In spatial analysis, the focus has traditionally been on modeling spatial correlation in the residuals of the mean structure, often neglecting the consideration of spatial effects on other parameters. The implications of disregarding the modeling of these parameters and their impact on parameter estimates and model goodness of fit remain unclear. Motivated by a real-world application, our findings uncover spatial correlation not only in the mean but also in the variance of disease incidence. We also investigate the consequences of mismodeling the structure in various components of the regression model. Through simulation studies, we assess the sensitivity of parameter estimates to model misspecification. This research contributes to a deeper understanding of disease dynamics and emphasizes the need for robust modeling across all parameters.