10.3 Return to the data on the efficacy of lithium as a treatment for amyotrophic lateral sclerosis

(Section 7.5). Define

????2 1 =variance component for term ‘id’

????2 2 =variance component for term ‘id.visit_day’ and

????12 =correlation coefficient between effects of ‘id’ and ‘id.visit_day’.

Specify a single covariance matrix, with 168 rows, representing the 84 levels of ‘id’ and the 84 levels of ‘id.visit_day’. Indicate the covariance in every element of the matrix, that is, every row.column combination.

10.4 Records of matings and of phenotypic variables were kept in a pedigree of the shrimp Penaeus vannamei. The variables recorded were as shown in Table 10.11, and the first and last few rows of the spreadsheet holding the data are presented in Table 10.12:
the full data set is held in the file ‘shrimp pedigree.xlsx’ on this book’s website (see Preface). (Data reproduced by kind permission of Dr Shaun Moss, Director, Shrimp Department, Oceanic Institute, Hawaii, USA.) The variable of economic interest is the weekly growth rate.