## Retrospective Theses and Dissertations

#### Title

The split-plot design with covariance

Dissertation

1985

#### Degree Name

Doctor of Philosophy

Statistics

#### Abstract

A split-plot data structure is usually modelled by a linear classificatory model with a 0,1 model matrix and with error consisting additively of independent Gaussian errors. Statistical analysis of such a data structure in the usual mode involves then two components of error variance. The usual model is then a special case of what is commonly called a mixed linear model. Consequently, the well-known problems of mixed linear models are encountered. However, the standard balance split-plot data structure has special features of balance that enable progress, as will be explained;With the presence of a concomitant variable and the assumed error structure, the problem of estimation of the dependence of the observations to be explained on the concomitant variable becomes complicated. The model considered is y(,ijk) = (mu) + (alpha)(,i) + (gamma)(,j) + (nu)(,k) + (eta)(,jk) + x(,ijk)c + e(,ij) + s(,ijk) where x(,ijk) is the value of the concomitant variable or the covariate, c is the regression coefficient, e(,ij) and s(,ijk) are errors. The difficulties arise from the existence of the two types of error;The nature of split-plot designs will be exposited, along with special features arising from the balance in the structure;The problem considered is estimation of c, the regression coefficient, because if this is solved, the remainder of the problem of fitting the model seems clear. There is no best way of estimating c because var(e(,ij)) and var(s(,ijk)) are not known and various methods of doing this are discussed;The problem is simple if the ratio of the two variance components is known. So, attention is turned to estimation of a basic parameter related to this ratio, with consideration of various methods, including Bayesian estimation;The widely used method of maximum likelihood fitting of the model is examined. Also, a method of restricted maximum likelihood estimation is examined;Residual problems such as attaching "reasonable" standard errors to estimates are not solved. It seems that understanding these problems can be achieved only by simulation.

#### DOI

https://doi.org/10.31274/rtd-180813-12365

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

en

AAI8604515

application/pdf

180 pages

COinS