. * do-file for part of lecture 11b of VHM 802/812, Winter 2016 . version 14 /* works also with version 13 */ . set more off . cd "h:\vhm\vhm802\data_stata" h:\vhm\vhm802\data_stata . . * unadjusted and mixed model results (for reference) . use simcont_clustherd.dta, clear . regress milk X Source | SS df MS Number of obs = 11,626 -------------+---------------------------------- F(1, 11624) = 317.72 Model | 36598.5078 1 36598.5078 Prob > F = 0.0000 Residual | 1338999 11,624 115.192618 R-squared = 0.0266 -------------+---------------------------------- Adj R-squared = 0.0265 Total | 1375597.51 11,625 118.330968 Root MSE = 10.733 ------------------------------------------------------------------------------ milk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 3.55661 .199534 17.82 0.000 3.16549 3.94773 _cons | 30.0215 .1457715 205.95 0.000 29.73576 30.30723 ------------------------------------------------------------------------------ . mixed milk X || herd:, reml Performing EM optimization: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -40902.479 Iteration 1: log restricted-likelihood = -40902.479 Computing standard errors: Mixed-effects REML regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Wald chi2(1) = 6.44 Log restricted-likelihood = -40902.479 Prob > chi2 = 0.0112 ------------------------------------------------------------------------------ milk | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 3.796004 1.495943 2.54 0.011 .864009 6.727999 _cons | 31.13696 1.058717 29.41 0.000 29.06191 33.21201 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | 54.91499 7.998621 41.27713 73.05877 -----------------------------+------------------------------------------------ var(Residual) | 64.20087 .8457062 62.56453 65.88001 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 6374.40 Prob >= chibar2 = 0.0000 . use simcont_clustcow.dta, clear . regress milk X Source | SS df MS Number of obs = 11,626 -------------+---------------------------------- F(1, 11624) = 624.90 Model | 72138.7619 1 72138.7619 Prob > F = 0.0000 Residual | 1341880.62 11,624 115.440522 R-squared = 0.0510 -------------+---------------------------------- Adj R-squared = 0.0509 Total | 1414019.39 11,625 121.636076 Root MSE = 10.744 ------------------------------------------------------------------------------ milk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 4.982006 .1992962 25.00 0.000 4.591352 5.37266 _cons | 29.25664 .1412627 207.11 0.000 28.97974 29.53354 ------------------------------------------------------------------------------ . mixed milk X || herd:, reml Performing EM optimization: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -40947.175 Iteration 1: log restricted-likelihood = -40947.175 Computing standard errors: Mixed-effects REML regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Wald chi2(1) = 1108.56 Log restricted-likelihood = -40947.175 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ milk | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 4.968194 .1492174 33.30 0.000 4.675733 5.260655 _cons | 30.64647 .7281276 42.09 0.000 29.21936 32.07357 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | 51.41189 7.459591 38.68644 68.32323 -----------------------------+------------------------------------------------ var(Residual) | 64.71069 .8524578 63.06129 66.40324 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 6310.00 Prob >= chibar2 = 0.0000 . use simbin_clustherd.dta, clear . logit Y X Iteration 0: log likelihood = -6894.3552 Iteration 1: log likelihood = -6815.0583 Iteration 2: log likelihood = -6814.7785 Iteration 3: log likelihood = -6814.7785 Logistic regression Number of obs = 11,626 LR chi2(1) = 159.15 Prob > chi2 = 0.0000 Log likelihood = -6814.7785 Pseudo R2 = 0.0115 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5287317 .0423191 12.49 0.000 .4457877 .6116757 _cons | -1.241768 .0325699 -38.13 0.000 -1.305604 -1.177932 ------------------------------------------------------------------------------ . meqrlogit Y X || herd: Refining starting values: Iteration 0: log likelihood = -6065.2694 Iteration 1: log likelihood = -6065.1778 Iteration 2: log likelihood = -6065.0871 Performing gradient-based optimization: Iteration 0: log likelihood = -6065.0871 Iteration 1: log likelihood = -6065.0867 Mixed-effects logistic regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Integration points = 7 Wald chi2(1) = 9.25 Log likelihood = -6065.0867 Prob > chi2 = 0.0024 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .619974 .2038516 3.04 0.002 .2204322 1.019516 _cons | -1.305417 .1455518 -8.97 0.000 -1.590693 -1.020141 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | .9416185 .1492971 .6901029 1.284802 ------------------------------------------------------------------------------ LR test vs. logistic model: chibar2(01) = 1499.38 Prob >= chibar2 = 0.0000 . di .619974/(sqrt(1+.346*0.9416185)) /* PA estimate, for later use */ .53843647 . use simbin_clustcow.dta, clear . logit Y X Iteration 0: log likelihood = -6910.3442 Iteration 1: log likelihood = -6811.48 Iteration 2: log likelihood = -6811.0741 Iteration 3: log likelihood = -6811.0741 Logistic regression Number of obs = 11,626 LR chi2(1) = 198.54 Prob > chi2 = 0.0000 Log likelihood = -6811.0741 Pseudo R2 = 0.0144 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5863084 .0419748 13.97 0.000 .5040393 .6685775 _cons | -1.25032 .0316033 -39.56 0.000 -1.312261 -1.188379 ------------------------------------------------------------------------------ . meqrlogit Y X || herd: Refining starting values: Iteration 0: log likelihood = -5999.0538 Iteration 1: log likelihood = -5995.9727 Iteration 2: log likelihood = -5995.9698 Performing gradient-based optimization: Iteration 0: log likelihood = -5995.9698 Iteration 1: log likelihood = -5995.9698 Mixed-effects logistic regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Integration points = 7 Wald chi2(1) = 229.28 Log likelihood = -5995.9698 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .697479 .046063 15.14 0.000 .6071972 .7877609 _cons | -1.361173 .1112103 -12.24 0.000 -1.579141 -1.143204 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | 1.068172 .1682549 .7844459 1.45452 ------------------------------------------------------------------------------ LR test vs. logistic model: chibar2(01) = 1630.21 Prob >= chibar2 = 0.0000 . di .697479/(sqrt(1+.346*1.068172)) /* PA estimate, for later use */ .59598625 . . * fixed effects modelling . use simcont_clustcow.dta, clear . regress milk X i.herd Source | SS df MS Number of obs = 11,626 -------------+---------------------------------- F(100, 11525) = 103.27 Model | 668233.58 100 6682.3358 Prob > F = 0.0000 Residual | 745785.805 11,525 64.7102651 R-squared = 0.4726 -------------+---------------------------------- Adj R-squared = 0.4680 Total | 1414019.39 11,625 121.636076 Root MSE = 8.0443 ------------------------------------------------------------------------------ milk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 4.967911 .149217 33.29 0.000 4.67542 5.260401 | herd | 2 | 21.11033 2.513358 8.40 0.000 16.18373 26.03694 3 | 7.236815 2.413283 3.00 0.003 2.506371 11.96726 4 | 10.38913 2.392565 4.34 0.000 5.699296 15.07897 5 | 1.856204 2.373225 0.78 0.434 -2.79572 6.508128 6 | 22.3249 2.355121 9.48 0.000 17.70846 26.94134 7 | 19.67363 2.355121 8.35 0.000 15.05719 24.29006 8 | 20.58936 2.338142 8.81 0.000 16.0062 25.17252 9 | 4.836125 2.338142 2.07 0.039 .2529695 9.419281 10 | -4.982617 2.338142 -2.13 0.033 -9.565773 -.3994617 11 | 10.95127 2.32218 4.72 0.000 6.399398 15.50313 12 | 3.61817 2.32218 1.56 0.119 -.9336981 8.170038 13 | -.9090294 2.32218 -0.39 0.695 -5.460898 3.642839 14 | 6.437472 2.307151 2.79 0.005 1.915064 10.95988 15 | 1.814185 2.292969 0.79 0.429 -2.680425 6.308795 16 | 3.944011 2.254858 1.75 0.080 -.4758925 8.363915 17 | 11.9281 2.254858 5.29 0.000 7.508197 16.348 18 | 3.93309 2.254858 1.74 0.081 -.4868133 8.352994 19 | 20.00963 2.232587 8.96 0.000 15.63338 24.38588 20 | 14.6525 2.232587 6.56 0.000 10.27625 19.02875 21 | 10.9608 2.222254 4.93 0.000 6.604801 15.31679 22 | 7.190073 2.222254 3.24 0.001 2.834076 11.54607 23 | 5.612255 2.212409 2.54 0.011 1.275557 9.948953 24 | 3.203415 2.203014 1.45 0.146 -1.114866 7.521696 25 | 2.956442 2.194041 1.35 0.178 -1.344251 7.257135 26 | 11.80699 2.18546 5.40 0.000 7.523121 16.09086 27 | .0918443 2.18546 0.04 0.966 -4.192028 4.375716 28 | -1.178179 2.18546 -0.54 0.590 -5.462051 3.105693 29 | 4.578893 2.161833 2.12 0.034 .3413331 8.816453 30 | 6.631271 2.161833 3.07 0.002 2.393711 10.86883 31 | 5.551421 2.15459 2.58 0.010 1.328058 9.774783 32 | -2.206988 2.15459 -1.02 0.306 -6.430351 2.016374 33 | 5.821662 2.15459 2.70 0.007 1.598299 10.04502 34 | -1.102839 2.147634 -0.51 0.608 -5.312565 3.106888 35 | 8.300868 2.147634 3.87 0.000 4.091142 12.51059 36 | 9.826285 2.147634 4.58 0.000 5.616558 14.03601 37 | 18.43057 2.147634 8.58 0.000 14.22084 22.6403 38 | -.1458487 2.147634 -0.07 0.946 -4.355575 4.063878 39 | 16.57678 2.140945 7.74 0.000 12.38016 20.77339 40 | 7.425361 2.140945 3.47 0.001 3.228746 11.62198 41 | 14.93193 2.13451 7.00 0.000 10.74793 19.11593 42 | 11.21274 2.13451 5.25 0.000 7.028737 15.39674 43 | 19.93934 2.128314 9.37 0.000 15.76748 24.1112 44 | 13.77498 2.122344 6.49 0.000 9.614824 17.93513 45 | 1.333881 2.122344 0.63 0.530 -2.826274 5.494036 46 | 11.4609 2.116587 5.41 0.000 7.312026 15.60977 47 | 5.715232 2.111034 2.71 0.007 1.577247 9.853217 48 | 9.789586 2.111034 4.64 0.000 5.651601 13.92757 49 | 12.30603 2.100492 5.86 0.000 8.188707 16.42335 50 | 2.699361 2.100492 1.29 0.199 -1.417959 6.816682 51 | 7.424841 1.986609 3.74 0.000 3.530749 11.31893 52 | 8.593715 1.959664 4.39 0.000 4.75244 12.43499 53 | 2.399339 1.958235 1.23 0.221 -1.439133 6.237812 54 | .0153907 1.944042 0.01 0.994 -3.795261 3.826042 55 | 9.623738 1.944042 4.95 0.000 5.813087 13.43439 56 | 16.41427 1.936256 8.48 0.000 12.61887 20.20966 57 | 1.699915 1.931187 0.88 0.379 -2.08554 5.485371 58 | 14.31867 1.922948 7.45 0.000 10.54936 18.08797 59 | 7.084435 1.922096 3.69 0.000 3.316801 10.85207 60 | 1.817823 1.919607 0.95 0.344 -1.944933 5.580578 61 | 9.88462 1.915675 5.16 0.000 6.129572 13.63967 62 | 6.613898 1.911991 3.46 0.001 2.866071 10.36173 63 | 12.70136 1.911991 6.64 0.000 8.953534 16.44919 64 | 8.013387 1.910582 4.19 0.000 4.268322 11.75845 65 | -13.06771 1.90989 -6.84 0.000 -16.81142 -9.323999 66 | 7.752948 1.909207 4.06 0.000 4.010578 11.49532 67 | -5.62285 1.902812 -2.96 0.003 -9.352685 -1.893016 68 | 7.35862 1.900457 3.87 0.000 3.633402 11.08384 69 | 10.45819 1.899319 5.51 0.000 6.735205 14.18118 70 | 9.985111 1.897659 5.26 0.000 6.265378 13.70484 71 | 8.920595 1.897117 4.70 0.000 5.201923 12.63927 72 | 12.01857 1.896582 6.34 0.000 8.300952 15.7362 73 | 7.489065 1.896052 3.95 0.000 3.77248 11.20565 74 | 20.08057 1.894498 10.60 0.000 16.36703 23.79411 75 | -3.11481 1.892014 -1.65 0.100 -6.823479 .5938582 76 | -11.08463 1.888746 -5.87 0.000 -14.7869 -7.38237 77 | 14.00118 1.886979 7.42 0.000 10.30238 17.69998 78 | -8.43247 1.883247 -4.48 0.000 -12.12395 -4.740986 79 | -3.531187 1.882852 -1.88 0.061 -7.221896 .1595233 80 | -.1802846 1.88246 -0.10 0.924 -3.870227 3.509658 81 | 8.714384 1.882073 4.63 0.000 