. * do-file for lecture 12 of VHM 802, Winter 2016 . version 14 /* works also with version 13 */ . set more off . cd "h:\vhm\vhm802\data_csv" h:\vhm\vhm802\data_csv . . import delimited guinea_long.csv, clear (4 vars, 90 obs) . * profile plots . twoway (connected weight week), by(group animal) . overlay weight week, by(animal) c(l) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- weight | 90 559.1 58.90881 436 702 Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- week | 90 4.333333 1.983074 1 7 . overlay weight week if group==1, by(animal) c(l) /* similar for groups 2,3 */ (60 observations deleted) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- weight | 30 539.1333 57.39022 436 619 Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- week | 30 4.333333 2.005739 1 7 . * mean plot . preserve /* run together with next 2 lines */ . collapse (mean) weight, by(group week) . overlay weight week, by(group) c(l) Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- weight | 18 559.1 44.83503 466.4 644 Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- week | 18 4.333333 2.029199 1 7 . end of do-file . do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp" . * disregarding repeated measures (wrong!) . anova weight group##week Number of obs = 90 R-squared = 0.5532 Root MSE = 43.7777 Adj R-squared = 0.4477 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | 170865.3 17 10050.9 5.24 0.0000 | group | 18548.067 2 9274.0333 4.84 0.0107 week | 142554.5 5 28510.9 14.88 0.0000 group#week | 9762.7333 10 976.27333 0.51 0.8781 | Residual | 137986.8 72 1916.4833 -----------+---------------------------------------------------- Total | 308852.1 89 3470.2483 . * separate analyses for each week . bysort week: oneway weight group ------------------------------------------------------------------------------------------------------ -> week = 1 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 2969.2 2 1484.6 2.10 0.1651 Within groups 8481.2 12 706.766667 ------------------------------------------------------------------------ Total 11450.4 14 817.885714 Bartlett's test for equal variances: chi2(2) = 1.4766 Prob>chi2 = 0.478 ------------------------------------------------------------------------------------------------------ -> week = 3 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 2497.6 2 1248.8 0.87 0.4427 Within groups 17170.4 12 1430.86667 ------------------------------------------------------------------------ Total 19668 14 1404.85714 Bartlett's test for equal variances: chi2(2) = 0.4744 Prob>chi2 = 0.789 ------------------------------------------------------------------------------------------------------ -> week = 4 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 302.533333 2 151.266667 0.14 0.8710 Within groups 12992.4 12 1082.7 ------------------------------------------------------------------------ Total 13294.9333 14 949.638095 Bartlett's test for equal variances: chi2(2) = 0.5086 Prob>chi2 = 0.775 ------------------------------------------------------------------------------------------------------ -> week = 5 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 260.4 2 130.2 0.05 0.9476 Within groups 28906 12 2408.83333 ------------------------------------------------------------------------ Total 29166.4 14 2083.31429 Bartlett's test for equal variances: chi2(2) = 0.9006 Prob>chi2 = 0.637 ------------------------------------------------------------------------------------------------------ -> week = 6 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 8550.93333 2 4275.46667 1.39 0.2863 Within groups 36898 12 3074.83333 ------------------------------------------------------------------------ Total 45448.9333 14 3246.35238 Bartlett's test for equal variances: chi2(2) = 0.6487 Prob>chi2 = 0.723 ------------------------------------------------------------------------------------------------------ -> week = 7 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 13730.1333 2 6865.06667 2.46 0.1276 Within groups 33538.8 12 2794.9 ------------------------------------------------------------------------ Total 47268.9333 14 3376.35238 Bartlett's test for equal variances: chi2(2) = 1.1559 Prob>chi2 = 0.561 . . * response features . * mean . preserve /* run together with next 2 lines */ . collapse (mean) weight, by(group animal) . oneway weight group Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 3091.34348 2 1545.67174 1.06 0.3782 Within groups 17572.3646 12 1464.36372 ------------------------------------------------------------------------ Total 20663.7081 14 1475.97915 Bartlett's test for equal variances: chi2(2) = 0.2914 Prob>chi2 = 0.864 . end of do-file . do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp" . * gain . preserve /* run together with next 3 lines */ . import delimited guinea_wide.csv, clear (7 vars, 15 obs) . gen gain=w7-w5 . oneway gain group Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 11286.5333 2 5643.26667 13.04 0.0010 Within groups 5194.4 12 432.866667 ------------------------------------------------------------------------ Total 16480.9333 14 1177.20952 Bartlett's test for equal variances: chi2(2) = 11.8859 Prob>chi2 = 0.003 . end of do-file . do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp" . * slope . anova weight animal c.week#animal Number of obs = 90 R-squared = 0.8947 Root MSE = 23.2769 Adj R-squared = 0.8439 Source | Partial SS df MS F Prob>F ------------+---------------------------------------------------- Model | 276343.16 29 9529.0744 17.59 0.0000 | animal | 9525.4621 14 680.39015 1.26 0.2618 animal#week | 152360.89 15 10157.393 18.75 0.0000 | Residual | 32508.943 60 541.81571 ------------+---------------------------------------------------- Total | 308852.1 89 3470.2483 . regress Source | SS df MS Number of obs = 90 -------------+---------------------------------- F(29, 60) = 17.59 Model | 276343.157 29 9529.07438 Prob > F = 0.0000 Residual | 32508.9429 60 541.815714 R-squared = 0.8947 -------------+---------------------------------- Adj R-squared = 0.8439 Total | 308852.1 89 3470.24831 Root MSE = 23.277 ------------------------------------------------------------------------------- weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] --------------+---------------------------------------------------------------- animal | 2 | 24.82857 32.44488 0.77 0.447 -40.07086 89.728 3 | -30 32.44488 -0.92 0.359 -94.89943 34.89943 4 | 7.157143 32.44488 0.22 0.826 -57.74229 72.05657 5 | -7.757143 32.44488 -0.24 0.812 -72.65657 57.14229 6 | 41.6 32.44488 1.28 0.205 -23.29943 106.4994 7 | -50.97143 32.44488 -1.57 0.121 -115.8709 13.928 8 | 4.628571 32.44488 0.14 0.887 -60.27086 69.528 9 | 22.37143 32.44488 0.69 0.493 -42.528 87.27086 10 | .8142857 32.44488 0.03 0.980 -64.08515 65.71372 11 | 9.271429 32.44488 0.29 0.776 -55.628 74.17086 12 | 21.41429 32.44488 0.66 0.512 -43.48515 86.31372 13 | -11.44286 32.44488 -0.35 0.726 -76.34229 53.45657 14 | 46.1 32.44488 1.42 0.161 -18.79943 110.9994 15 | -15.34286 32.44488 -0.47 0.638 -80.24229 49.55657 | animal#c.week | 1 | .2285714 4.818783 0.05 0.962 -9.410431 9.867573 2 | 15.11429 4.818783 3.14 0.003 5.475284 24.75329 3 | 27.22857 4.818783 5.65 0.000 17.58957 36.86757 4 | 21.5 4.818783 4.46 0.000 11.861 31.139 5 | 16.05714 4.818783 3.33 0.001 6.418141 25.69614 6 | 9.128571 4.818783 1.89 0.063 -.5104305 18.76757 7 | 21.41429 4.818783 4.44 0.000 11.77528 31.05329 8 | 23.81429 4.818783 4.94 0.000 14.17528 33.45329 9 | 29.64286 4.818783 6.15 0.000 20.00386 39.28186 10 | 28.77143 4.818783 5.97 0.000 19.13243 38.41043 11 | 27.74286 4.818783 5.76 0.000 18.10386 37.38186 12 | 15.67143 4.818783 3.25 0.002 6.032427 25.31043 13 | 20.6 4.818783 4.27 0.000 10.961 30.239 14 | 18.12857 4.818783 3.76 0.000 8.489569 27.76757 15 | 16 4.818783 3.32 0.002 