# offset in logistic regression to take into account a priori individual probability estimates

I am performing a logistic regression (LR) model on a set of data on which an initial probability estimate for event occurrence, sai $\hat{p_i}^{base}$ has been provided. I have supplementary regressors and I want to update my model starting from the initial estimate. I was thinking to insert $logit\left(\hat{p_i}^{base}\right)$ as offset of the (LR) model, thus $logit\left(\hat{p_i}^{new}\right)=1*logit\left(\hat{p_i}^{base}\right)+x_i^T*\beta$. I am asking whether the offset form (logit) is the right functional form to allow for an initial "guessing" of the probability and if this is the most appropriate approach to update a logistic regression model, given initial updates. Thanks in advance for the attention.