Table 8.1, page 253.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/basins, clear (Hicks et al. (1990)) gen logro=log10(runoff) gen logpre=log10(precip) gen logglac=log10(glacier+1) gen logarea=log10(area) egen zlogro=std(logro) egen zlogpre=std(logpre) egen zlogglac=std(logglac) egen zlogarea=std(logarea) list basin zlogro zlogpre zlogglac zlogarea basin zlogro zlogpre zlogglac zlogarea 1. Ivory 1.30585 1.253279 1.974755 -1.74394 2. Cropp 1.321216 1.467827 .1666327 -1.612833 3. Upper Waitangitoana .8610425 1.030452 -.6078176 -.2809038 4. Hokitika 1.093791 1.374215 -.1191939 .3364316 5. Haast .7470333 .8726353 -.1191939 .7685862 6. Little Hopwood Burn -.5045639 -.6635709 -.6078176 -.8944885 7. Shotover -.7667871 -1.033303 -.1191939 .7948009 8. Arrow -1.598691 -1.542749 -.6078176 .1047718 9. Manuherikia -2.604667 -1.925677 -.6078176 .356689 10. Karamea .1025019 -.0490354 -.6078176 .8208289 11. Buller A -.373943 -.4820166 -.6078176 1.376861 12. Buller B -.1806241 -.3731881 -.6078176 1.511363 13. Inangahua A -.3277019 -.4265141 -.6078176 .170581 14. Inangahua B -.0883481 -.1786223 -.6078176 .7605425 15. Grey -.0657941 -.1786223 -.1191939 .5805332 16. Butchers Creek -.0807653 -.2247163 -.6078176 -1.48221 17. Cleddau .8228721 .973395 -.1191939 .0032735 18. Hooker .812043 .8726353 2.135663 -.1627341 19. Tsidjiore Nouve -.4744647 -.7664243 2.397095 -1.408153
Figure 8.2, page 254.
graph twoway scatter zlogro zlogpre, xlabel(0) ylabel(0) xline(0) yline(0)
Table 8.2, page 254.
corr zlogro zlogpre zlogglac zlogarea
(obs=19) | zlogro zlogpre zlogglac zlogarea -------------+------------------------------------ zlogro | 1.0000 zlogpre | 0.9738 1.0000 zlogglac | 0.3385 0.3025 1.0000 zlogarea | -0.2872 -0.2829 -0.5121 1.0000
Figure 8.3, page 254.
graph matrix zlogro zlogpre zlogglac zlogarea, half
Table 8.3, page 255.
factor zlogro zlogpre zlogglac zlogarea, pcf (obs=19) (principal component factors; 2 factors retained) Factor Eigenvalue Difference Proportion Cumulative ------------------------------------------------------------------ 1 2.39152 1.29575 0.5979 0.5979 2 1.09578 0.60839 0.2739 0.8718 3 0.48739 0.46207 0.1218 0.9937 4 0.02532 . 0.0063 1.0000 Factor Loadings Variable | 1 2 Uniqueness -------------+-------------------------------- zlogro | 0.90586 0.40821 0.01278 zlogpre | 0.89510 0.43040 0.01356 zlogglac | 0.63697 -0.58522 0.25178 zlogarea | -0.60333 0.63357 0.23458
Figure 8.4, page 258.
greigen, yline(1)
Table 8.4, page 259.
rotate (varimax rotation) Rotated Factor Loadings Variable | 1 2 Uniqueness -------------+-------------------------------- zlogro | 0.16443 0.97989 0.01278 zlogpre | 0.14001 0.98328 0.01356 zlogglac | 0.84060 0.20399 0.25178 zlogarea | -0.86208 -0.14915 0.23458
Table 8.5, page 262. Obliquely rotated loadings for mountain basin factors (compare with Tables 8.3 and 8.4).
rotate, promax (promax rotation) Rotated Factor Loadings Variable | 1 2 Uniqueness -------------+-------------------------------- zlogro | 0.01768 0.98744 0.01278 zlogpre | -0.00854 0.99607 0.01356 zlogglac | 0.85152 0.03752 0.25178 zlogarea | -0.88279 0.02413 0.23458
Table 8.6, page 264.
