# Encyclopedia of Statistical Scis. [Vol. 11] by S. Kotz

By S. Kotz

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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 [10] generalizes redundancy factoring to qualitative variables utilizing optimal scaling techniques. Muller [18] shows the relationship between Van Den Wollenberg’s [26] 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).