6.360998 25.639 | _cons | 470.8429 22.942 20.52 0.000 424.952 516.7337 ------------------------------------------------------------------------------- . matrix parms_slp=e(b)' /* creates a column of all estimates from */ . svmat parms_slp /* which the relevant ones must be extracted */ . preserve /* run together with next 3 lines */ . drop if _n<16 | _n>30 (75 observations deleted) . egen float group2 = seq(), from(1) to(3) block(5) . oneway parms_slp1 group2 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 106.93772 2 53.4688601 0.83 0.4608 Within groups 775.75174 12 64.6459783 ------------------------------------------------------------------------ Total 882.68946 14 63.0492471 Bartlett's test for equal variances: chi2(2) = 1.6927 Prob>chi2 = 0.429 . end of do-file . do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp" . * curvature . anova weight animal c.week#animal c.week#c.week#animal Number of obs = 90 R-squared = 0.9275 Root MSE = 22.3061 Adj R-squared = 0.8566 Source | Partial SS df MS F Prob>F -----------------+---------------------------------------------------- Model | 286461.82 44 6510.496 13.08 0.0000 | animal | 9070.0298 14 647.85927 1.30 0.2439 animal#week | 23997.013 15 1599.8009 3.22 0.0012 animal#week#week | 10118.667 15 674.57778 1.36 0.2110 | Residual | 22390.276 45 497.56169 -----------------+---------------------------------------------------- Total | 308852.1 89 3470.2483 . regress Source | SS df MS Number of obs = 90 -------------+---------------------------------- F(44, 45) = 13.08 Model | 286461.824 44 6510.496 Prob > F = 0.0000 Residual | 22390.2762 45 497.561693 R-squared = 0.9275 -------------+---------------------------------- Adj R-squared = 0.8566 Total | 308852.1 89 3470.24831 Root MSE = 22.306 -------------------------------------------------------------------------------------- weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------------------+---------------------------------------------------------------- animal | 2 | -21.74286 51.69736 -0.42 0.676 -125.8667 82.38097 3 | -37.71429 51.69736 -0.73 0.469 -141.8381 66.40954 4 | 15.87143 51.69736 0.31 0.760 -88.2524 119.9953 5 | 38.38571 51.69736 0.74 0.462 -65.73811 142.5095 6 | 94.45714 51.69736 1.83 0.074 -9.666686 198.581 7 | -2.971429 51.69736 -0.06 0.954 -107.0953 101.1524 8 | 68.34286 51.69736 1.32 0.193 -35.78097 172.4667 9 | 67.51429 51.69736 1.31 0.198 -36.60954 171.6381 10 | 54.1 51.69736 1.05 0.301 -50.02383 158.2238 11 | 26.84286 51.69736 0.52 0.606 -77.28097 130.9667 12 | 52.12857 51.69736 1.01 0.319 -51.99526 156.2524 13 | 27.84286 51.69736 0.54 0.593 -76.28097 131.9667 14 | 114.5286 51.69736 2.22 0.032 10.40474 218.6524 15 | 38.37143 51.69736 0.74 0.462 -65.7524 142.4953 | animal#c.week | 1 | 31.37143 20.01046 1.57 0.124 -8.931716 71.67457 2 | 77.30476 20.01046 3.86 0.000 37.00162 117.6079 3 | 63.51429 20.01046 3.17 0.003 23.21114 103.8174 4 | 46.83333 20.01046 2.34 0.024 6.530189 87.13648 5 | 16.4381 20.01046 0.82 0.416 -23.86505 56.74124 6 | 5.033333 20.01046 0.25 0.803 -35.26981 45.33648 7 | 20.55714 20.01046 1.03 0.310 -19.746 60.86029 8 | 12.48095 20.01046 0.62 0.536 -27.82219 52.7841 9 | 30.69048 20.01046 1.53 0.132 -9.612668 70.99362 10 | 24.39048 20.01046 1.22 0.229 -15.91267 64.69362 11 | 47.17143 20.01046 2.36 0.023 6.868284 87.47457 12 | 26.3381 20.01046 1.32 0.195 -13.96505 66.64124 13 | 25.55238 20.01046 1.28 0.208 -14.75076 65.85553 14 | 3.652381 20.01046 0.18 0.856 -36.65076 43.95553 15 | 11.33333 20.01046 0.57 0.574 -28.96981 51.63648 | animal#c.week#c.week | 1 | -3.892857 2.433794 -1.60 0.117 -8.79477 1.009056 2 | -7.77381 2.433794 -3.19 0.003 -12.67572 -2.871897 3 | -4.535714 2.433794 -1.86 0.069 -9.437627 .3661986 4 | -3.166667 2.433794 -1.30 0.200 -8.06858 1.735246 5 | -.047619 2.433794 -0.02 0.984 -4.949532 4.854294 6 | .5119048 2.433794 0.21 0.834 -4.390008 5.413818 7 | .1071429 2.433794 0.04 0.965 -4.79477 5.009056 8 | 1.416667 2.433794 0.58 0.563 -3.485246 6.31858 9 | -.1309524 2.433794 -0.05 0.957 -5.032865 4.77096 10 | .547619 2.433794 0.23 0.823 -4.354294 5.449532 11 | -2.428571 2.433794 -1.00 0.324 -7.330484 2.473341 12 | -1.333333 2.433794 -0.55 0.587 -6.235246 3.56858 13 | -.6190476 2.433794 -0.25 0.800 -5.52096 4.282865 14 | 1.809524 2.433794 0.74 0.461 -3.092389 6.711437 15 | .5833333 2.433794 0.24 0.812 -4.31858 5.485246 | _cons | 424.1286 36.55555 11.60 0.000 350.5019 497.7552 -------------------------------------------------------------------------------------- . matrix parms_crv=e(b)' /* creates a column of all estimates from */ . svmat parms_crv /* which the relevant ones must be extracted */ . preserve /* run together with next 3 lines */ . drop if _n<31 | _n>45 (75 observations deleted) . egen float group2 = seq(), from(1) to(3) block(5) . oneway parms_crv1 group2 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 53.4485435 2 26.7242718 7.45 0.0079 Within groups 43.0655887 12 3.58879906 ------------------------------------------------------------------------ Total 96.5141323 14 6.89386659 Bartlett's test for equal variances: chi2(2) = 6.6432 Prob>chi2 = 0.036 . end of do-file . do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp" . * split-plot or hierarchical model . anova weight group / animal|group week##group Number of obs = 90 R-squared = 0.8946 Root MSE = 23.2926 Adj R-squared = 0.8437 Source | Partial SS df MS F Prob>F -------------+---------------------------------------------------- Model | 276299.5 29 9527.569 17.56 0.0000 | group | 18548.067 2 9274.0333 1.06 0.3782 animal|group | 105434.2 12 8786.1833 -------------+---------------------------------------------------- week | 142554.5 5 28510.9 52.55 0.0000 week#group | 9762.7333 10 976.27333 1.80 0.0801 | Residual | 32552.6 60 542.54333 -------------+---------------------------------------------------- Total | 308852.1 89 3470.2483 . mixed weight group##week || animal:, reml Performing EM optimization: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -360.02217 Iteration 1: log restricted-likelihood = -360.02217 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 282.86 Log restricted-likelihood = -360.02217 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 27.68743 1.01 0.312 -26.26637 82.26637 3 | 31.4 27.68743 1.13 0.257 -22.86637 85.66637 | week | 3 | 53 14.73151 3.60 0.000 24.12678 81.87322 4 | 102.4 14.73151 6.95 0.000 73.52678 131.2732 5 | 95.2 14.73151 6.46 0.000 66.32678 124.0732 6 | 80.2 14.73151 5.44 0.000 51.32678 109.0732 7 | 105.6 14.73151 7.17 0.000 76.72678 134.4732 | group#week | 2 3 | 3.6 20.8335 0.17 0.863 -37.2329 44.4329 2 4 | -22.6 20.8335 -1.08 0.278 -63.4329 18.2329 2 5 | -22.6 20.8335 -1.08 0.278 -63.4329 18.2329 2 6 | 28.4 20.8335 1.36 0.173 -12.4329 69.2329 2 7 | 44 20.8335 2.11 0.035 3.167097 84.8329 3 3 | -16.2 20.8335 -0.78 0.437 -57.0329 24.6329 3 4 | -20.4 20.8335 -0.98 0.327 -61.2329 20.4329 3 5 | -21.2 20.8335 -1.02 0.309 -62.0329 19.6329 3 6 | 10.2 20.8335 0.49 0.624 -30.6329 51.0329 3 7 | 19.8 20.8335 0.95 0.342 -21.0329 60.6329 | _cons | 466.4 19.57797 23.82 0.000 428.0279 504.7721 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: Identity | var(_cons) | 1373.942 598.0528 585.4031 3224.642 -----------------------------+------------------------------------------------ var(Residual) | 542.5432 99.05438 379.3385 775.9643 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 57.45 Prob >= chibar2 = 0.0000 . testparm group#week /* note: P-values smaller (too small) in chi^2-distrib */ ( 1) [weight]2.group#3.week = 0 ( 2) [weight]2.group#4.week = 0 ( 3) [weight]2.group#5.week = 0 ( 4) [weight]2.group#6.week = 0 ( 5) [weight]2.group#7.week = 0 ( 6) [weight]3.group#3.week = 0 ( 7) [weight]3.group#4.week = 0 ( 8) [weight]3.group#5.week = 0 ( 9) [weight]3.group#6.week = 0 (10) [weight]3.group#7.week = 