score (based on rotated factors) Scoring Coefficients Variable | 1 2 -------------+--------------------- zlogro | 0.00522 0.50140 zlogpre | -0.01226 0.50595 zlogglac | 0.56570 0.01343 zlogarea | -0.58689 0.01810
Table 8.7, page 265.
score f1 f2 (based on rotated factors) Scoring Coefficients Variable | 1 2 -------------+--------------------- zlogro | 0.00522 0.50140 zlogpre | -0.01226 0.50595 zlogglac | 0.56570 0.01343 zlogarea | -0.58689 0.01810
Table 8.8, page 266.
gen logsed=log10(yield) regress logsed zlogro zlogpre zlogglac zlogarea Source | SS df MS Number of obs = 19 -------------+------------------------------ F( 4, 14) = 13.77 Model | 10.265554 4 2.5663885 Prob > F = 0.0001 Residual | 2.60862507 14 .186330362 R-squared = 0.7974 -------------+------------------------------ Adj R-squared = 0.7395 Total | 12.8741791 18 .715232171 Root MSE = .43166 ------------------------------------------------------------------------------ logsed | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- zlogro | -.1151779 .4575377 -0.25 0.805 -1.096499 .8661428 zlogpre | .7751374 .4527634 1.71 0.109 -.1959435 1.746218 zlogglac | .1315507 .1231924 1.07 0.304 -.1326706 .3957721 zlogarea | -.1008783 .1200595 -0.84 0.415 -.3583802 .1566236 _cons | 3.200158 .0990296 32.32 0.000 2.98776 3.412555 ------------------------------------------------------------------------------ regress logsed f1 f2 Source | SS df MS Number of obs = 19 -------------+------------------------------ F( 2, 16) = 28.91 Model | 10.0835282 2 5.04176408 Prob > F = 0.0000 Residual | 2.79065092 16 .174415683 R-squared = 0.7832 -------------+------------------------------ Adj R-squared = 0.7561 Total | 12.8741791 18 .715232171 Root MSE = .41763 ------------------------------------------------------------------------------ logsed | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- f1 | .192415 .1046676 1.84 0.085 -.0294705 .4143005 f2 | .6608587 .1046676 6.31 0.000 .4389732 .8827442 _cons | 3.200158 .0958111 33.40 0.000 2.997047 3.403268 ------------------------------------------------------------------------------
Figure 8.9, page 268.
graph twoway scatter f2 f1, /// mlabel(location) msymbol(i) xlabel(-1(1)2) ylabel(-2(1)2) yline(0) xline(0)
Table 8.9, page 268.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/planets, clear (Beatty et al. (1981)) list planet dsun radius masskg density moons rings, nodis planet dsun radius masskg density moons rings 1. Mercury 57.9 2439 3.30e+23 5.42 0 none 2. Venus 108.2 6050 4.87e+24 5.25 0 none 3. Earth 149.6 6378 5.98e+24 5.52 1 none 4. Mars 227.9 3398 6.42e+23 3.94 2 none 5. Jupiter 778.3 71900 1.90e+27 1.314 16 rings 6. Saturn 1427 60000 5.69e+26 .69 17 rings 7. Uranus 2869.6 26145 8.66e+25 1.19 15 rings 8. Neptune 4496.6 24750 1.03e+26 1.66 8 rings 9. Pluto 5900 1550 1.10e+22 1.2 1 none
Figure 8.10, page 269.
gen logdsun=log(dsun) gen lograd=log(radius) gen logmass=log(masskg) gen logden=log(density) gen logmoon=log(moons+1) graph matrix logdsun lograd logmass logden logmoon rings, half
Figure 8.11, page 270.
factor logdsun lograd logmass logden logmoon rings, pcf factor(2) (obs=9) (principal component factors; 2 factors retained) Factor Eigenvalue Difference Proportion Cumulative ------------------------------------------------------------------ 1 4.62365 3.45469 0.7706 0.7706 2 1.16896 1.05664 0.1948 0.9654 3 0.11232 0.05395 0.0187 0.9842 4 0.05837 0.02174 0.0097 0.9939 5 0.03663 0.03657 0.0061 1.0000 6 0.00006 . 0.0000 1.0000 Factor Loadings Variable | 1 2 Uniqueness -------------+-------------------------------- logdsun | 0.67105 -0.71093 0.04427 lograd | 0.92287 0.37357 0.00875 logmass | 0.83377 0.54463 0.00821 logden | -0.84511 0.47053 0.06439 logmoon | 0.97647 0.00028 0.04651 rings | 0.97917 0.07720 0.03526 greigen, yline(1) xlabel(1(1)6) ylabel(0(1)4)
Table 8.10, page 270. We have skipped this for now.
