. * do-file for lecture 6 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 ch03ex1.csv, clear (2 vars, 29 obs) . oneway liverwgt diet, tabulate | Summary of liverwgt diet | Mean Std. Dev. Freq. ------------+------------------------------------ 1 | 3.7457143 .28401046 7 2 | 3.58 .18213024 8 3 | 3.5983333 .09621159 6 4 | 3.9225 .19710402 8 ------------+------------------------------------ Total | 3.7182759 .23998614 29 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups .578208876 3 .192736292 4.66 0.0102 Within groups 1.0344049 25 .041376196 ------------------------------------------------------------------------ Total 1.61261378 28 .057593349 Bartlett's test for equal variances: chi2(3) = 5.1211 Prob>chi2 = 0.163 . anova liverwgt diet /* allows postestimation commands */ Number of obs = 29 R-squared = 0.3586 Root MSE = .203411 Adj R-squared = 0.2816 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | .57820888 3 .19273629 4.66 0.0102 | diet | .57820888 3 .19273629 4.66 0.0102 | Residual | 1.0344049 25 .0413762 -----------+---------------------------------------------------- Total | 1.6126138 28 .05759335 . regress /* estimates corresponding to anova model */ Source | SS df MS Number of obs = 29 -------------+---------------------------------- F(3, 25) = 4.66 Model | .578208876 3 .192736292 Prob > F = 0.0102 Residual | 1.0344049 25 .041376196 R-squared = 0.3586 -------------+---------------------------------- Adj R-squared = 0.2816 Total | 1.61261378 28 .057593349 Root MSE = .20341 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- diet | 2 | -.1657143 .1052754 -1.57 0.128 -.382533 .0511045 3 | -.147381 .1131677 -1.30 0.205 -.3804541 .0856922 4 | .1767857 .1052754 1.68 0.106 -.0400331 .3936044 | _cons | 3.745714 .0768823 48.72 0.000 3.587372 3.904056 ------------------------------------------------------------------------------ . regress liverwgt i.diet /* totally identical */ Source | SS df MS Number of obs = 29 -------------+---------------------------------- F(3, 25) = 4.66 Model | .578208876 3 .192736292 Prob > F = 0.0102 Residual | 1.0344049 25 .041376196 R-squared = 0.3586 -------------+---------------------------------- Adj R-squared = 0.2816 Total | 1.61261378 28 .057593349 Root MSE = .20341 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- diet | 2 | -.1657143 .1052754 -1.57 0.128 -.382533 .0511045 3 | -.147381 .1131677 -1.30 0.205 -.3804541 .0856922 4 | .1767857 .1052754 1.68 0.106 -.0400331 .3936044 | _cons | 3.745714 .0768823 48.72 0.000 3.587372 3.904056 ------------------------------------------------------------------------------ . xi: boxcox liverwgt i.diet /* Box-Cox analysis; note: needs xi: */ i.diet _Idiet_1-4 (naturally coded; _Idiet_1 omitted) Fitting comparison model Iteration 0: log likelihood = .74765532 Iteration 1: log likelihood = 1.6767683 Iteration 2: log likelihood = 1.6782923 Iteration 3: log likelihood = 1.6782967 Iteration 4: log likelihood = 1.6782967 Fitting full model Iteration 0: log likelihood = 7.1860909 Iteration 1: log likelihood = 8.0100122 Iteration 2: log likelihood = 8.0113804 Iteration 3: log likelihood = 8.0113804 Number of obs = 29 LR chi2(3) = 12.67 Log likelihood = 8.0113804 Prob > chi2 = 0.005 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- /theta | -2.161941 2.514124 -0.86 0.390 -7.089534 2.765652 ------------------------------------------------------------------------------ Estimates of scale-variant parameters ---------------------------- | Coef. -------------+-------------- Notrans | _Idiet_2 | -.0025137 _Idiet_3 | -.0020231 _Idiet_4 | .002801 _cons | .4354793 -------------+-------------- /sigma | .0029048 ---------------------------- --------------------------------------------------------- Test