Mixed geographically weighted regression (MGWR) models, assuming that some regression coefficients are constant and the others are spatially varying, have been a powerful tool for comprehensively exploring spatial variation characteristics of impact of the exploratory variables on the response variable. Based on the local-linear geographically weighted regression estimators of the coefficients, we propose in this paper a coefficient-average-based estimation method for the MGWR models, on which a bootstrap test is formulated to identify constant coefficients in the models. In addition, the estimation and test methods are extended to the estimation of the multi-type MGWR models and the identification of special types of the coefficients. The simulation studies show that, compared with the existing two-step estimation of the MGWR models, the proposed estimation method can yield more accurate estimators for the spatially varying coefficients and the test method is of valid size and satisfactory power. A real-life example is finally given to demonstrate the applicability of the proposed estimation and test methods.