5.025202 12.40357 82 | -3.744767 1.880556 -1.99 0.046 -7.430977 -.0585577 83 | 5.663561 1.880556 3.01 0.003 1.977352 9.34977 84 | .1282536 1.880556 0.07 0.946 -3.557956 3.814463 85 | 5.25524 1.879818 2.80 0.005 1.570477 8.940003 86 | .601706 1.879455 0.32 0.749 -3.082344 4.285756 87 | 3.362022 1.879094 1.79 0.074 -.3213211 7.045365 88 | 1.979885 1.879094 1.05 0.292 -1.703458 5.663228 89 | 3.037238 1.876321 1.62 0.106 -.6406698 6.715146 90 | 6.268529 1.875005 3.34 0.001 2.5932 9.943857 91 | 11.79651 1.871607 6.30 0.000 8.127848 15.46518 92 | 2.798214 1.870732 1.50 0.135 -.8687376 6.465166 93 | 8.956046 1.870445 4.79 0.000 5.289657 12.62244 94 | -9.05919 1.86877 -4.85 0.000 -12.7223 -5.396084 95 | .1418222 1.86877 0.08 0.940 -3.521284 3.804928 96 | 11.83867 1.867171 6.34 0.000 8.1787 15.49864 97 | .5145903 1.862333 0.28 0.782 -3.135899 4.165079 98 | .2560854 1.861666 0.14 0.891 -3.393095 3.905266 99 | 14.01656 1.85642 7.55 0.000 10.37766 17.65546 100 | -.3351337 1.85569 -0.18 0.857 -3.972601 3.302334 | _cons | 24.32444 1.8003 13.51 0.000 20.79555 27.85333 ------------------------------------------------------------------------------ . use simbin_clustcow.dta, clear . logit Y X i.herd, asis Iteration 0: log likelihood = -6910.3442 Iteration 1: log likelihood = -5871.9702 Iteration 2: log likelihood = -5810.5761 Iteration 3: log likelihood = -5808.037 Iteration 4: log likelihood = -5807.961 Iteration 5: log likelihood = -5807.9609 Logistic regression Number of obs = 11,626 LR chi2(100) = 2204.77 Prob > chi2 = 0.0000 Log likelihood = -5807.9609 Pseudo R2 = 0.1595 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .7037681 .0462786 15.21 0.000 .6130636 .7944726 | herd | 2 | 1.464052 .7736212 1.89 0.058 -.0522174 2.980322 3 | 1.170623 .7593863 1.54 0.123 -.3177464 2.658993 4 | 1.618762 .7468126 2.17 0.030 .1550363 3.082488 5 | -.3622129 .8817161 -0.41 0.681 -2.090345 1.365919 6 | 2.547188 .7525714 3.38 0.001 1.072175 4.022201 7 | 2.907366 .770109 3.78 0.000 1.39798 4.416752 8 | 2.272912 .7409149 3.07 0.002 .8207457 3.725079 9 | .3856383 .7825535 0.49 0.622 -1.148138 1.919415 10 | -1.622873 1.199061 -1.35 0.176 -3.972989 .7272438 11 | 1.915425 .7323036 2.62 0.009 .480136 3.350713 12 | .1271594 .8013326 0.16 0.874 -1.443424 1.697742 13 | .1271594 .8013326 0.16 0.874 -1.443424 1.697742 14 | .5002686 .7658501 0.65 0.514 -1.00077 2.001307 15 | -.5407558 .8772847 -0.62 0.538 -2.260202 1.178691 16 | -.3271922 .8268742 -0.40 0.692 -1.947836 1.293451 17 | 1.349539 .7216192 1.87 0.061 -.0648087 2.763887 18 | .3443184 .761653 0.45 0.651 -1.148494 1.837131 19 | 2.523936 .7244937 3.48 0.000 1.103955 3.943918 20 | 1.600434 .7143851 2.24 0.025 .2002652 3.000603 21 | .8535915 .7275448 1.17 0.241 -.5723701 2.279553 22 | 1.559832 .712662 2.19 0.029 .1630404 2.956624 23 | .2093641 .7584782 0.28 0.783 -1.277226 1.695954 24 | .3543194 .7465973 0.47 0.635 -1.108984 1.817623 25 | -.2512472 .7929482 -0.32 0.751 -1.805397 1.302903 26 | 1.38016 .7070654 1.95 0.051 -.0056627 2.765983 27 | -.2705637 .7924538 -0.34 0.733 -1.823745 1.282617 28 | -.2705637 .7924538 -0.34 0.733 -1.823745 1.282617 29 | .9513724 .7103156 1.34 0.180 -.4408206 2.343565 30 | 1.351809 .7024931 1.92 0.054 -.025052 2.72867 31 | .5879134 .7212949 0.82 0.415 -.8257986 2.001625 32 | -.6242464 .821278 -0.76 0.447 -2.233922 .9854288 33 | 1.322313 .7015163 1.88 0.059 -.0526338 2.69726 34 | -.4061465 .790207 -0.51 0.607 -1.954924 1.142631 35 | 1.370376 .6993817 1.96 0.050 -.0003874 2.741138 36 | 1.088843 .7039312 1.55 0.122 -.2908367 2.468523 37 | 2.451419 .7039883 3.48 0.000 1.071627 3.83121 38 | .2917802 .7335553 0.40 0.691 -1.145962 1.729522 39 | 2.396693 .7013308 3.42 0.001 1.02211 3.771276 40 | 1.063799 .7031859 1.51 0.130 -.3144201 2.442018 41 | 2.71341 .7076245 3.83 0.000 1.326492 4.100329 42 | 1.473795 .6957181 2.12 0.034 .1102122 2.837377 43 | 2.649916 .7042126 3.76 0.000 1.269685 4.030147 44 | 1.892143 .6923309 2.73 0.006 .5351993 3.249086 45 | .3222867 .7244805 0.44 0.656 -1.097669 1.742242 46 | 2.01674 .6917662 2.92 0.004 .6609029 3.372577 47 | .6155321 .7087622 0.87 0.385 -.7736163 2.004681 48 | 1.254889 .693386 1.81 0.070 -.1041221 2.613901 49 | 1.507312 .6887245 2.19 0.029 .1574369 2.857187 50 | .2279885 .7228601 0.32 0.752 -1.188791 1.644768 51 | 1.093577 .6696441 1.63 0.102 -.2189013 2.406056 52 | 1.75509 .6608457 2.66 0.008 .4598563 3.050324 53 | -.3494651 .7021245 -0.50 0.619 -1.725604 1.026674 54 | -.462057 .7012843 -0.66 0.510 -1.836549 .9124349 55 | 1.2621 .6594879 1.91 0.056 -.0304724 2.554673 56 | 3.018589 .6663273 4.53 0.000 1.712611 4.324567 57 | -.3178017 .6887097 -0.46 0.644 -1.667648 1.032044 58 | 1.836669 .6539541 2.81 0.005 .5549426 3.118396 59 | .5157728 .6628867 0.78 0.437 -.7834612 1.815007 60 | .1771838 .6688583 0.26 0.791 -1.133754 1.488122 61 | 1.650583 .6526415 2.53 0.011 .3714294 2.929737 62 | .4430613 .6614298 0.67 0.503 -.8533174 1.73944 63 | 1.481111 .6522875 2.27 0.023 .2026513 2.759571 64 | .9428472 .6549982 1.44 0.150 -.3409256 2.22662 65 | -1.203757 .7284121 -1.65 0.098 -2.631419 .2239041 66 | 1.462062 .6518104 2.24 0.025 .1845372 2.739587 67 | -1.03609 .7107443 -1.46 0.145 -2.429124 .356943 68 | .5836485 .6564051 0.89 0.374 -.7028818 1.870179 69 | 1.63526 .6495967 2.52 0.012 .3620738 2.908446 70 | 1.009096 .651701 1.55 0.122 -.2682148 2.286406 71 | 1.106806 .6509832 1.70 0.089 -.1690977 2.382709 72 | 1.764194 .6490061 2.72 0.007 .4921657 3.036223 73 | 1.454343 .6493218 2.24 0.025 .1816959 2.72699 74 | 2.645304 .6518276 4.06 0.000 1.367745 3.922863 75 | -.4566702 .6762469 -0.68 0.499 -1.78209 .8687494 76 | -2.441802 .8586407 -2.84 0.004 -4.124707 -.7588972 77 | 1.703338 .6472359 2.63 0.008 .4347787 2.971897 78 | -1.37405 .717516 -1.92 0.055 -2.780356 .0322552 79 | -.6994571 .6802396 -1.03 0.304 -2.032702 .633788 80 | -.4161735 .6704249 -0.62 0.535 -1.730182 .8978352 81 | 1.267766 .6472003 1.96 0.050 -.0007232 2.536255 82 | -1.106402 .6978069 -1.59 0.113 -2.474079 .2612743 83 | .8230967 .6493033 1.27 0.205 -.4495144 2.095708 84 | -.1682734 .6631341 -0.25 0.800 -1.467992 1.131446 85 | .8790128 .6487414 1.35 0.175 -.3924968 2.150523 86 | .3069123 .6543537 0.47 0.639 -.9755974 1.589422 87 | -.1488085 .6621338 -0.22 0.822 -1.446567 1.14895 88 | .3585251 .6535491 0.55 0.583 -.9224076 1.639458 89 | .3130271 .6533424 0.48 0.632 -.9675004 1.593555 90 | .0773685 .6563783 0.12 0.906 -1.209109 1.363846 91 | 1.641164 .6444201 2.55 0.011 .3781236 2.904204 92 | .3000771 .6518837 0.46 0.645 -.9775916 1.577746 93 | 1.006892 .6459791 1.56 0.119 -.2592041 2.272988 94 | -.9668609 .6821546 -1.42 0.156 -2.303859 .3701376 95 | -.3907563 .6633882 -0.59 0.556 -1.690973 .9094607 96 | 1.841699 .6435616 2.86 0.004 .5803409 3.103056 97 | .2936752 .6495229 0.45 0.651 -.9793664 1.566717 98 | .2063121 .6502998 0.32 0.751 -1.068252 1.480876 99 | 2.02631 .64172 3.16 0.002 .7685615 3.284058 100 | .1299544 .6493153 0.20 0.841 -1.14268 1.402589 | _cons | -2.129608 .631634 -3.37 0.001 -3.367588 -.8916277 ------------------------------------------------------------------------------ . . * Mantel-Haenszel procedure . use simbin_clustcow.dta, clear . cc Y X, by(herd) herd | OR [95% Conf. Interval] M-H Weight -----------------+------------------------------------------------- 1 | . .9048609 . 0 (exact) 2 | 1.25 .1626352 9.892487 1.142857 (exact) 3 | 5.833333 .7077892 70.40121 .48 (exact) 4 | .5357143 .0853896 3.264111 2.153846 (exact) 5 | . .7951185 . 0 (exact) 6 | 2.75 .4092367 21.5737 .8571429 (exact) 7 | 3.333333 .4045859 40.9002 .6428571 (exact) 8 | 2.75 .4622328 17.56168 .9655172 (exact) 9 | 6.5 .5552238 330.517 .3448276 (exact) 10 | . 0 . 0 (exact) 11 | 1.714286 .3243022 9.247996 1.4 (exact) 12 | 1.625 .1542296 22.28922 .8 (exact) 13 | .6153846 .0448629 6.483884 1.3 (exact) 14 | 2.954545 .3729396 35.64326 .7096774 (exact) 15 | .4666667 .0074234 10.13893 .9375 (exact) 16 | 3.2 .2206377 178.2772 .4285714 (exact) 17 | .9090909 .1914922 4.326952 2.2 (exact) 18 | 1.333333 .1849703 10.74942 1.2 (exact) 19 | 1.781818 .3609598 9.173558 1.486486 (exact) 20 | 2.75 .6028725 12.98858 1.297297 (exact) 21 | 3.878788 .6954999 26.8677 .8684211 (exact) 22 | 1.2375 .2872619 5.364267 2.105263 (exact) 23 | 7.714286 .7574556 374.0486 .3589744 (exact) 24 | 10.23077 1.04612 484.685 .325 (exact) 25 | 4.470588 .3785522 231.49 .4146341 (exact) 26 | 1.818182 .4426808 7.646529 1.833333 (exact) 27 | 4.705882 .3995133 243.07 .4047619 (exact) 28 | 4.705882 .3995133 243.07 .4047619 (exact) 29 | 2.185714 .5033592 10.19969 1.555556 (exact) 30 | 1.346154 .3473786 5.289449 2.311111 (exact) 31 | 6.75 1.105351 70.43244 .6086957 (exact) 32 | 3.3 .2363841 180.9459 .4347826 (exact) 33 | 1.442308 .3753545 5.614642 2.26087 (exact) 34 | 4.4 .3808243 226.3113 .4255319 (exact) 35 | 1.586538 .4215339 6.072896 2.212766 (exact) 36 | 3.046154 .7310814 13.76903 1.382979 (exact) 37 | 2.307692 .5715921 9.726768 1.659574 (exact) 38 | 2.222222 .3953127 15.5077 1.148936 (exact) 39 | 3.8 .9207688 17.01576 1.25 (exact) 40 | 2.142857 .5366468 8.95608 1.75 (exact) 41 | 1.058824 .2550643 4.389841 2.428571 (exact) 42 | .7878788 .218652 2.832178 3.367347 (exact) 43 | 4.125 .9439785 20.85567 1.12 (exact) 44 | 1.477273 .4268405 5.139578 2.588235 (exact) 45 | 1.575 .3149334 8.701329 1.568627 (exact) 46 | 6.296296 1.615629 25.78857 1.038462 (exact) 47 | .3285024 .0642865 1.45527 3.90566 (exact) 48 | 3.589744 .9603942 14.2219 1.471698 (exact) 49 | 1.7 .5097952 5.73953 2.545455 (exact) 50 | .9565217 .190967 4.796742 2.090909 (exact) 51 | 1.935185 .7341281 5.179395 3.56044 (exact) 52 | 1.899209 .8232199 4.399525 4.728972 (exact) 53 | 1.459574 .367796 6.240886 2.175926 (exact) 54 | .9814815 .2452764 3.928224 2.722689 (exact) 55 | 2.933333 1.267148 6.883933 3.781513 (exact) 56 | 1.890909 .7493979 4.910543 3.928571 (exact) 57 | 1.142857 .3369456 3.962716 3.099237 (exact) 58 | 2 .967757 4.145337 6 (exact) 59 | 1.895425 .7884736 4.681192 4.340426 (exact) 60 | 1.631579 .6253286 4.400487 3.958333 (exact) 61 | 3.72205 1.790853 7.781826 4.322148 (exact) 62 | 2.4 1.004589 5.961365 3.928571 (exact) 63 | 2.368889 1.172023 4.809167 5.844156 (exact) 64 | 2.695652 1.25491 5.894686 4.717949 (exact) 65 | 1.689189 .3145984 11.2302 1.414013 (exact) 66 | 2.737269 1.357276 5.549848 5.468354 (exact) 67 | 1.538462 .3485597 7.686526 1.857143 (exact) 68 | 1.793033 .8293041 3.940985 5.674419 (exact) 69 | 2.216283 1.155521 4.261833 6.988506 (exact) 70 | 1.274536 .6457513 2.522527 8.519774 (exact) 71 | 2.643343 1.32713 5.315913 5.780899 (exact) 72 | 1.755061 .9313773 3.312375 8.27933 (exact) 73 | 1.903226 1.001306 3.627241 7.75 (exact) 74 | 1.463889 .7390993 2.912365 7.868852 (exact) 75 | 1.818815 .6222934 5.716085 3.053191 (exact) 76 | 2 .1021853 119.1905 .4923077 (exact) 77 | 1.728997 .9497046 3.15195 9.271357 (exact) 78 | .2717087 .0270621 1.479965 3.432692 (exact) 79 | 1.125 .3677098 3.503059 3.674641 (exact) 80 | 3.863636 1.291432 13.87083 2.095238 (exact) 81 | 2.888889 1.556936 5.393682 6.781991 (exact) 82 | .6934813 .1680196 2.638256 3.353488 (exact) 83 | 1.241429 .656701 2.353241 9.767442 (exact) 84 | 3.448276 1.324761 10.02351 2.832558 (exact) 85 | 2.450475 1.283746 4.730079 6.792627 (exact) 86 | 2.676923 1.244167 5.97691 4.770642 (exact) 87 | 4.538314 1.686463 14.15979 2.383562 (exact) 