Split-Plot Model With Covariate A Cautionary Tale

• Published in: The American statistician Vol. 56; no. 4; pp. 284 - 289
• Main Authors: Aldworth, Jeremy, Hoffman, Wherly P
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.11.2002; American Statistical Association
• Subjects: Analysis of covariance; Approximation; Biometrics; Compound symmetry; Covariance; Datasets; Degrees of freedom; Exact sciences and technology; Linear inference, regression; Mathematics; Modeling; Parameterization; Plot (Narrative); Probability and statistics; PROC MIXED; Repeated measures; Sciences and techniques of general use; Statistical Practice; Statistical variance; Statistics; Syntax; Variance components; Error analysis; Compound symmetry; Covariance analysis; Statistical model; PROC MIXED; Model specification; Repeated measurement; Parameterization; Variance analysis; Variance component
• ISSN: 0003-1305; 1537-2731
• DOI: 10.1198/000313002597

Consider a split-plot model with one whole-plot factor, one sub-plot factor, and a covariate that does not depend on the subplot factor. We discuss the following three key areas where errors in the analysis of this simple model may occur: (1) correct specification of the model, (2) parameterization of variance components, and (3)the final analysis using PROC MIXED (SASv8.2). A further complication arises in cases where the within-whole-plot variability is larger than the between-whole-plot variability. We suggest two options, based on different assumptions, to accommodate cases like these, and the user is to decide which is most appropriate.