--------------------------------------------------------------------------------------------------- log: C:\mydocs\MPH\Text\SecondEdition\WebDoFiles\3.12.1.Framingham.log log type: text opened on: 28 Dec 2007, 11:13:06 . * 3.12.1.Framingham.log . * . * Plot a scatterplot matrix of log(sbp), log(bmi), age and log(scl) for . * women from the Framingham Heart Study who were recruited in January. . * . use C:\WDDtext\2.20.Framingham.dta . generate logsbp = log(sbp) . label variable logsbp "Log Systolic Blood Pressure" . generate logbmi = log(bmi) (9 missing values generated) . label variable logbmi "Log Body Mass Index" . generate logscl = log(scl) (33 missing values generated) . label variable logscl "Log Serum Cholesterol" . graph matrix logsbp logbmi age logscl if month==1 & sex==2, symbol(Oh) . more . * . * Use multiple regression models to analyze the effects of log(sbp), . * log(bmi), age and log(scl) on log(sbp) . * . generate woman = sex - 1 . generate wo_lbmi = woman * logbmi (9 missing values generated) . generate wo_age = woman * age . generate wo_lscl = woman * logscl (33 missing values generated) . regress logsbp logbmi age logscl woman wo_lbmi wo_age wo_lscl Source | SS df MS Number of obs = 4658 -------------+------------------------------ F( 7, 4650) = 227.38 Model | 30.876434 7 4.41091915 Prob > F = 0.0000 Residual | 90.2060097 4650 .019399142 R-squared = 0.2550 -------------+------------------------------ Adj R-squared = 0.2539 Total | 121.082444 4657 .026000095 Root MSE = .13928 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logbmi | .2497811 .0239594 10.43 0.000 .2028094 .2967529 age | .0035143 .0003651 9.63 0.000 .0027985 .00423 logscl | .065112 .017266 3.77 0.000 .0312624 .0989616 woman | -.2291666 .1432109 -1.60 0.110 -.5099279 .0515948 wo_lbmi | .0189226 .0292785 0.65 0.518 -.0384772 .0763224 wo_age | .004867 .0005184 9.39 0.000 .0038508 .0058833 wo_lscl | -.0090283 .0231018 -0.39 0.696 -.0543187 .0362622 _cons | 3.549397 .1114748 31.84 0.000 3.330853 3.76794 ------------------------------------------------------------------------------ . regress logsbp logbmi age logscl woman wo_lbmi wo_age Source | SS df MS Number of obs = 4658 -------------+------------------------------ F( 6, 4651) = 265.30 Model | 30.8734712 6 5.14557854 Prob > F = 0.0000 Residual | 90.2089725 4651 .019395608 R-squared = 0.2550 -------------+------------------------------ Adj R-squared = 0.2540 Total | 121.082444 4657 .026000095 Root MSE = .13927 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logbmi | .250923 .0237784 10.55 0.000 .2043061 .2975399 age | .0035217 .0003645 9.66 0.000 .002807 .0042363 logscl | .0600689 .0114703 5.24 0.000 .0375818 .0825561 woman | -.2714501 .0938155 -2.89 0.004 -.455373 -.0875273 wo_lbmi | .0175727 .0290714 0.60 0.546 -.039421 .0745665 wo_age | .0048195 .0005038 9.57 0.000 .0038317 .0058072 _cons | 3.572628 .0942943 37.89 0.000 3.387767 3.757489 ------------------------------------------------------------------------------ . regress logsbp logbmi age logscl woman wo_age Source | SS df MS Number of obs = 4658 -------------+------------------------------ F( 5, 4652) = 318.33 Model | 30.8663845 5 6.1732769 Prob > F = 0.0000 Residual | 90.2160593 4652 .019392962 R-squared = 0.2549 -------------+------------------------------ Adj R-squared = 0.2541 Total | 121.082444 4657 .026000095 Root MSE = .13926 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logbmi | .262647 .0137549 19.09 0.000 .2356808 .2896131 age | .0035167 .0003644 9.65 0.000 .0028023 .0042311 logscl | .0595923 .0114423 5.21 0.000 .0371599 .0820247 woman | -.2165261 .0233469 -9.27 0.000 -.2622971 -.1707551 wo_age | .0048624 .0004988 9.75 0.000 .0038846 .0058403 _cons | 3.537356 .0740649 47.76 0.000 3.392153 3.682558 ------------------------------------------------------------------------------ . * . * Calculate 95% confidence and prediction intervals for a 60 . * year-old woman with a SCL of 400 and a BMI of 40. . * . edit - preserve . set obs 4700 obs was 4699, now 4700 . replace scl = 400 in 4700 (1 real change made) . replace age = 60 in 4700 (1 real change made) . replace bmi = 40 in 4700 (1 real change made) . replace woman = 1 in 4700 (1 real change made) . replace id = 9999 in 4700 (1 real change made) . replace logbmi = log(bmi) if id == 9999 (1 real change made) . replace logscl = log(scl) if id == 9999 (1 real change made) . replace wo_age = woman*age if id == 9999 (1 real change made) . predict yhat,xb (41 missing values generated) . label variable yhat "Expected log[BMI]" . predict h, leverage (41 missing values generated) . predict std_yhat, stdp (41 missing values generated) . predict std_f, stdf (41 missing values generated) . generate cil_yhat = yhat - invttail(4658-5-1,.025)*std_yhat (41 missing values generated) . generate ciu_yhat = yhat + invttail(4658-5-1,.025)*std_yhat (41 missing values generated) . generate cil_f = yhat - invttail(4658-5-1,.025)*std_f (41 missing values generated) . generate ciu_f = yhat + invttail(4658-5-1,.025)*std_f (41 missing values generated) . generate cil_sbpf = exp(cil_f) (41 missing values generated) . generate ciu_sbpf = exp(ciu_f) (41 missing values generated) . list bmi age scl woman logbmi logscl yhat h std_yhat std_f /// > cil_yhat ciu_yhat cil_f ciu_f cil_sbpf ciu_sbpf if id==9999 +----------------------------------------------------------------------------------------+ 4700. | bmi | age | scl | woman | logbmi | logscl | yhat | h | std_yhat | std_f | | 40 | 60 | 400 | 1 | 3.688879 | 5.991465 | 5.149496 | .003901 | .0086978 | .13953 | |----------------------------------------------------------+-----------------------------| | cil_yhat | ciu_yhat | cil_f | ciu_f | cil_sbpf | ciu_sbpf | | 5.132444 | 5.166547 | 4.875951 | 5.42304 | 131.0987 | 226.5669 | +----------------------------------------------------------------------------------------+ . display invttail(4652,.025) 1.9604741 . * . * Repeat the preceding analysis using an automatic forward . * selection algorithm . * . drop if id == 9999 (1 observation deleted) . stepwise, pe(.1): regress logsbp logbmi age logscl woman /// > wo_lbmi wo_age wo_lscl begin with empty model p = 0.0000 < 0.1000 adding age p = 0.0000 < 0.1000 adding logbmi p = 0.0000 < 0.1000 adding logscl p = 0.0005 < 0.1000 adding wo_age p = 0.0000 < 0.1000 adding woman Source | SS df MS Number of obs = 4658 -------------+------------------------------ F( 5, 4652) = 318.33 Model | 30.8663845 5 6.1732769 Prob > F = 0.0000 Residual | 90.2160593 4652 .019392962 R-squared = 0.2549 -------------+------------------------------ Adj R-squared = 0.2541 Total | 121.082444 4657 .026000095 Root MSE = .13926 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- age | .0035167 .0003644 9.65 0.000 .0028023 .0042311 logbmi | .262647 .0137549 19.09 0.000 .2356808 .2896131 logscl | .0595923 .0114423 5.21 0.000 .0371599 .0820247 wo_age | .0048624 .0004988 9.75 0.000 .0038846 .0058403 woman | -.2165261 .0233469 -9.27 0.000 -.2622971 -.1707551 _cons | 3.537356 .0740649 47.76 0.000 3.392153 3.682558 ------------------------------------------------------------------------------ . * . * Draw a scatterplot of studentized