[U] User's Guide

104 [ U ] 11 Language syntax11.4.3.1 Factor-variable operatorsi.group is called a factor variable, although more correctly, we should say that group is a categoricalvariable to which factor-variable operators have been applied. There are four factor-variable operators:operatordescriptioni. unary operator to specify indicatorsc. unary operator to treat as continuous# binary operator to specify interactions## binary operator to specify full-factorial interactionsWhen you type i.group, it forms the indicators for the unique values of group. We will usuallysay this more briefly as i.group forms indicators for the levels of group, and sometimes we willabbreviate the statement even more and say i.group forms indicators for group.The c. operator means continuous. We will get to that below.# and ##, pronounced cross and factorial cross, are operators for use with pairs of variables.i.group#i.sex means to form indicators for each combination of the levels of group and sex.group#sex means the same thing, which is to say that use of # implies the i. prefix.group#c.age (or i.group#c.age) means the interaction of the levels of group with the continuousvariable age. This amounts to forming i.group and then multiplying each level by age. Wealready know that i.group expands to the virtual variables 1b.group, 2.group, and 3.group,so group#c.age results in the collection of variables equal to 1b.group*age, 2.group*age, and3.group*age. 1b.group*age will just be zero because 1b.group is zero. 2.group*age will beage when group = 2, and 0 otherwise. 3.group*age will be age when group = 3, and 0 otherwise.In a linear regression of y on age and group#c.age, 1b.group*age will be omitted, 2.group*agewill measure the change in the age coefficient for group = 2 relative to the base group, and3.group*age will measure the change for group = 3 relative to the base.