Restricted LR statistic P-value H0: log likelihood chi2 Prob > chi2 --------------------------------------------------------- theta = -1 7.9027094 0.22 0.641 theta = 0 7.6300907 0.76 0.383 theta = 1 7.1860909 1.65 0.199 --------------------------------------------------------- . * means and SE with CI . anova liverwgt diet Number of obs = 29 R-squared = 0.3586 Root MSE = .203411 Adj R-squared = 0.2816 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | .57820888 3 .19273629 4.66 0.0102 | diet | .57820888 3 .19273629 4.66 0.0102 | Residual | 1.0344049 25 .0413762 -----------+---------------------------------------------------- Total | 1.6126138 28 .05759335 . lincom _cons+1.diet /* similar for diets 2-4 */ ( 1) 1b.diet + _cons = 0 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | 3.745714 .0768823 48.72 0.000 3.587372 3.904056 ------------------------------------------------------------------------------ . margins diet Adjusted predictions Number of obs = 29 Expression : Linear prediction, predict() ------------------------------------------------------------------------------ | Delta-method | Margin Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- diet | 1 | 3.745714 .0768823 48.72 0.000 3.587372 3.904056 2 | 3.58 .0719168 49.78 0.000 3.431885 3.728115 3 | 3.598333 .0830424 43.33 0.000 3.427304 3.769362 4 | 3.9225 .0719168 54.54 0.000 3.774385 4.070615 ------------------------------------------------------------------------------ . marginsplot /* interval plot */ Variables that uniquely identify margins: diet . * pairwise comparisons . oneway liverwgt diet, bonferroni /* bonferroni comparisons */ Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups .578208876 3 .192736292 4.66 0.0102 Within groups 1.0344049 25 .041376196 ------------------------------------------------------------------------ Total 1.61261378 28 .057593349 Bartlett's test for equal variances: chi2(3) = 5.1211 Prob>chi2 = 0.163 Comparison of liverwgt by diet (Bonferroni) Row Mean-| Col Mean | 1 2 3 ---------+--------------------------------- 2 | -.165714 | 0.768 | 3 | -.147381 .018333 | 1.000 1.000 | 4 | .176786 .3425 .324167 | 0.633 0.015 0.041 . * general method for anova and regression . anova liverwgt diet Number of obs = 29 R-squared = 0.3586 Root MSE = .203411 Adj R-squared = 0.2816 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | .57820888 3 .19273629 4.66 0.0102 | diet | .57820888 3 .19273629 4.66 0.0102 | Residual | 1.0344049 25 .0413762 -----------+---------------------------------------------------- Total | 1.6126138 28 .05759335 . pwcompare diet, pv mcomp(noadjust) /* no adjustment - the default */ Pairwise comparisons of marginal linear predictions Margins : asbalanced ----------------------------------------------------- | Unadjusted | Contrast Std. Err. t P>|t| -------------+--------------------------------------- diet | 2 vs 1 | -.1657143 .1052754 -1.57 0.128 3 vs 1 | -.147381 .1131677 -1.30 0.205 4 vs 1 | .1767857 .1052754 1.68 0.106 3 vs 2 | .0183333 .1098547 0.17 0.869 4 vs 2 | .3424999 .1017057 3.37 0.002 4 vs 3 | .3241666 .1098547 2.95 0.007 ----------------------------------------------------- . pwcompare diet, pv mcomp(bon) /* Bonferroni methodt */ Pairwise comparisons of marginal linear predictions Margins : asbalanced --------------------------- | Number of | Comparisons -------------+------------- diet | 6 --------------------------- ----------------------------------------------------- | Bonferroni | Contrast Std. Err. t P>|t| -------------+--------------------------------------- diet | 2 vs 1 | -.1657143 .1052754 -1.57 0.768 3 vs 1 | -.147381 .1131677 -1.30 1.000 4 vs 1 | .1767857 .1052754 