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Extra info for Encyclopedia of Statistical Scis. [Vol. 11]
The exchangeable prior distribution f (β) means that the distribution would be unaltered by any permutation of the suffixes. In particular, it implies that E(βi ) = µ for i = 1, . . , p, and hence the parameters exhibit a linear structure analogous to that assumed for the dependent variable. It may, of course, be necessary to rescale the predictor variables so that the assumption of exchangeability∗ is reasonable. , fixed effects, random effects). For example, suppose that in the linear multiple regression model where X is a k × p matrix of given values for the independent variables in the k future periods, and is a k × 1 vector of k future is assumed to error terms.
Israels  generalizes redundancy factoring to qualitative variables utilizing optimal scaling techniques. Muller  shows the relationship between Van Den Wollenberg’s  redundancy factoring and multivariate multiple linear regression on rotated component scores. REFERENCES 1. Anderson, T. W. (1958). Introduction to Multivariate Statistical Analysis. Wiley, New York. (Rxy Ryx − u1 Rxx )w = 0 (21) (Ryx Rxy − u2 Ryy )v = 0. (22) 2. Cramer, E. M. and Nicewander, W. A. (1979). Psychometrika, 44, 43–54.
L. (1983). Manag. , 29, 622–632. ) 10. Winkler, R. , Smith, W. , and Kulkarni, R. B. (1978). Manag. , 24, 977–986. ) 11. Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. Wiley, New York. (Bayesian inference in a wide variety of econometric models, including multivariate regression and simultaneous equation models. ) BIBLIOGRAPHY See the following works, as well as the references just given, for more information on the topic of Bayesian regression. DeGroot, M. H. (1970).