International Scholarly Research Notices / 2012 / Article / Tab 1 / Research Article
On Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models: A Computational Study Table 1 Mean estimate (and standard error) of
π
using Newtonβs unidimensional method,
ξ
π
π
, based on 200 simulated contingency tables with a specified value of
π
and
π
=
1
0
0
0
.
Size of contingency table True
π
2 Γ 2 2 Γ 3 2 Γ 4 2 Γ 5 3 Γ 3 3 Γ 4 3 Γ 5 4 Γ 4 4 Γ 5 5 Γ 5 0.00 β0.00068 (0.2014) 0.00020 (0.1160) 0.00235 (0.0829) 0.00042 (0.0583) β0.00023 (0.0611) β0.00029 (0.0488) β0.00007 (0.0346) 0.00008 (0.0312) 0.00004 (0.0239) 0.00005 (0.0178) 0.01 0.01617 (0.2765) 0.00740 (0.1237) 0.01503 (0.0792) 0.00868 (0.0631) 0.01040 (0.0631) 0.01016 (0.0446) 0.01012 (0.0344) 0.01020 (0.0307) 0.01002 (0.0241) 0.01000 (0.0179) 0.05 0.05454 (0.2188) 0.05134 (0.1194) 0.05046 (0.0824) 0.04911 (0.0621) 0.04964 (0.0615) 0.05009 (0.0424) 0.05021 (0.0338) 0.04997 (0.0301) 0.05001 (0.0236) 0.05009 (0.0183) 0.10 0.10278 (0.2165) 0.09998 (0.1089) 0.10087 (0.0775) 0.10061 (0.0608) 0.09994 (0.0690) 0.09990 (0.0436) 0.09980 (0.0341) 0.10006 (0.0301) 0.10024 (0.0234) 0.10001 (0.0181) 0.20 0.20473 (0.2048) 0.20097 (0.1149) 0.19999 (0.0770) 0.20010 (0.0580) 0.19969 (0.0605) 0.19970 (0.0431) 0.20021 (0.0317) 0.19995 (0.0290) 0.20008 (0.0223) 0.19995 (0.0165) 0.30 0.30392 (0.2016) 0.30622 (0.1130) 0.30312 (0.0770) 0.30040 (0.0558) 0.30019 (0.0616) 0.30022 (0.0404) 0.30008 (0.0314) 0.30007 (0.0278) 0.29995 (0.0202) 0.30001 (0.0149) 0.40 0.40491 (0.2295) 0.39656 (0.1170) 0.40184 (0.0771) 0.40082 (0.0629) 0.40079 (0.0649) 0.40080 (0.0412) 0.40030 (0.0295) 0.40001 (0.0263) 0.40015 (0.0187) 0.40036 (0.0129) 0.50 0.50762 (0.2353) 0.50533 (0.1164) 0.50139 (0.0869) 0.50326 (0.0564) 0.49981 (0.0591) 0.49788 (0.0422) 0.50018 (0.0284) 0.50030 (0.0249) 0.50022 (0.0167) 0.50025 (0.0113) 0.60 0.61482 (0.2229) 0.60065 (0.1102) 0.60149 (0.0751) 0.60076 (0.0561) 0.59980 (0.0577) 0.59945 (0.0373) 0.59976 (0.0272) 0.60012 (0.0230) 0.59999 (0.0156) 0.60015 (0.0096) 0.70 0.71150 (0.2131) 0.70272 (0.1175) 0.69969 (0.0690) 0.70033 (0.0524) 0.69953 (0.0547) 0.70031 (0.0359) 0.70049 (0.0250) 0.70026 (0.0209) 0.70015 (0.0139) 0.69996 (0.0078) 0.80 0.80482 (0.2773) 0.80215 (0.1081) 0.79924 (0.0785) 0.79978 (0.0485) 0.79985 (0.0524) 0.80013 (0.0345) 0.80002 (0.0226) 0.80009 (0.0197) 0.79995 (0.0117) 0.80038 (0.0066) 0.90 0.89570 (0.2133) 0.89081 (0.1033) 0.90338 (0.0687) 0.90103 (0.0513) 0.89998 (0.0519) 0.90018 (0.0314) 0.90058 (0.0214) 0.89980 (0.0174) 0.90041 (0.0102) 0.90025 (0.0055) 1.00 1.01856 (0.2358) 0.99917 (0.1074) 0.99251 (0.0804) 1.00302 (0.0504) 0.99954 (0.0517) 0.99992 (0.0301) 1.00014 (0.0188) 0.99983 (0.0167) 0.99987 (0.0091) 0.99659 (0.0045) 1.10 1.10279 (0.2169) 1.10185 (0.1187) 1.10167 (0.0646) 1.10041 (0.0472) 1.10064 (0.0475) 1.10020 (0.0282) 1.09998 (0.0174) 1.10030 (0.0146) 1.10028 (0.0076) 1.09676 (0.0035) 1.20 1.20637 (0.2047) 1.20018 (0.1057) 1.20161 (0.0626) 1.20078 (0.0430) 1.20001 (0.0444) 1.20077 (0.0260) 1.19968 (0.0160) 1.19960 (0.0132) 1.19975 (0.0066) 1.19886 (0.0030) 1.30 1.32157 (0.2372) 1.30192 (0.1100) 1.30332 (0.0551) 1.30048 (0.0396) 1.30092 (0.0452) 1.30039 (0.0241) 1.29982 (0.0143) 1.30007 (0.0121) 1.30016 (0.0057) 1.28541 (0.0023) 1.40 1.41818 (0.2433) 1.40873 (0.0898) 1.40110 (0.0564) 1.39902 (0.0395) 1.40079 (0.0423) 1.40040 (0.0224) 1.40003 (0.0132) 1.40001 (0.0106) 1.39921 (0.0051) 1.38124 (0.0021) 1.50 1.49777 (0.1907) 1.50079 (0.0939) 1.50105 (0.0531) 1.50184 (0.0384) 1.49974 (0.0427) 1.49900 (0.0223) 1.50036 (0.0118) 1.50045 (0.0091) 1.49371 (0.0045) 1.47004 (0.0017)
