Tham khảo tài liệu 'data analysis machine learning and applications episode 2 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 306 Mario Larch and Janette Walde When the null hypothesis is tested whether the spatial correlation parameter p is zero in the presence of spatial correlation in the error term the Wald test has a very good power although the power is higher with the sparser weighting matrix. The latter characteristic is a general feature for all conducted tests. The power for the spatial error parameter in the presence of a non-zero spatial lag parameter is lower. However the power of the Wald test in this circumstances is much greater than the power achievable by using Lagrange Multiplier tests. In Figure 1c the best performing LM test is plotted . LMA. All LM tests relying on OLS residuals fail seriously to detect the true DGP. Comparable to the performance of the Wald test based on MLE estimates is the Wald test based on GMM estimates but only in detecting the significant lag parameter in the presence of a significant spatial error parameter. In the reverse case the Wald test using GMM estimates is much worse. As a further model selection approach the performance of information criteria is analyzed. The performance of the classical Akaike information criterion and the bias corrected AIC are almost identical. In Figure 1d the share of cases in which AIC AICc identifies the correct DGP is plotted on the y-axis. All information criteria fail in more than 15 of the cases to identify the correct more parsimonious model . SARAR 1 0 or SARAR 0 1 instead of SARAR 1 1 . However in the remaining experiments p . or À .05 . A1C A1C . is comparable to the performance of the Wald test. BIC performs better than AIC AICc to detect SARAR 1 0 or SARAR 0 1 instead of SARAR 1 1 but much worse in the remaining experiments. In order to be able to propose a general procedure for model selection the approach must also be suitable if the true DGP is SARAR 1 0 or SARAR 0 1 . In this case the Wald test based on the general model has again the appropriate size and a very good power. .