88 | 1.393189 .6801907 2.883222 7.374429 (exact) 89 | 1.559343 .7615576 3.238469 6.977974 (exact) 90 | 5.38206 2.165676 15.13253 2.606061 (exact) 91 | 1.889362 1.097655 3.256022 10.68182 (exact) 92 | 3.203111 1.529742 7.003147 4.722449 (exact) 93 | 2.220123 1.237445 4.008197 8.605691 (exact) 94 | 3.210526 .9342177 13.99336 1.809524 (exact) 95 | 2.166667 .8767537 5.70404 3.857143 (exact) 96 | 2.498798 1.468905 4.257137 9.674419 (exact) 97 | 2.045113 1.057989 4.028883 7.176259 (exact) 98 | 1.794737 .9199104 3.562613 7.437722 (exact) 99 | 1.354032 .8402866 2.182873 16.15635 (exact) 100 | 1.088372 .5740342 2.067865 10.36977 (exact) -----------------+------------------------------------------------- Crude | 1.797341 1.65396 1.953169 (exact) M-H combined | 2.008957 1.83547 2.198841 ------------------------------------------------------------------- Test of homogeneity (Tarone) chi2(99) = 101.38 Pr>chi2 = 0.4148 Test that combined OR = 1: Mantel-Haenszel chi2(1) = 233.10 Pr>chi2 = 0.0000 . di "approx SE: " (ln(2.008957)-ln(1.83547))/1.96 approx SE: .04607913 . . * robust variance . use simcont_clustherd.dta, clear . regress milk X, vce(cluster herd) Linear regression Number of obs = 11,626 F(1, 99) = 4.32 Prob > F = 0.0403 R-squared = 0.0266 Root MSE = 10.733 (Std. Err. adjusted for 100 clusters in herd) ------------------------------------------------------------------------------ | Robust milk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 3.55661 1.711824 2.08 0.040 .1599804 6.95324 _cons | 30.0215 1.092129 27.49 0.000 27.85448 32.18852 ------------------------------------------------------------------------------ . use simcont_clustcow.dta, clear . regress milk X, vce(cluster herd) Linear regression Number of obs = 11,626 F(1, 99) = 1232.30 Prob > F = 0.0000 R-squared = 0.0510 Root MSE = 10.744 (Std. Err. adjusted for 100 clusters in herd) ------------------------------------------------------------------------------ | Robust milk | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 4.982006 .1419208 35.10 0.000 4.700404 5.263607 _cons | 29.25664 .8738122 33.48 0.000 27.5228 30.99047 ------------------------------------------------------------------------------ . use simbin_clustherd.dta, clear . logit Y X, vce(cluster herd) Iteration 0: log pseudolikelihood = -6894.3552 Iteration 1: log pseudolikelihood = -6815.0583 Iteration 2: log pseudolikelihood = -6814.7785 Iteration 3: log pseudolikelihood = -6814.7785 Logistic regression Number of obs = 11,626 Wald chi2(1) = 6.31 Prob > chi2 = 0.0120 Log pseudolikelihood = -6814.7785 Pseudo R2 = 0.0115 (Std. Err. adjusted for 100 clusters in herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5287317 .2105488 2.51 0.012 .1160637 .9413998 _cons | -1.241768 .145627 -8.53 0.000 -1.527192 -.9563443 ------------------------------------------------------------------------------ . use simbin_clustcow.dta, clear . logit Y X, vce(cluster herd) Iteration 0: log pseudolikelihood = -6910.3442 Iteration 1: log pseudolikelihood = -6811.48 Iteration 2: log pseudolikelihood = -6811.0741 Iteration 3: log pseudolikelihood = -6811.0741 Logistic regression Number of obs = 11,626 Wald chi2(1) = 179.23 Prob > chi2 = 0.0000 Log pseudolikelihood = -6811.0741 Pseudo R2 = 0.0144 (Std. Err. adjusted for 100 clusters in herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5863084 .0437941 13.39 0.000 .5004736 .6721432 _cons | -1.25032 .1144647 -10.92 0.000 -1.474667 -1.025973 ------------------------------------------------------------------------------ . . * GEE for binary outcome . use simbin_clustherd.dta, clear . xtgee Y X, fam(bin) link(logit) robust i(herd) corr(indep) /* same as robust variance */ Iteration 1: tolerance = 2.181e-09 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: independent avg = 116.3 max = 311 Wald chi2(1) = 6.31 Scale parameter: 1 Prob > chi2 = 0.0120 Pearson chi2(11626): 11626.00 Deviance = 13629.56 Dispersion (Pearson): 1 Dispersion = 1.172334 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5287317 .2105488 2.51 0.012 .1160637 .9413998 _cons | -1.241768 .145627 -8.53 0.000 -1.527192 -.9563443 ------------------------------------------------------------------------------ . xtgee Y X, fam(bin) robust i(herd) corr(indep) /* logit is default link for fam(bin) */ Iteration 1: tolerance = 2.181e-09 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: independent avg = 116.3 max = 311 Wald chi2(1) = 6.31 Scale parameter: 1 Prob > chi2 = 0.0120 Pearson chi2(11626): 11626.00 Deviance = 13629.56 Dispersion (Pearson): 1 Dispersion = 1.172334 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5287317 .2105488 2.51 0.012 .1160637 .9413998 _cons | -1.241768 .145627 -8.53 0.000 -1.527192 -.9563443 ------------------------------------------------------------------------------ . xtgee Y X, fam(bin) vce(robust) i(herd) corr(indep) /* same as above */ Iteration 1: tolerance = 2.181e-09 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: independent avg = 116.3 max = 311 Wald chi2(1) = 6.31 Scale parameter: 1 Prob > chi2 = 0.0120 Pearson chi2(11626): 11626.00 Deviance = 13629.56 Dispersion (Pearson): 1 Dispersion = 1.172334 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5287317 .2105488 2.51 0.012 .1160637 .9413998 _cons | -1.241768 .145627 -8.53 0.000 -1.527192 -.9563443 ------------------------------------------------------------------------------ . xtgee Y X, fam(bin) robust i(herd) corr(exch) Iteration 1: tolerance = .06052491 Iteration 2: tolerance = .00166018 Iteration 3: tolerance = .00001941 Iteration 4: tolerance = 1.325e-07 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: exchangeable avg = 116.3 max = 311 Wald chi2(1) = 9.98 Scale parameter: 1 Prob > chi2 = 0.0016 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5588542 .1768743 3.16 0.002 .2121869 .9055215 _cons | -1.109623 .1251571 -8.87 0.000 -1.354926 -.8643196 ------------------------------------------------------------------------------ . estat wcor, compact /* displays working correlation(s) */ Error structure: exchangeable Estimated within-herd correlation: .15134071 . use simbin_clustcow.dta, clear . xtgee Y X, fam(bin) robust i(herd) corr(indep) Iteration 1: tolerance = 3.102e-09 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: independent avg = 116.3 max = 311 Wald chi2(1) = 179.23 Scale parameter: 1 Prob > chi2 = 0.0000 Pearson chi2(11626): 11626.00 Deviance = 13622.15 Dispersion (Pearson): 1 Dispersion = 1.171697 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5863084 .0437941 13.39 0.000 .5004736 .6721432 _cons | -1.25032 .1144647 -10.92 0.000 -1.474667 -1.025973 ------------------------------------------------------------------------------ . xtgee Y X, fam(bin) robust i(herd) corr(exch) Iteration 1: tolerance = .06275994 Iteration 2: tolerance = .00152416 Iteration 3: tolerance = .00003718 Iteration 4: tolerance = 1.113e-06 Iteration 5: tolerance = 2.966e-08 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: exchangeable avg = 116.3 max = 311 Wald chi2(1) = 184.02 Scale parameter: 1 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .5687287 .0419247 13.57 0.000 .4865578 .6508997 _cons | -1.112355 .0948099 -11.73 0.000 -1.298179 -.9265314 ------------------------------------------------------------------------------ . estat wcor, compact Error structure: exchangeable Estimated within-herd correlation: .15631633 . . * GEE for continuous outcome . use simcont_clustherd.dta, clear . xtgee milk X, fam(gauss) link(iden) robust i(herd) corr(exch) Iteration 1: tolerance = .05318109 Iteration 2: tolerance = .00034544 Iteration 3: tolerance = 6.094e-07 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: identity Obs per group: Family: Gaussian min = 20 Correlation: exchangeable avg = 116.3 max = 311 Wald chi2(1) = 6.51 Scale parameter: 116.7291 Prob > chi2 = 0.0107 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust milk | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 3.797275 1.488196 2.55 0.011 .8804645 6.714085 _cons | 31.13476 1.040243 29.93 0.000 29.09592 33.1736 ------------------------------------------------------------------------------ . use simcont_clustcow.dta, clear . xtgee milk X, fam(gauss) link(iden) robust i(herd) corr(exch) Iteration 1: tolerance = .04589737 Iteration 2: tolerance = .00008274 Iteration 3: tolerance = 1.942e-07 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: identity Obs per group: Family: Gaussian min = 20 Correlation: exchangeable avg = 116.3 max = 311 Wald chi2(1) = 1234.47 Scale parameter: 117.3372 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust milk | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 4.968177 .1414023 35.14 0.000 4.691034 5.245321 _cons | 30.64796 .7217876 42.46 0.000 29.23328 32.06264 ------------------------------------------------------------------------------ . . * analyses for pig data . use pig_adg, clear (Growth Performance and Abattoir Surveillance Data on Pigs, Real Data) . generate ar_g1=ar>1 if ar~=. . * ordinary logistic regression . logit pn ar_g1 Iteration 0: log likelihood = -234.95215 Iteration 1: log likelihood = -230.59287 Iteration 2: log likelihood = -230.59173 Iteration 3: log likelihood = -230.59173 Logistic regression Number of obs = 341 LR chi2(1) = 8.72 Prob > chi2 = 0.0031 Log likelihood = -230.59173 Pseudo R2 = 0.0186 ------------------------------------------------------------------------------ pn | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ar_g1 | .6465241 .2203379 2.93 0.003 .2146697 1.078378 _cons | -.1448309 .1556373 -0.93 0.352 -.4498744 .1602125 ------------------------------------------------------------------------------ . * fixed effects logistic regression . logit pn ar_g1 i.farm, asis Iteration 0: log likelihood = -234.95215 Iteration 1: log likelihood = -194.7543 Iteration 2: log likelihood = -193.88065 Iteration 3: log likelihood = -193.86711 Iteration 4: log likelihood = -193.8671 Logistic regression Number of obs = 341 LR chi2(15) = 82.17 Prob > chi2 = 0.0000 Log likelihood = -193.8671 Pseudo R2 = 0.1749 ------------------------------------------------------------------------------ pn | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ar_g1 | .3651127 .2678889 1.36 0.173 -.1599398 .8901652 | farm | 2 | -.6608706 .7345805 -0.90 0.368 -2.100622 .7788806 3 | -3.181252 .7360392 -4.32 0.000 -4.623862 -1.738642 4 | -1.658611 .6726559 -2.47 0.014 -2.976992 -.3402299 5 | -.8748085 .7372227 -1.19 0.235 -2.319738 .5701213 6 | 1.411727 1.158223 1.22 0.223 -.8583474 3.681801 7 | -1.241977 .7120953 -1.74 0.081 -2.637658 .1537041 8 | -.6862302 .7012406 -0.98 0.328 -2.060636 .688176 9 | -1.644387 .6834869 -2.41 0.016 -2.983997 -.3047778 10 | -1.536526 .7318713 -2.10 0.036 -2.970967 -.1020843 11 | -1.310881 .7055684 -1.86 0.063 -2.693769 .072008 12 | -1.40703 .7684634 -1.83 0.067 -2.91319 .0991308 13 | -2.973781 .7437175 -4.00 0.000 -4.43144 -1.516121 14 | -1.904232 .6830497 -2.79 0.005 -3.242985 -.5654794 15 | -2.792443 .7512611 -3.72 0.000 -4.264887 -1.319998 | _cons | 1.461934 .5707978 2.56 0.010 .3431912 2.580678 ------------------------------------------------------------------------------ . * Mantel-Haenszel procedure . cc pn ar_g1, by(farm) Farm identificat | OR [95% Conf. Interval] M-H Weight -----------------+------------------------------------------------- 1 | 0 0 1.987843 1.230769 (exact) 2 | 3.333333 .249723 183.4806 .4285714 (exact) 3 | 1.636364 .15285 22.6999 .7857143 (exact) 4 | 1 .1657092 6.035157 1.615385 (exact) 5 | .125 .0023556 1.791506 2.105263 (exact) 6 | . 