Value Mean Est. Abs. Bias Absolute Percentage Bias (APB) Finite Sample St. Dev (FSSD) Asymptotic St. Err. (ASE) APB of the St. Err. (APBASE) Approx. error as a % of FSSD (APERR) 0.50 0.502 0.002 0.304 0.0433 0.0431 0.46 3.00 0.80 0.791 0.009 1.074 0.1005 0.0948 5.67 1.69 1.00 0.977 0.023 2.288 0.1107 0.127 14.72 1.90 0.90 0.876 0.024 2.696 0.1217 0.1332 9.45 2.88 0.60 0.614 0.014 2.297 0.1082 0.1186 9.61 2.96 0.80 0.794 0.006 0.787 0.1436 0.1142 20.47 2.50 0.25 0.252 0.002 0.789 0.0497 0.0455 8.45 1.21 0.25 0.251 0.001 0.403 0.0035 0.0036 2.85 42.86 0.25 0.246 0.004 1.753 0.0187 0.0163 12.84 39.57 Overall mean value across parameters 0.009 1.377 0.0778 0.0774 9.39 10.95 a The mean composite log-likelihood for the low spatial dependency and low spatial drift model at converged parameter is -19710.55 Table 2b: Simulation results for the four-alternative case with 20 datasets for low spatial dependency and high spatial drift (based on a total of 20×10 runs/dataset=200 runs)
Table 2d: Simulation results for the four-alternative case with 20 datasets for high spatial dependency and high spatial drift (based on a total of 20×10 runs/dataset=200 runs) Parameter True Value Parameter Estimates Standard Error Estimates Mean Est. Abs. Bias Absolute Percentage Bias (APB) Finite Sample St. Dev (FSSD) Asymptotic St. Err. (ASE) Abs.Bias of the asymt. St. Err. (APBASE) Approx. error as a % of FSSD (APERR 0.50 0.514 0.014 2.732 0.1155 0.1122 2.86 1.47 0.80 0.843 0.043 5.370 0.2605 0.2396 8.02 1.27 1.00 1.014 0.014 1.391 0.2627 0.2924 11.31 1.37 0.90 0.925 0.025 2.824 0.2341 0.2506 7.05 1.75 0.60 0.628 0.028 4.705 0.1649 0.1637 0.73 2.00 0.80 0.769 0.031 3.887 0.1870 0.2294 14.77 2.46 0.75 0.754 0.004 0.540 0.0210 0.0148 29.52 0.95 0.75 0.680 0.070 9.333 0.1721 0.1748 1.57 3.37 0.75 0.696 0.054 7.165 0.1470 0.1317 10.41 0.88 Overall mean value across parameters 0.031 4.216 0.1739 0.1788 9.58 1.72 a The mean composite log-likelihood value for the low spatial dependency and low spatial drift model at converged parameter is -11693.61
3: Effects of ignoring spatial effects when present Evaluation Metric Low spatial lag- Low spatial drift Low spatial lag-High spatial High spatial lag- Low spatial drift High spatial lag- High spatial GS NSL Model NSD Model GS NSL Model NSD Model GS Model NSL NSD Model GS Model NSL NSD Model Mean APB For comparison of GS with the no-spatial lag (NSL) model 1.23 2.88 - 5.50 7.89 - 0.80 41.93 - 6.24 44.21 - For comparison of GS model with the drift (NSD) model 1.50 - 3.03 4.58 - 6.66 0.99 - 2.36 3.05 - 3.72 Mean composite log-likelihood value at convergence -19,711 -20,047 -19,946 -19,768 -19,997 -19,914 -11,535 -21,590 -11,735 -11,694 -21,915 -11,929 Number of the adjusted composite likelihood ratio test (ADCLRT) statistic favors the ORSH model - All twenty times when compared with value (mean ADCLRT statistic is 166.49) All twenty when compared with value (mean ADCLRT statistic is 135.63) - All twenty times when compared with value (mean ADCLRT statistic is 127.03) All twenty times when compared with value (mean ADCLRT statistic is 109.96) - All twenty when compared with value (mean ADCLRT statistic is 267.76) All twenty when compared with value (mean ADCLRT statistic is 118.10) - All twenty times when compared with value (mean ADCLRT statistic is 287.62) All twenty times when compared with value (mean ADCLRT statistic is 166.80)