0 chi2( 10) = 17.99 Prob > chi2 = 0.0551 . * repeated measures ANOVA . anova weight group / animal|group week##group, repeated(week) Number of obs = 90 R-squared = 0.8946 Root MSE = 23.2926 Adj R-squared = 0.8437 Source | Partial SS df MS F Prob>F -------------+---------------------------------------------------- Model | 276299.5 29 9527.569 17.56 0.0000 | group | 18548.067 2 9274.0333 1.06 0.3782 animal|group | 105434.2 12 8786.1833 -------------+---------------------------------------------------- week | 142554.5 5 28510.9 52.55 0.0000 week#group | 9762.7333 10 976.27333 1.80 0.0801 | Residual | 32552.6 60 542.54333 -------------+---------------------------------------------------- Total | 308852.1 89 3470.2483 Between-subjects error term: animal|group Levels: 15 (12 df) Lowest b.s.e. variable: animal Covariance pooled over: group (for repeated variable) Repeated variable: week Huynh-Feldt epsilon = 0.7191 Greenhouse-Geisser epsilon = 0.4856 Box's conservative epsilon = 0.2000 ------------ Prob > F ------------ Source | df F Regular H-F G-G Box -------------+---------------------------------------------------- week | 5 52.55 0.0000 0.0000 0.0000 0.0000 week#group | 10 1.80 0.0801 0.1103 0.1457 0.2073 Residual | 60 ------------------------------------------------------------------ . . * mixed models with correlation structure, assuming equidistant times . gen weekeq=week+(week==1) /* equidistant time points 2-7*/ . * ar(1) autoregressive correlations . mixed weight group##weekeq || animal:, res(ar 1, t(weekeq)) nocons reml Obtaining starting values by EM: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -388.74541 (not concave) Iteration 1: log restricted-likelihood = -354.4239 Iteration 2: log restricted-likelihood = -354.31402 Iteration 3: log restricted-likelihood = -354.31239 Iteration 4: log restricted-likelihood = -354.31239 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 162.42 Log restricted-likelihood = -354.31239 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 27.20166 1.03 0.303 -25.31427 81.31427 3 | 31.4 27.20166 1.15 0.248 -21.91427 84.71427 | weekeq | 3 | 53 11.6093 4.57 0.000 30.24619 75.75381 4 | 102.4 15.65256 6.54 0.000 71.72154 133.0785 5 | 95.2 18.30716 5.20 0.000 59.31863 131.0814 6 | 80.2 20.22081 3.97 0.000 40.56794 119.8321 7 | 105.6 21.66058 4.88 0.000 63.14605 148.0539 | group#weekeq | 2 3 | 3.6 16.41803 0.22 0.826 -28.57874 35.77874 2 4 | -22.6 22.13606 -1.02 0.307 -65.98589 20.78589 2 5 | -22.6 25.89023 -0.87 0.383 -73.34392 28.14392 2 6 | 28.4 28.59654 0.99 0.321 -27.64819 84.44819 2 7 | 44 30.63268 1.44 0.151 -16.03895 104.039 3 3 | -16.2 16.41803 -0.99 0.324 -48.37874 15.97874 3 4 | -20.4 22.13606 -0.92 0.357 -63.78589 22.98589 3 5 | -21.2 25.89023 -0.82 0.413 -71.94392 29.54392 3 6 | 10.2 28.59654 0.36 0.721 -45.84819 66.24819 3 7 | 19.8 30.63268 0.65 0.518 -40.23895 79.83895 | _cons | 466.4 19.23448 24.25 0.000 428.7011 504.0989 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: (empty) | -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .8178534 .0563492 .6732989 .9021861 var(e) | 1849.826 528.377 1056.81 3237.91 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(1) = 68.87 Prob > chi2 = 0.0000 Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the reported test is conservative. . estat wcor Standard deviations and correlations for animal = 7: Standard deviations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ sd | 43.010 43.010 43.010 43.010 43.010 43.010 Correlations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ 2 | 1.000 3 | 0.818 1.000 4 | 0.669 0.818 1.000 5 | 0.547 0.669 0.818 1.000 6 | 0.447 0.547 0.669 0.818 1.000 7 | 0.366 0.447 0.547 0.669 0.818 1.000 . * random effects and ar(1) errors . mixed weight group##weekeq || animal:, res(ar 1, t(weekeq)) reml Obtaining starting values by EM: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -360.02217 