In simple words, how we can force any logistic regression coefficient be 1. Is there any steps/algorithm that used behind offset term?
There is no "trick" behind the use of an offset term ( * ), while the other coefficients will be estimated, that is, their values will be updated at each step of the IRLS ( * ) fitting algorithm, the offset coefficient will not be updated, it will keep its value of 1.
( * ) IRLS is iteratively reweighted least squares, the fitting algorithm usually used for generalized linear models such as logistic regression. For an overview, see Can you give a simple intuitive explanation of IRLS method to find the MLE of a GLM?
The offset term is included with a term
offset(x1) in the model formula, or via the use of a separate
offset= argument. The first way is the preferred one. This will force the coefficient of
x1 to be one.