residuals against the estimated expected . * value of logsbp together with the corresponding lowess regression curve. . * . predict t, rstudent (41 missing values generated) . lowess t yhat, bwidth(0.2) color(gray) symbol(Oh) lineopts(lwidth(thick)) /// > ylabel(-3(1)5) yline(-1.96 0 1.96) xlabel(4.7(.1)5.1) . more . generate out = abs(t) > 1.96 . tabulate out out | Freq. Percent Cum. ------------+----------------------------------- 0 | 4,425 94.17 94.17 1 | 274 5.83 100.00 ------------+----------------------------------- Total | 4,699 100.00 . * . * Perform an influence analysis on patients 2000 through 2050 . * . keep if id >= 2000 & id <= 2050 (4648 observations deleted) . regress logsbp logbmi age logscl woman wo_age Source | SS df MS Number of obs = 50 -------------+------------------------------ F( 5, 44) = 2.49 Model | .381164541 5 .076232908 Prob > F = 0.0456 Residual | 1.34904491 44 .030660112 R-squared = 0.2203 -------------+------------------------------ Adj R-squared = 0.1317 Total | 1.73020945 49 .035310397 Root MSE = .1751 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logbmi | .1659182 .1696326 0.98 0.333 -.1759538 .5077902 age | -.0006515 .0048509 -0.13 0.894 -.0104278 .0091249 logscl | .0983239 .1321621 0.74 0.461 -.1680314 .3646791 woman | -.4856951 .294151 -1.65 0.106 -1.078517 .1071272 wo_age | .0116644 .0063781 1.83 0.074 -.0011899 .0245187 _cons | 3.816949 .9136773 4.18 0.000 1.975553 5.658344 ------------------------------------------------------------------------------ . drop t h . predict h, leverage (1 missing value generated) . predict z, rstandard (1 missing value generated) . predict t, rstudent (1 missing value generated) . predict deltab1, dfbeta(logbmi) (1 missing value generated) . predict cook, cooksd (1 missing value generated) . display invttail(43,.025) 2.0166922 . label variable deltab1 "Delta Beta for log[BMI]" . scatter deltab1 t, ylabel(-1.5(.5)0) yline(0) symbol(Oh) /// > xlabel(-2(1)4) xtick(-2.5(.5)4.5) xline(-2 2) . sort t . list id h z t deltab1 cook in -3/-1 +--------------------------------------------------------------+ | id h z t deltab1 cook | |--------------------------------------------------------------| 49. | 2048 .0655644 2.429988 2.581686 -.0063142 .069052 | 50. | 2049 .1545165 3.730179 4.459472 -1.420916 .4238165 | 51. | 2046 . . . . . | +--------------------------------------------------------------+ . regress logsbp logbmi age logscl woman wo_age if id !=2049 Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 5, 43) = 3.13 Model | .336072673 5 .067214535 Prob > F = 0.0169 Residual | .922432819 43 .021451926 R-squared = 0.2670 -------------+------------------------------ Adj R-squared = 0.1818 Total | 1.25850549 48 .026218864 Root MSE = .14646 ------------------------------------------------------------------------------ logsbp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logbmi | .3675337 .1489199 2.47 0.018 .0672082 .6678592 age | -.0006212 .0040576 -0.15 0.879 -.0088042 .0075617 logscl | .0843428 .110593 0.76 0.450 -.1386894 .3073749 woman | -.3053762 .2493465 -1.22 0.227 -.8082314 .197479 wo_age | .0072062 .0054279 1.33 0.191 -.0037403 .0181527 _cons | 3.244073 .7749778 4.19 0.000 1.681181 4.806965 ------------------------------------------------------------------------------ . display ( .1659182 - .3675337 )/.1489199 -1.353852 . log close log: C:\mydocs\MPH\Text\SecondEdition\WebDoFiles\3.12.1.Framingham.log log type: text closed on: 28 Dec 2007, 11:13:59 -------------------------------------------------------------------------------------------------