International Scholarly Research Notices / 2012 / Article / Tab 3 / Research Article
On Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models: A Computational Study Table 3 Mean estimate (and standard error) of
𝜙
using
𝜙
L
o
g
N
I
1
based on 200 simulated contingency tables with a specified value of
𝜙
and
𝑛
≈
1
0
0
0
. The values in bold are where the mean of the 200
𝑃
values obtained from the Wald test (of the difference between the estimated and true parameter) is significant at the 1% level. The italicised values are significant at the 5% level.
Size of contingency table True
𝜙
2 × 2 2 × 3 2 × 4 2 × 5 3 × 3 3 × 4 3 × 5 4 × 4 4 × 5 5 × 5 0.00 −0.00068 (0.2014) −0.00008 (0.1160) 0.00299 (0.0829) 0.00032 (0.0583) −0.00024 (0.0611) −0.00030 (0.0448) −0.00004 (0.0346) 0.00005 (0.0312) 0.00006 (0.0239) 0.00005 (0.0178) 0.01 0.01610 (0.2759) 0.00633 (0.1234) 0.01424 (0.0785) 0.00836 (0.0630) 0.01029 (0.0631) 0.01020 (0.0446) 0.01011 (0.0344) 0.01021 (0.0307) 0.01004 (0.0241) 0.01001 (0.0179) 0.05 0.05446 (0.2187) 0.05152 (0.1193) 0.05075 (0.0824) 0.04922 (0.0620) 0.04962 (0.0615) 0.05008 (0.0423) 0.05016 (0.0338) 0.04996 (0.0300) 0.04992 (0.0236) 0.05000 (0.0182) 0.10 0.10231 (0.2154) 0.09998 (0.1099) 0.10078 (0.0773) 0.10046 (0.0607) 0.09993 (0.0689) 0.09975 (0.0434) 0.09954 (0.0339) 0.09969 (0.0299) 0.09964 (0.0231) 0.09911 (0.0177) 0.20 0.20451 (0.2045) 0.20025 (0.1145) 0.19952 (0.0765) 0.19932 (0.0574) 0.19893 (0.0600) 0.19818 (0.0424) 0.19766 (0.0308) 0.19676 (0.0281) 0.19492 (0.0213) 0.19101 (0.0153) 0.30 0.30337 (0.2007) 0.30434 (0.1110) 0.29977 (0.0753) 0.29721 (0.0546) 0.29743 (0.0604) 0.29481 (0.0390) 0.29092 (0.0297) 0.28925 (0.0261) 0.28149 (0.0182) 0.26891 (0.0129) 0.40 0.40352 (0.2275) 0.39385 (0.1155) 0.39791 (0.0749) 0.39275 (0.0602) 0.39458 (0.0629) 0.38791 (0.0388) 0.37732 (0.0269) 0.37233 (0.0236) 0.35294 (0.0159) 0.32652 (0.0103) 0.50 0.50350 (0.2310) 0.49954 (0.1134) 0.48823 (0.0846) 0.48801 (0.0526) 0.48693 (0.0563) 0.47029 (0.0389) 0.45542 (0.0248) 0.44396 (0.0214) 0.40896 (0.0135) 0.36225 (0.0086) 0.60 0.60742 (0.2165) 0.59252 (0.1070) 0.58724 (0.0709) 0.57402 (0.0516) 0.57580 (0.0539) 0.55214 (0.0331) 0.52330 (0.0231) 0.50859 (0.0189) 0.45332 (0.0121) 0.38300 (0.0070)0.70 0.70298 (0.2073) 0.69001 (0.1127) 0.67442 (0.0644) 0.65328 (0.0473) 0.66050 (0.0499) 0.62525 (0.0311) 0.57783 (0.0204) 0.55366 (0.0166) 0.48359 0.38935 (0.0054)0.80 0.79400 (0.2685) 0.78320 (0.1027) 0.75942 (0.0726) 0.73482 (0.0431) 0.74372 (0.0469) 0.68976 (0.0291) 0.62194 (0.0178) 0.59053 (0.0151) 0.49281 (0.0085)0.39437 (0.0043)0.90 0.88478 (0.2076) 0.86906 (0.0972) 0.84284 (0.0619) 0.80984 (0.0446) 0.81907 (0.0456) 0.74370 (0.0256) 0.65549 0.61944 (0.0130)0.50525 (0.0071)0.39864 (0.0034)1.00 0.99208 (0.2242) 0.95982 (0.1003) 0.91896 (0.0711) 0.87180 (0.0428) 0.88914 (0.0447) 0.78265 (0.0240) 0.68186 (0.0140)0.64302 (0.0122)0.51164 (0.0061)0.39090 (0.0026)1.10 1.07792 (0.2070) 1.04284 (0.1102) 0.99425 (0.0563) 0.93162 (0.0397) 0.94721 (0.0399) 0.82129 0.69747 (0.0127)0.65111 (0.0103)0.50923 (0.0048)0.38387 (0.0019)1.20 1.17866 (0.1918) 1.12713 (0.0961) 1.06491 (0.0539) 0.98924 (0.0355) 1.00068 (0.0366) 0.85517 (0.0198)0.71206 (0.0114)0.66053 (0.0091)0.51300 (0.0040)0.38100 (0.0016)1.30 1.27633 (0.2260) 1.20889 (0.0981) 1.12928 (0.0542) 1.05000 (0.0322) 1.05912 (0.0370) 0.88164 (0.0181)0.71797 (0.0099)0.67223 (0.0081)0.51028 (0.0033)0.37375 (0.011)1.40 1.37037 (0.2244) 1.29294 (0.0806) 1.19599 (0.0470) 1.07872 (0.0317) 1.09808 (0.0340) 0.90062 (0.0146)0.73551 (0.0089)0.66730 (0.0068)0.50864 (0.0029)0.37198 (0.0011)1.50 1.44834 (0.1785) 1.37143 (0.0823) 1.24810 (0.0439) 1.12323 1.14909 0.92568 (0.0161)0.73350 (0.0077)0.66406 (0.0056)0.50923 (0.0025)0.36991 (0.0009)
