I understand how to make sense of the design matrix in a general linear model (GLM). Basically, each column of the design matrix describes one condition under which the data are observed.
For example, I wish to model 4 factors, i.e., diagnosis, age, gender, and weight. Then, I would have a design matrix as follows.
/0 26 1 75\ - 1st subject: a 26 year-old and 75 kg female, no disease |2 13 0 60| - 2nd subject: a 13 year-old and 60 kg male, severe stage |1 12 1 77| - 3rd subject: a 12 year-old and 77 kg female, intermediate disease | ... | \ /
- diagnosis: 0 means normal, 1 means intermediate, and 2 means severe;
- age: 13 means 13 years old, and etc.;
- gender: 0 means male, and 1 means female;
- weight: 75 means 75 kg, and etc..
Now comes the question, is there a way to make sense of the contrast? Or equivalently, how could I design a contrast based on what I want? I believe only by making sense of it first can one design it.