Matvec Users’ Guide

60 CHAPTER 10. LINEAR MODEL ANALYSES
• either the pedigree file or the raw data file can contain comments which is started from the double
backslash. This could be very handy when you want to write down a note about your data. Comments
and empty lines will be quietly ignored by Matvec.
• missing values must be represented by a dot(.) with an exception that unknown parents in the pedigree
file can also be represented by 0 (the cost is that we can’t use 0 as a legitimate animal identification any
more). Missing values can appear anywhere in both files. Matvec will automatically and appropriately
handle missing values for you.
• animal or herd identification can be either a string or a number.
In the following several sections, we will demonstrate how to analyze the above data using linear model
methodology.
10.3.2 Model
A single trait animal model is assumed:
y i = µ + h i + a i + e i
10.3.3 Obtain BLUP using matrix algebra
First of all, we write down a script using matrix tools and functions provided by Matvec. You can use any
of you favorable ASCII editor, and save the file as try1 in your current working directory.
A = [1.0, 0.0, 0.5, 0.0, 0.25;
0.0, 1.0, 0.5, 0.5, 0.25;
0.5, 0.5, 1.0, 0.25, 0.5;
0.0, 0.5, 0.25,1.0, 0.125;
0.25,0.25,0.5, 0.125,1.0]; // A = relationship matrix
X = [1.0, 1.0, 0.0;
1.0, 1.0, 0.0;
1.0, 1.0, 0.0;
1.0, 0.0, 1.0;
1.0, 0.0, 1.0;
1.0, 0.0, 1.0];
Z = [0.0, 1.0, 0.0, 0.0, 0.0;
0.0, 1.0, 0.0, 0.0, 0.0;
0.0, 0.0, 1.0, 0.0, 0.0;
0.0, 0.0, 0.0, 1.0, 0.0;
0.0, 0.0, 0.0, 0.0, 1.0;
0.0, 0.0, 0.0, 0.0, 1.0];
y = [6.0;
8.0;
8.0;
7.0;
9.0;
12.0];
XPX = X’*X;
XPZ = X’*Z;
ZPZ = Z’*Z;