {\v X}c)with {\v X}j, j = 1,...,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.",

keywords = "Commutative Jordan algebras, Cross-nested models, L models, Multiple regression models, Orthogonal models",

author = "Elsa Moreira and Mexia, {Jo{\~a}o Tiago} and Miguel Fonseca and Roman Zmy{\'s}lony",

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doi = "10.1007/s00362-009-0255-3",

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journal = "Statistical Papers",

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T1 - L models and multiple regressions designs

AU - Moreira, Elsa

AU - Mexia, João Tiago

AU - Fonseca, Miguel

AU - Zmyślony, Roman

PY - 2009/8/5

Y1 - 2009/8/5

N2 - Given an orthogonal model an L model is obtained, and the only restriction is the linear independency of the column vectors of matrix L. Special cases of the L models correspond to blockwise diagonal matrices L = D(L1,..., Lc). In multiple regression designs this matrix will be of the form L = D(X̌1,..., X̌c)with X̌j, j = 1,...,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.

AB - Given an orthogonal model an L model is obtained, and the only restriction is the linear independency of the column vectors of matrix L. Special cases of the L models correspond to blockwise diagonal matrices L = D(L1,..., Lc). In multiple regression designs this matrix will be of the form L = D(X̌1,..., X̌c)with X̌j, j = 1,...,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.

KW - Commutative Jordan algebras

KW - Cross-nested models

KW - L models

KW - Multiple regression models

KW - Orthogonal models

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U2 - 10.1007/s00362-009-0255-3

DO - 10.1007/s00362-009-0255-3

M3 - Conference article

AN - SCOPUS:70350767209

SN - 0932-5026

VL - 50

SP - 869

EP - 885

JO - Statistical Papers

JF - Statistical Papers

IS - 4

T2 - International Conference on Trends and Perspectives in Linear Statistical Inference, LinStat'2008

Y2 - 21 April 2008 through 25 April 2008

ER -

L models and multiple regressions designs

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Keywords

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