Figure 8.12, page 271. We have skipped this for now.
Table 8.12, page 274.
use https://stats.idre.ucla.edu/stat/stata/examples/rwg/tulsa, clear (Blocker & Eckberg (1989)) corr deepwell chandler tornados floods airpol rivpol (obs=199) | deepwell chandler tornados floods airpol rivpol -------------+------------------------------------------------------ deepwell | 1.0000 chandler | 0.4726 1.0000 tornados | 0.1131 0.2027 1.0000 floods | 0.0928 0.0480 0.4052 1.0000 airpol | 0.2805 0.1661 0.1524 0.0712 1.0000 rivpol | 0.3365 0.2587 0.1007 0.1511 0.3861 1.0000
Figure 8.13, page 274.
graph matrix deepwell chandler tornados floods airpol rivpol, half jitter(5)
NOTE: This graph looks slightly different than the graph in the book because of the jittering. Jittering adds a small random number to each value graphed, so each time the graph is made, the small random addition to the points will make the graph look slightly different.
Figure 8.14, page 275.
factor deepwell chandler tornados floods airpol rivpol (obs=199) (principal factors; 3 factors retained) Factor Eigenvalue Difference Proportion Cumulative ------------------------------------------------------------------ 1 1.35194 0.88877 0.9929 0.9929 2 0.46317 0.29830 0.3402 1.3331 3 0.16487 0.28236 0.1211 1.4542 4 -0.11749 0.07032 -0.0863 1.3679 5 -0.18781 0.12528 -0.1379 1.2299 6 -0.31309 . -0.2299 1.0000 Factor Loadings Variable | 1 2 3 Uniqueness -------------+------------------------------------------- deepwell | 0.59374 -0.20135 -0.11690 0.59327 chandler | 0.53406 -0.13881 -0.23460 0.64047 tornados | 0.36576 0.42706 -0.05948 0.68031 floods | 0.29282 0.45047 0.02034 0.71092 airpol | 0.46081 -0.08334 0.23495 0.72551 rivpol | 0.53134 -0.10543 0.19240 0.66954 greigen, yline(0, 1) xlabel(1(1)6) ylabel(0 1) ytick(-.2 0 .2 .4 .6 .8 1 1.2 1.4)
Table 8.13, page 276.
factor deepwell chandler tornados floods airpol rivpol (obs=199) (principal factors; 3 factors retained) Factor Eigenvalue Difference Proportion Cumulative ------------------------------------------------------------------ 1 1.35194 0.88877 0.9929 0.9929 2 0.46317 0.29830 0.3402 1.3331 3 0.16487 0.28236 0.1211 1.4542 4 -0.11749 0.07032 -0.0863 1.3679 5 -0.18781 0.12528 -0.1379 1.2299 6 -0.31309 . -0.2299 1.0000 Factor Loadings Variable | 1 2 3 Uniqueness -------------+------------------------------------------- deepwell | 0.59374 -0.20135 -0.11690 0.59327 chandler | 0.53406 -0.13881 -0.23460 0.64047 tornados | 0.36576 0.42706 -0.05948 0.68031 floods | 0.29282 0.45047 0.02034 0.71092 airpol | 0.46081 -0.08334 0.23495 0.72551 rivpol | 0.53134 -0.10543 0.19240 0.66954 rotate, promax (promax rotation) Rotated Factor Loadings Variable | 1 2 3 Uniqueness -------------+------------------------------------------- deepwell | 0.54661 -0.02946 0.14547 0.59327 chandler | 0.61054 0.03497 -0.03720 0.64047 tornados | 0.06995 0.54955 -0.02505 0.68031 floods | -0.06653 0.54282 0.03733 0.71092 airpol | 0.04270 0.00781 0.49339 0.72551 rivpol | 0.13743 0.01013 0.47524 0.66954 score f1 f2 f3 (based on rotated factors) Scoring Coefficients Variable | 1 2 3 -------------+-------------------------------- deepwell | 0.36499 0.04240 0.21836 chandler | 0.34685 0.06944 0.10044 tornados | 0.07552 0.38228 0.06128 floods | 0.01167 0.35768 0.06601 airpol | 0.11423 0.06009 0.30260 rivpol | 0.17054 0.07305 0.33196 corr f1 f2 f3 (obs=199) | f1 f2 f3 -------------+--------------------------- f1 | 1.0000 f2 | 0.4957 1.0000 f3 | 0.8732 0.5503 1.0000
Figure 8.16, page 277.