Iteration 1: log restricted-likelihood = -354.8883 Iteration 2: log restricted-likelihood = -354.10492 Iteration 3: log restricted-likelihood = -354.06675 Iteration 4: log restricted-likelihood = -354.06643 Iteration 5: log restricted-likelihood = -354.06643 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 191.08 Log restricted-likelihood = -354.06643 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 27.22117 1.03 0.304 -25.35251 81.35251 3 | 31.4 27.22117 1.15 0.249 -21.95251 84.75251 | weekeq | 3 | 53 11.64353 4.55 0.000 30.1791 75.8209 4 | 102.4 14.97297 6.84 0.000 73.05352 131.7465 5 | 95.2 16.79631 5.67 0.000 62.27984 128.1202 6 | 80.2 17.88798 4.48 0.000 45.1402 115.2598 7 | 105.6 18.56691 5.69 0.000 69.20952 141.9905 | group#weekeq | 2 3 | 3.6 16.46644 0.22 0.827 -28.67363 35.87363 2 4 | -22.6 21.17498 -1.07 0.286 -64.10219 18.90219 2 5 | -22.6 23.75357 -0.95 0.341 -69.15613 23.95613 2 6 | 28.4 25.29743 1.12 0.262 -21.18205 77.98205 2 7 | 44 26.25758 1.68 0.094 -7.463908 95.46391 3 3 | -16.2 16.46644 -0.98 0.325 -48.47363 16.07363 3 4 | -20.4 21.17498 -0.96 0.335 -61.90219 21.10219 3 5 | -21.2 23.75357 -0.89 0.372 -67.75613 25.35613 3 6 | 10.2 25.29743 0.40 0.687 -39.38205 59.78205 3 7 | 19.8 26.25758 0.75 0.451 -31.66391 71.26391 | _cons | 466.4 19.24827 24.23 0.000 428.6741 504.1259 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: Identity | var(_cons) | 873.8739 771.5022 154.8685 4930.995 -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .6536608 .2213377 .0242068 .9119718 var(e) | 978.606 607.2897 289.9887 3302.438 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(2) = 69.36 Prob > chi2 = 0.0000 Note: LR test is conservative and provided only for reference. . estat wcor Standard deviations and correlations for animal = 7: Standard deviations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ sd | 43.040 43.040 43.040 43.040 43.040 43.040 Correlations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ 2 | 1.000 3 | 0.817 1.000 4 | 0.697 0.817 1.000 5 | 0.619 0.697 0.817 1.000 6 | 0.568 0.619 0.697 0.817 1.000 7 | 0.535 0.568 0.619 0.697 0.817 1.000 . * Toeplitz . mixed weight group##weekeq || animal:, res(toeplitz, t(weekeq)) nocons reml Obtaining starting values by EM: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -388.74541 (not concave) Iteration 1: log restricted-likelihood = -377.15901 (not concave) Iteration 2: log restricted-likelihood = -370.597 (not concave) Iteration 3: log restricted-likelihood = -366.6394 (not concave) Iteration 4: log restricted-likelihood = -363.07347 (not concave) Iteration 5: log restricted-likelihood = -361.39529 (not concave) Iteration 6: log restricted-likelihood = -359.88913 Iteration 7: log restricted-likelihood = -355.00099 (not concave) Iteration 8: log restricted-likelihood = -353.35211 Iteration 9: log restricted-likelihood = -351.18936 Iteration 10: log restricted-likelihood = -349.84522 Iteration 11: log restricted-likelihood = -349.1903 Iteration 12: log restricted-likelihood = -349.18007 Iteration 13: log restricted-likelihood = -349.18002 Iteration 14: log restricted-likelihood = -349.18002 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 178.00 Log restricted-likelihood = -349.18002 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 26.79561 1.04 0.296 -24.51843 80.51843 3 | 31.4 26.79561 1.17 0.241 -21.11843 83.91843 | weekeq | 3 | 53 11.72339 4.52 0.000 30.02259 75.97741 4 | 102.4 13.27407 7.71 0.000 76.38329 128.4167 5 | 95.2 17.23542 5.52 0.000 61.41919 128.9808 6 | 80.2 18.37799 4.36 0.000 44.17981 116.2202 7 | 105.6 22.88712 4.61 0.000 60.74207 150.4579 | group#weekeq | 2 3 | 3.6 16.57937 0.22 0.828 -28.89497 36.09497 2 4 | -22.6 18.77238 -1.20 0.229 -59.39318 14.19318 2 5 | -22.6 24.37457 -0.93 0.354 -70.37328 25.17328 2 6 | 28.4 25.9904 1.09 0.275 -22.54024 79.34024 2 7 | 44 32.36728 1.36 0.174 -19.4387 107.4387 3 3 | -16.2 16.57937 -0.98 0.329 -48.69497 16.29497 3 4 | -20.4 18.77238 -1.09 0.277 -57.19318 16.39318 3 5 | -21.2 24.37457 -0.87 0.384 -68.97328 26.57328 3 6 | 10.2 25.9904 0.39 0.695 -40.74024 61.14024 3 7 | 19.8 32.36728 0.61 0.541 -43.6387 83.2387 | _cons | 466.4 18.94736 24.62 0.000 429.2639 503.5361 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: (empty) | -----------------------------+------------------------------------------------ Residual: Toeplitz(5) | cov1 | 1451.417 503.0803 465.3977 2437.436 cov2 | 1354.509 491.8142 390.5707 2318.447 cov3 | 1052.362 478.1299 115.2444 1989.479 cov4 | 950.6354 472.6153 24.32647 1876.944 cov5 | 485.4607 524.4629 -542.4678 1513.389 var(e) | 1795.011 510.734 1027.721 3135.157 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(5) = 79.13 Prob > chi2 = 0.0000 Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the reported test is conservative. . estat wcor Standard deviations and correlations for animal = 7: Standard deviations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ sd | 42.368 42.368 42.368 42.368 42.368 42.368 Correlations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ 2 | 1.000 3 | 0.809 1.000 4 | 0.755 0.809 1.000 5 | 0.586 0.755 0.809 1.000 6 | 0.530 0.586 0.755 0.809 1.000 7 | 0.270 0.530 0.586 0.755 0.809 1.000 . * unstructured (not in lecture) . mixed weight group##weekeq || animal:, res(uns, t(weekeq)) nocons reml Obtaining starting values by EM: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -388.74541 (not concave) Iteration 1: log restricted-likelihood = -364.29311 (not concave) Iteration 2: log restricted-likelihood = -358.15621 (not concave) Iteration 3: log restricted-likelihood = -353.6126 (not concave) Iteration 4: log restricted-likelihood = -346.69775 (not concave) Iteration 5: log restricted-likelihood = -340.44418 (not concave) Iteration 6: log restricted-likelihood = -336.85397 (not concave) Iteration 7: log restricted-likelihood = -335.45781 Iteration 8: log restricted-likelihood = -334.38419 Iteration 9: log restricted-likelihood = -331.29317 Iteration 10: log restricted-likelihood = -330.71346 Iteration 11: log restricted-likelihood = -330.68088 Iteration 12: log restricted-likelihood = -330.68074 Iteration 13: log restricted-likelihood = -330.68074 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 354.56 Log restricted-likelihood = -330.68074 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 16.8138 1.67 0.096 -4.954449 60.95445 3 | 31.4 16.8138 1.87 0.062 -1.554449 64.35445 | weekeq | 3 | 53 11.95408 4.43 0.000 29.57043 76.42957 4 | 102.4 14.04398 7.29 0.000 74.87431 129.9257 5 | 95.2 18.42101 5.17 0.000 59.09547 131.3045 6 | 80.2 21.58675 3.72 0.000 37.89076 122.5092 7 | 105.6 20.44653 5.16 0.000 65.52554 145.6745 | group#weekeq | 2 3 | 3.6 16.90563 0.21 0.831 -29.53442 36.73442 2 4 | -22.6 19.86118 -1.14 0.255 -61.5272 16.3272 2 5 | -22.6 26.05125 -0.87 0.386 -73.65951 28.45951 2 6 | 28.4 30.52827 0.93 0.352 -31.43431 88.23431 2 7 | 44 28.91576 1.52 0.128 -12.67385 100.6738 3 3 | -16.2 16.90563 -0.96 0.338 -49.33442 16.93442 3 4 | -20.4 19.86118 -1.03 0.304 -59.3272 18.5272 3 5 | -21.2 26.05125 -0.81 0.416 -72.25951 29.85951 3 6 | 10.2 30.52827 0.33 0.738 -49.63431 70.03431 3 7 | 19.8 28.91576 0.68 0.494 -36.87385 76.47385 | _cons | 466.4 11.88915 39.23 0.000 443.0977 489.7023 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: (empty) | -----------------------------+------------------------------------------------ Residual: Unstructured | var(e2) | 706.76 287.9053 318.0731 1570.424 var(e3) | 1430.86 578.8167 647.5393 3161.756 var(e4) | 1082.699 439.1876 488.9054 2397.675 var(e5) | 2408.829 975.396 1089.263 5326.955 var(e6) | 3074.831 1248.37 1387.511 6814.062 var(e7) | 2794.896 1132.279 1263.35 6183.119 cov(e2,e3) | 711.5599 352.514 20.64519 1402.475 cov(e2,e4) | 401.6462 274.2313 -135.8373 939.1297 cov(e2,e5) | 709.4599 423.5298 -120.6432 1539.563 cov(e2,e6) | 725.8264 468.3629 -192.148 1643.801 cov(e2,e7) | 705.6766 447.8352 -172.0642 1583.417 cov(e3,e4) | 1107.747 476.4334 173.9542 2041.539 cov(e3,e5) | 1623.027 704.2989 242.6266 3003.428 cov(e3,e6) | 1419.51 721.3132 5.762214 2833.258 cov(e3,e7) | 1669.611 743.2281 212.9103 3126.311 cov(e4,e5) | 1423.114 616.0996 215.5807 2630.647 cov(e4,e6) | 1440.647 665.1582 136.9612 2744.333 cov(e4,e7) | 1474.764 652.4671 195.9518 2753.576 cov(e5,e6) | 2185.529 998.295 228.9062 4142.151 cov(e5,e7) | 2385.429 1008.51 408.7858 4362.072 cov(e6,e7) | 2625.48 1127.343 415.9283 4835.031 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(20) = 116.13 Prob > chi2 = 0.0000 Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the reported test is conservative. . estat wcor Standard deviations and correlations for animal = 7: Standard deviations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ sd | 26.585 37.827 32.904 49.080 55.451 52.867 Correlations: weekeq | 2 3 4 5 6 7 -------------+------------------------------------------------ 2 | 1.000 3 | 0.708 1.000 4 | 0.459 0.890 1.000 5 | 0.544 0.874 0.881 1.000 6 | 0.492 0.677 0.790 0.803 1.000 7 | 0.502 0.835 0.848 0.919 0.896 1.000 . * models with non-equidistant time points: replace weekeq by week . * example: ar(1) (not in lecture) . mixed weight group##week || animal:, res(ar 1, t(week)) nocons reml Note: time gaps exist in the estimation data Obtaining starting values by EM: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -388.74541 (not concave) Iteration 1: log restricted-likelihood = -355.13854 Iteration 2: log restricted-likelihood = -354.73193 Iteration 3: log restricted-likelihood = -354.69208 Iteration 4: log restricted-likelihood = -354.69198 Iteration 5: log restricted-likelihood = -354.69198 Computing standard errors: Mixed-effects REML regression Number of obs = 90 Group variable: animal Number of groups = 15 Obs per group: min = 6 avg = 6.0 max = 6 Wald chi2(17) = 150.10 Log restricted-likelihood = -354.69198 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ weight | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- group | 2 | 28 26.75228 1.05 0.295 -24.43351 80.43351 3 | 31.4 26.75228 1.17 0.241 -21.03351 83.83351 | week | 3 | 53 15.00046 3.53 0.000 23.59964 82.40036 4 | 102.4 17.58992 5.82 0.000 67.92438 136.8756 5 | 95.2 19.47517 4.89 0.000 57.02936 133.3706 6 | 80.2 20.90792 3.84 0.000 39.22124 121.1788 7 | 105.6 22.02381 4.79 0.000 62.43412 148.7659 | group#week | 2 3 | 3.6 21.21385 0.17 0.865 -37.97838 45.17838 2 4 | -22.6 24.87591 -0.91 0.364 -71.35588 26.15588 2 5 | -22.6 27.54205 -0.82 0.412 -76.58143 31.38143 2 6 | 28.4 29.56826 0.96 0.337 -29.55272 86.35272 2 7 | 44 31.14638 1.41 0.158 -17.04577 105.0458 3 3 | -16.2 21.21385 -0.76 0.445 -57.77838 25.37838 3 4 | -20.4 24.87591 -0.82 0.412 -69.15588 28.35588 3 5 | -21.2 27.54205 -0.77 0.441 -75.18143 32.78143 3 6 | 10.2 29.56826 0.34 0.730 -47.75272 68.15272 3 7 | 19.8 31.14638 0.64 0.525 -41.24577 80.84577 | _cons | 466.4 18.91672 24.66 0.000 429.3239 503.4761 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ animal: (empty) | -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .8280075 .0531303 .6913597 .9074657 var(e) | 1789.211 500.2773 1034.33 3095.025 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(1) = 68.11 Prob > chi2 = 0.0000 Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the reported test is conservative. . estat wcor Standard deviations and correlations for animal = 7: Standard deviations: week | 1 3 4 5 6 7 -------------+------------------------------------------------ sd | 42.299 42.299 42.299 42.299 42.299 42.299 Correlations: week | 1 3 4 5 6 7 -------------+------------------------------------------------ 1 | 1.000 3 | 0.686 1.000 4 | 0.568 0.828 1.000 5 | 0.470 0.686 0.828 1.000 6 | 0.389 0.568 0.686 0.828 1.000 7 | 0.322 0.470 0.568 0.686 0.828 1.000 .