1.68 0.633 3 vs 2 | .0183333 .1098547 0.17 1.000 4 vs 2 | .3424999 .1017057 3.37 0.015 4 vs 3 | .3241666 .1098547 2.95 0.041 ----------------------------------------------------- . pwcompare diet, pv mcomp(tukey) /* Tukey method */ Pairwise comparisons of marginal linear predictions Margins : asbalanced --------------------------- | Number of | Comparisons -------------+------------- diet | 6 --------------------------- ----------------------------------------------------- | Tukey | Contrast Std. Err. t P>|t| -------------+--------------------------------------- diet | 2 vs 1 | -.1657143 .1052754 -1.57 0.411 3 vs 1 | -.147381 .1131677 -1.30 0.570 4 vs 1 | .1767857 .1052754 1.68 0.355 3 vs 2 | .0183333 .1098547 0.17 0.998 4 vs 2 | .3424999 .1017057 3.37 0.012 4 vs 3 | .3241666 .1098547 2.95 0.032 ----------------------------------------------------- . * general approach to testing . anova liverwgt diet Number of obs = 29 R-squared = 0.3586 Root MSE = .203411 Adj R-squared = 0.2816 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | .57820888 3 .19273629 4.66 0.0102 | diet | .57820888 3 .19273629 4.66 0.0102 | Residual | 1.0344049 25 .0413762 -----------+---------------------------------------------------- Total | 1.6126138 28 .05759335 . test, showorder Order of columns in the design matrix 1: (diet==1) 2: (diet==2) 3: (diet==3) 4: (diet==4) 5: _cons . matrix input mycon=(1,-1,0,0,0\1,0,-1,0,0\1,0,0,-1,0\0,1,-1,0,0\0,1,0,-1,0\0,0 > ,1,-1,0) . test, test(mycon) mtest ( 1) 1b.diet - 2.diet = 0 ( 2) 1b.diet - 3.diet = 0 ( 3) 1b.diet - 4.diet = 0 ( 4) 2.diet - 3.diet = 0 ( 5) 2.diet - 4.diet = 0 ( 6) 3.diet - 4.diet = 0 Constraint 3 dropped Constraint 4 dropped Constraint 6 dropped --------------------------------------- | F(df,25) df p -------+------------------------------- (1) | 2.48 1 0.1280 # (2) | 1.70 1 0.2047 # (3) | 2.82 1 0.1056 # (4) | 0.03 1 0.8688 # (5) | 11.34 1 0.0025 # (6) | 8.71 1 0.0068 # -------+------------------------------- all | 4.66 3 0.0102 --------------------------------------- # unadjusted p-values . test, test(mycon) mtest(bon) /* Bonferroni method*/ ( 1) 1b.diet - 2.diet = 0 ( 2) 1b.diet - 3.diet = 0 ( 3) 1b.diet - 4.diet = 0 ( 4) 2.diet - 3.diet = 0 ( 5) 2.diet - 4.diet = 0 ( 6) 3.diet - 4.diet = 0 Constraint 3 dropped Constraint 4 dropped Constraint 6 dropped --------------------------------------- | F(df,25) df p -------+------------------------------- (1) | 2.48 1 0.7682 # (2) | 1.70 1 1.0000 # (3) | 2.82 1 0.6333 # (4) | 0.03 1 1.0000 # (5) | 11.34 1 0.0147 # (6) | 8.71 1 0.0408 # -------+------------------------------- all | 4.66 3 0.0102 --------------------------------------- # Bonferroni-adjusted p-values . test, test(mycon) mtest(holm) /* Holm method*/ ( 1) 1b.diet - 2.diet = 0 ( 2) 1b.diet - 3.diet = 0 ( 3) 1b.diet - 4.diet = 0 ( 4) 2.diet - 3.diet = 0 ( 5) 2.diet - 4.diet = 0 ( 6) 3.diet - 4.diet = 0 Constraint 3 dropped Constraint 4 dropped Constraint 6 dropped --------------------------------------- | F(df,25) df p -------+------------------------------- (1) | 2.48 1 0.3841 # (2) | 1.70 1 0.4094 # (3) | 2.82 1 0.4222 # (4) | 0.03 1 0.8688 # (5) | 11.34 1 0.0147 # (6) | 8.71 1 0.0340 # -------+------------------------------- all | 4.66 3 0.0102 --------------------------------------- # Holm-adjusted p-values . * contrasts . lincom (1.diet+2.diet+3.diet)/3-4.diet ( 1) .3333333*1b.diet + .3333333*2.diet + .3333333*3.diet - 4.diet = 0 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.2811507 .084674 -3.32 0.003 -.4555401 -.1067614 ------------------------------------------------------------------------------ . scalar tval=-.2811507/.084674 /* to get more decimals than in listing */ . di "SS: " tval^2*0.0413762 " in %: " tval^2*0.0413762/.57820888*100 SS: .45617217 in %: 78.89401 . di "Scheffe test: F = " tval^2/3 " P = " Ftail(3,25,tval^2/3) Scheffe test: F = 3.6749965 P = .02546919 . lincom (2.diet+3.diet)/2-1.diet ( 1) - 1b.diet + .5*2.diet + .5*3.diet = 0 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.1565476 .0944876 -1.66 0.110 -.3511484 .0380532 ------------------------------------------------------------------------------ . lincom 2.diet-3.diet ( 1) 2.diet - 3.diet = 0 ------------------------------------------------------------------------------ liverwgt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.0183333 .1098547 -0.17 0.869 -.2445833 .2079167 ------------------------------------------------------------------------------ . . import delimited ch03ta1.csv, clear (2 vars, 37 obs) . regress logtime temp Source | SS df MS Number of obs = 37 -------------+---------------------------------- F(1, 35) = 325.41 Model | 3.45926188 1 3.45926188 Prob > F = 0.0000 Residual | .372062445 35 .010630356 R-squared = 0.9029 -------------+---------------------------------- Adj R-squared = 0.9001 Total | 3.83132433 36 .106425676 Root MSE = .1031 ------------------------------------------------------------------------------ logtime | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- temp | -.0118567 .0006573 -18.04 0.000 -.0131911 -.0105224 _cons | 3.956007 .1391174 28.44 0.000 3.673584 4.238431 ------------------------------------------------------------------------------ . anova logtime temp Number of obs = 37 R-squared = 0.9233 Root MSE = .095801 Adj R-squared = 0.9138 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | 3.537632 4 .88440801 96.36 0.0000 | temp | 3.537632 4 .88440801 96.36 0.0000 | Residual | .29369229 32 .00917788 -----------+---------------------------------------------------- Total | 3.8313243 36 .10642568 . scalar F=(.3721-.2937)/(35-32)/.009178 /* F-value for lack of fit test */ . display F _newline Ftail(3,32,F) /* display F and P-value */ 2.8473887 .05297014 . * polynomial contrasts . lincom -2*175.temp-1*194.temp+0*213.temp+1*231.temp+2*250.temp /* linear */ ( 1) - 2*175b.temp - 194.temp + 231.temp + 2*250.temp = 0 ------------------------------------------------------------------------------ logtime | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -2.186131 .1147427 -19.05 0.000 -2.419854 -1.952408 ------------------------------------------------------------------------------ . lincom 2*175.temp-1*194.temp-2*213.temp-1*231.temp+2*250.temp /* quadratic */ ( 1) 2*175b.temp - 194.temp - 2*213.temp - 231.temp + 2*250.temp = 0 ------------------------------------------------------------------------------ logtime | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | .4002977 .1332473 3.00 0.005 .1288819 .6717135 ------------------------------------------------------------------------------ . lincom -1*175.temp+2*194.temp+0*213.temp-2*231.temp+1*250.temp /* cubic */ ( 1) - 175b.temp + 2*194.temp - 2*231.temp + 250.temp = 0 ------------------------------------------------------------------------------ logtime | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.0069048 .1118496 -0.06 0.951 -.2347349 .2209254 ------------------------------------------------------------------------------ . lincom 1*175.temp-4*194.temp+6*213.temp-4*231.temp+1*250.temp /* quartic */ ( 1) 175b.temp - 4*194.temp + 6*213.temp - 4*231.temp + 250.temp = 0 ------------------------------------------------------------------------------ logtime | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | -.0379762 .2886367 -0.13 0.896 -.6259099 .5499576 ------------------------------------------------------------------------------ .