0 . 0 (exact) 7 | 2.666667 .1641335 157.1844 .4285714 (exact) 8 | 8 .3194679 494.706 .1785714 (exact) 9 | 3.928571 .4498158 49.3709 .56 (exact) 10 | 1.25 .1282001 12.298 .9411765 (exact) 11 | 1.428571 .1745708 13.12955 1 (exact) 12 | .8333333 .047384 11.9645 .8571429 (exact) 13 | 4.5 .3690823 64.38143 .4 (exact) 14 | .8 .0833334 7.784078 1.25 (exact) 15 | 2.166667 .1305404 26.50935 .5454545 (exact) -----------------+------------------------------------------------- Crude | 1.908894 1.21155 3.009556 (exact) M-H combined | 1.412829 .8470242 2.356586 ------------------------------------------------------------------- Test of homogeneity (Tarone) chi2(14) = 16.06 Pr>chi2 = 0.3096 Test that combined OR = 1: Mantel-Haenszel chi2(1) = 1.78 Pr>chi2 = 0.1821 . di "ln OR: " ln(1.412829) ln OR: .34559408 . di "SE: " (ln(1.412829)-ln(.8470242))/1.96 SE: .26103066 . * robust variance . logit pn ar_g1, vce(cluster farm) Iteration 0: log pseudolikelihood = -234.95215 Iteration 1: log pseudolikelihood = -230.59287 Iteration 2: log pseudolikelihood = -230.59173 Iteration 3: log pseudolikelihood = -230.59173 Logistic regression Number of obs = 341 Wald chi2(1) = 5.48 Prob > chi2 = 0.0192 Log pseudolikelihood = -230.59173 Pseudo R2 = 0.0186 (Std. Err. adjusted for 15 clusters in farm) ------------------------------------------------------------------------------ | Robust pn | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ar_g1 | .6465241 .2760887 2.34 0.019 .1054002 1.187648 _cons | -.1448309 .278696 -0.52 0.603 -.6910651 .4014032 ------------------------------------------------------------------------------ . * random effects model . meqrlogit pn ar_g1 || farm: Refining starting values: Iteration 0: log likelihood = -213.91344 Iteration 1: log likelihood = -213.51368 Iteration 2: log likelihood = -213.5118 Performing gradient-based optimization: Iteration 0: log likelihood = -213.5118 Iteration 1: log likelihood = -213.5118 Mixed-effects logistic regression Number of obs = 341 Group variable: farm Number of groups = 15 Obs per group: min = 14 avg = 22.7 max = 28 Integration points = 7 Wald chi2(1) = 2.86 Log likelihood = -213.5118 Prob > chi2 = 0.0905 ------------------------------------------------------------------------------ pn | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ar_g1 | .4369353 .2581461 1.69 0.091 -.0690217 .9428923 _cons | .0196485 .3009417 0.07 0.948 -.5701864 .6094834 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ farm: Identity | var(_cons) | .8773258 .4324896 .3338486 2.305537 ------------------------------------------------------------------------------ LR test vs. logistic model: chibar2(01) = 34.16 Prob >= chibar2 = 0.0000 . di .4369353/(sqrt(1+.346*.8773258)) .38269474 . * GEE with exchangeable correlation structure . xtgee pn ar_g1, fam(bin) robust i(farm) corr(exch) Iteration 1: tolerance = .17657314 Iteration 2: tolerance = .0013339 Iteration 3: tolerance = .00001851 Iteration 4: tolerance = 2.251e-07 GEE population-averaged model Number of obs = 341 Group variable: farm Number of groups = 15 Link: logit Obs per group: Family: binomial min = 14 Correlation: exchangeable avg = 22.7 max = 28 Wald chi2(1) = 2.71 Scale parameter: 1 Prob > chi2 = 0.1000 (Std. Err. adjusted for clustering on farm) ------------------------------------------------------------------------------ | Robust pn | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- ar_g1 | .3539583 .2151855 1.64 0.100 -.0677976 .7757142 _cons | .0183926 .2714184 0.07 0.946 -.5135777 .5503629 ------------------------------------------------------------------------------ . estat wcor, compact Error structure: exchangeable Estimated within-farm correlation: .17940234 . . * margins for linear mixed models . use simcont_clustcow.dta, clear . mixed milk i.X || herd:, reml Performing EM optimization: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -40947.175 Iteration 1: log restricted-likelihood = -40947.175 Computing standard errors: Mixed-effects REML regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Wald chi2(1) = 1108.56 Log restricted-likelihood = -40947.175 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ milk | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 1.X | 4.968194 .1492174 33.30 0.000 4.675733 5.260655 _cons | 30.64647 .7281276 42.09 0.000 29.21936 32.07357 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | 51.41189 7.459591 38.68644 68.32323 -----------------------------+------------------------------------------------ var(Residual) | 64.71069 .8524578 63.06129 66.40324 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 6310.00 Prob >= chibar2 = 0.0000 . margins X /* broad inference space predictions ~ zero random effects */ Adjusted predictions Number of obs = 11,626 Expression : Linear prediction, fixed portion, predict() ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | 30.64647 .7281276 42.09 0.000 29.21936 32.07357 1 | 35.61466 .7279903 48.92 0.000 34.18783 37.04149 ------------------------------------------------------------------------------ . . * margins for discrete models . use simbin_clustcow.dta, clear . * GLMM . melogit Y i.X || herd: Fitting fixed-effects model: Iteration 0: log likelihood = -6824.417 Iteration 1: log likelihood = -6811.0819 Iteration 2: log likelihood = -6811.0741 Iteration 3: log likelihood = -6811.0741 Refining starting values: Grid node 0: log likelihood = -5999.0535 Fitting full model: Iteration 0: log likelihood = -5999.0535 Iteration 1: log likelihood = -5995.9716 Iteration 2: log likelihood = -5995.9694 Iteration 3: log likelihood = -5995.9694 Mixed-effects logistic regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Integration method: mvaghermite Integration pts. = 7 Wald chi2(1) = 229.28 Log likelihood = -5995.9694 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- | 1.X | .6974798 .046063 15.14 0.000 .6071979 .7877616 _cons | -1.361196 .1111563 -12.25 0.000 -1.579059 -1.143334 -------------+---------------------------------------------------------------- herd | var(_cons)| 1.068314 .1682536 .7845836 1.45465 ------------------------------------------------------------------------------ LR test vs. logistic model: chibar2(01) = 1630.21 Prob >= chibar2 = 0.0000 . margins X /* PA prediction */ Adjusted predictions Number of obs = 11,626 Model VCE : OIM Expression : Marginal predicted mean, predict() ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | .244766 .0179262 13.65 0.000 .2096314 .2799006 1 | .3671156 .0212009 17.32 0.000 .3255626 .4086687 ------------------------------------------------------------------------------ . margins X, predict(xb) /* estimates on logit scale */ Adjusted predictions Number of obs = 11,626 Model VCE : OIM Expression : Linear prediction, fixed portion only, predict(xb) ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | -1.361196 .1111563 -12.25 0.000 -1.579059 -1.143334 1 | -.6637166 .1097788 -6.05 0.000 -.8788792 -.448554 ------------------------------------------------------------------------------ . * try same thing with meqrlogit . meqrlogit Y i.X || herd: Refining starting values: Iteration 0: log likelihood = -5999.0538 Iteration 1: log likelihood = -5995.9727 Iteration 2: log likelihood = -5995.9698 Performing gradient-based optimization: Iteration 0: log likelihood = -5995.9698 Iteration 1: log likelihood = -5995.9698 Mixed-effects logistic regression Number of obs = 11,626 Group variable: herd Number of groups = 100 Obs per group: min = 20 avg = 116.3 max = 311 Integration points = 7 Wald chi2(1) = 229.28 Log likelihood = -5995.9698 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 1.X | .697479 .046063 15.14 0.000 .6071972 .7877609 _cons | -1.361173 .1112103 -12.24 0.000 -1.579141 -1.143204 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ herd: Identity | var(_cons) | 1.068172 .1682549 .7844459 1.45452 ------------------------------------------------------------------------------ LR test vs. logistic model: chibar2(01) = 1630.21 Prob >= chibar2 = 0.0000 . margins X /* logit scale! */ Adjusted predictions Number of obs = 11,626 Expression : Linear prediction, fixed portion, predict(xb) ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | -1.361173 .1112103 -12.24 0.000 -1.579141 -1.143204 1 | -.6636935 .1098341 -6.04 0.000 -.8789643 -.4484227 ------------------------------------------------------------------------------ . * medians (broad inference space) . margins X, expression(1/(1+exp(-predict(xb)))) Adjusted predictions Number of obs = 11,626 Expression : 1/(1+exp(-predict(xb))) ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | .2040498 .018062 11.30 0.000 .1686488 .2394508 1 | .3399104 .0246436 13.79 0.000 .2916098 .388211 ------------------------------------------------------------------------------ . * means (broad inference space, approx PA predictions) . margins X, expression(1/(1+exp(-predict(xb)/(sqrt(1+.346*1.068314))))) Adjusted predictions Number of obs = 11,626 Expression : 1/(1+exp(-predict(xb)/(sqrt(1+.346*1.068314)))) ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | .2381076 .0172389 13.81 0.000 .2043201 .2718952 1 | .3619047 .0216728 16.70 0.000 .3194269 .4043825 ------------------------------------------------------------------------------ . * GEE with PA predictions . xtgee Y i.X, fam(bin) link(logit) robust i(herd) corr(exch) Iteration 1: tolerance = .06275994 Iteration 2: tolerance = .00152416 Iteration 3: tolerance = .00003718 Iteration 4: tolerance = 1.113e-06 Iteration 5: tolerance = 2.966e-08 GEE population-averaged model Number of obs = 11,626 Group variable: herd Number of groups = 100 Link: logit Obs per group: Family: binomial min = 20 Correlation: exchangeable avg = 116.3 max = 311 Wald chi2(1) = 184.02 Scale parameter: 1 Prob > chi2 = 0.0000 (Std. Err. adjusted for clustering on herd) ------------------------------------------------------------------------------ | Robust Y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- 1.X | .5687287 .0419247 13.57 0.000 .4865578 .6508997 _cons | -1.112355 .0948099 -11.73 0.000 -1.298179 -.9265314 ------------------------------------------------------------------------------ . margins X Adjusted predictions Number of obs = 11,626 Model VCE : Robust Expression : Pr(Y != 0), predict() ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | .247432 .0176545 14.02 0.000 .2128298 .2820342 1 | .3673443 .0217279 16.91 0.000 .3247585 .4099302 ------------------------------------------------------------------------------ . margins X, expression(1/(1+exp(-predict(xb)))) /* same as above */ Adjusted predictions Number of obs = 11,626 Model VCE : Robust Expression : 1/(1+exp(-predict(xb))) ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 0 | .247432 .0176545 14.02 0.000 .2128298 .2820342 1 | .3673443 .0217279 16.91 0.000 .3247585 .4099302 ------------------------------------------------------------------------------ .