This dissertation has three major aims: (1) obtain a better formula for the optimal tuning parameters in rGLS methods; (2) correct the performance of sandwich-type standard errors to make them closer to empirical standard errors; and (3) improve the Type I error control of corresponding test statistics by rescaling their means to the degrees of freedom of their nominal chi-square distributions. Analytical approaches could be taken to achieve these aims but they might be too complex to use in practice and analytical solutions also need to be examined empirically. Instead, an empirical modeling approach was taken in this dissertation. The idea of the empirical modeling approach is to first conduct a simulation study in a wide variety of conditions, and collect parameter estimates/test statistics/standard errors for every condition; then compare these empirical results with their theoretical counterparts (e.g., compare parameter estimates with the population values used in the simulation study, compare sandwich-type standard errors with the empirical ones, and refer test statistics to their nominal chi-square distributions); if these statistics do not perform as expected in this simulation study, the empirical modeling approach can be employed to correct their behavior based on simulation results.