Communications in statistics-theory and methods vol:33 issue:4 pages:873-890
For an orthogonally blocked experiment, Khuri [Khuri, A. I. (1992). Response surface models with random block effects. Technometrics 34:26-37] has shown that the ordinary least squares estimator, the generalized least squares estimator and the intra-block estimator of the factor effects in a response surface model with random block effects coincide. The ordinary least squares estimator ignores the blocks, whereas the generalized least squares and the intra-block estimators treat the block effects as random and fixed, respectively. As shown in this paper, the equivalence does not hold for the estimation of the intercept when the block sizes are heterogeneous. Practical examples are given to illustrate the theoretical results.