Abstract
In the MR regression model, the design matrix X is common to each variable. This limitation does not permit one to associate different design matrices with each dependent variable which in many regression problems may lead to overfitting some variables. To correct this problem, we must be able to model each dependent variable separately within a common, overall model. Using the vec (•) operator on the columns of the data matrix Y, Zellner (1962, 1963) formulated the seemingly unrelated regression (SUR) model as p correlated regression models. Srivastava (1966, 1967) called the design the multiple-design multi-variate (MDM) model. Hecker (1987) formulates the model using the vec (•) operator on the rows of Y nxp and calls the model the completely general MANOVA (CGMANOVA) model. In this chapter, we review the general theory of the SUR model and show how the model may be used to estimate parameters and test hypothesis in complex design situations including the generalized MANOVA (GMANOVA) model developed by Potthoff and Roy (1964), repeated measurement designs with changing covariates, and mixed MANOVA-GMANOVA designs. In addition, goodness of fit tests, tests for nonadditivity, and sum of profile models are discussed. Finally, the multivariate SUR (MSUR) is reviewed.
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Keywords
- Multivariate Regression Model
- Growth Curve Model
- Seemingly Unrelated Regression
- Good Linear Unbiased Predictor
- Feasible Generalize Little Square
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© 2002 Springer-Verlag New York, Inc.
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(2002). Seemingly Unrelated Regression Models. In: Timm, N.H. (eds) Applied Multivariate Analysis. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22771-9_5
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DOI: https://doi.org/10.1007/978-0-387-22771-9_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95347-2
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