histogram f3 if sex==0, /// fraction bin(8) start(-2) xlabel(-2(1)1) ylabel(0 .1 .2) xline(-.166)
histogram f3 if sex==1, /// fraction bin(8) start(-2) xlabel(-2(1)1) ylabel(0 .1 .2) xline(.128)
Table 8.15, page 279.
factor taxbabes manykids lessenvt toocons pollburd privown shutdown punish preserve, ml factor(3) (obs=241) Iteration 0: log likelihood = -25.277324 Iteration 1: log likelihood = -10.89083 Iteration 2: log likelihood = -10.463314 Iteration 3: log likelihood = -10.376172 Iteration 4: log likelihood = -10.356368 Iteration 5: log likelihood = -10.35112 Iteration 6: log likelihood = -10.349526 Iteration 7: log likelihood = -10.349001 Iteration 8: log likelihood = -10.348822 Iteration 9: log likelihood = -10.348759 Iteration 10: log likelihood = -10.348737 Iteration 11: log likelihood = -10.34873 Iteration 12: log likelihood = -10.348727 Iteration 13: log likelihood = -10.348726 Iteration 14: log likelihood = -10.348726 Iteration 15: log likelihood = -10.348726 Iteration 16: log likelihood = -10.348726 Iteration 17: log likelihood = -10.348726 Iteration 18: log likelihood = -10.348726 Iteration 19: log likelihood = -10.348726 (maximum likelihood factors; 3 factors retained) Factor Variance Difference Proportion Cumulative ------------------------------------------------------------------ 1 1.09150 -0.42946 0.3398 0.3398 2 1.52096 0.92086 0.4734 0.8132 3 0.60010 . 0.1868 1.0000 Test: 3 vs. no factors. Chi2( 27) = 223.59, Prob > chi2 = 0.0000 Test: 3 vs. more factors. Chi2( 12) = 20.20, Prob > chi2 = 0.0635 Factor Loadings Variable | 1 2 3 Uniqueness -------------+------------------------------------------- taxbabes | 0.94460 0.00065 -0.01496 0.10743 manykids | -0.33953 0.05576 0.15998 0.85602 lessenvt | 0.13347 0.51309 0.12787 0.70257 toocons | 0.05995 0.48555 0.42403 0.58085 pollburd | 0.02056 0.64636 0.17909 0.54973 privown | 0.01190 0.36004 0.01118 0.87010 shutdown | 0.00387 -0.49947 0.48407 0.51620 punish | 0.23087 -0.38692 0.32437 0.69177 preserve | 0.09313 -0.26878 0.07998 0.91269 rotate, promax (promax rotation) Rotated Factor Loadings Variable | 1 2 3 Uniqueness -------------+------------------------------------------- taxbabes | 0.94363 0.04826 0.00168 0.10743 manykids | -0.36004 0.15240 0.12783 0.85602 lessenvt | 0.12017 0.47899 -0.11160 0.70257 toocons | 0.00568 0.70413 0.19670 0.58085 pollburd | 0.00180 0.60911 -0.12521 0.54973 privown | 0.01370 0.26475 -0.15846 0.87010 shutdown | -0.06779 0.05460 0.72057 0.51620 punish | 0.18163 0.01425 0.51159 0.69177 preserve | 0.07924 -0.11676 0.20860 0.91269
Figure 8.17, page 280.
graph twoway (scatter nchldn f1, jitter(3)) (lfit nchldn f1), ylabel(0(1)7) xlabel(-3(1)1)
NOTE: Because of the jittering, this graph does not look exactly like the one in the book.