Mixed Response Surface Models With Heterogeneous Within-Block Error Variances

Abstract

The experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant. In some experimental situations, however, this variance may be different for the different blocks that compose the associated design. This article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks. The model includes interactions between the fixed polynomial effects and the block effect. Procedures for estimating and testing the fixed effects and the random effects in the model are described. In particular, ANOVA-based procedures for testing equality of the error variances and testing the random effects are introduced.

KEY WORDS :

• ANOVA tests
• Block effect
• Fixed effects
• Levene's test
• Likelihood ratio test
• PROC MIXED
• Random effects
• Restricted maximum likelihood
• Type III sums of squares
• Variance components