. * do-file for lecture 9 of VHM 802, Winter 2023 . version 17 /* works also with versions 14-16 */ . set more off . cd "r:\" r:\ . . * Manly Example 6.1 - sparrow data . import delimited sparrow.csv, clear (encoding automatically selected: ISO-8859-1) (6 vars, 49 obs) . pca total_length-l_keel_sternum Principal components/correlation Number of obs = 49 Number of comp. = 5 Trace = 5 Rotation: (unrotated = principal) Rho = 1.0000 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 3.61598 3.08447 0.7232 0.7232 Comp2 | .531504 .14508 0.1063 0.8295 Comp3 | .386425 .084859 0.0773 0.9068 Comp4 | .301566 .137038 0.0603 0.9671 Comp5 | .164527 . 0.0329 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) ------------------------------------------------------------------------------ Variable | Comp1 Comp2 Comp3 Comp4 Comp5 | Unexplained -------------+--------------------------------------------------+------------- total_length | 0.4518 0.0507 -0.6905 0.4204 -0.3739 | 0 alar_extent | 0.4617 -0.2996 -0.3405 -0.5479 0.5301 | 0 l_beak_head | 0.4505 -0.3246 0.4545 0.6063 0.3428 | 0 l_humerous | 0.4707 -0.1847 0.4109 -0.3883 -0.6517 | 0 l_keel_ste~m | 0.3977 0.8765 0.1785 -0.0689 0.1924 | 0 ------------------------------------------------------------------------------ . predict scor1-scor5, score Scoring coefficients sum of squares(column-loading) = 1 ---------------------------------------------------------------- Variable | Comp1 Comp2 Comp3 Comp4 Comp5 -------------+-------------------------------------------------- total_length | 0.4518 0.0507 -0.6905 0.4204 -0.3739 alar_extent | 0.4617 -0.2996 -0.3405 -0.5479 0.5301 l_beak_head | 0.4505 -0.3246 0.4545 0.6063 0.3428 l_humerous | 0.4707 -0.1847 0.4109 -0.3883 -0.6517 l_keel_ste~m | 0.3977 0.8765 0.1785 -0.0689 0.1924 ---------------------------------------------------------------- . scoreplot, comp(2) mlabel(survivorship) . loadingplot . screeplot . biplot total_length- l_keel_sternum, std Biplot of 49 observations and 5 variables Explained variance by component 1 = 0.7232 Explained variance by component 2 = 0.1063 Total explained variance = 0.8295 . * note: a separate command, not a postestimation command . encode survivorship, g(surv) . replace surv=surv-1 (49 real changes made) . logit surv total_length-l_keel_sternum Iteration 0: log likelihood = -33.462497 Iteration 1: log likelihood = -32.041086 Iteration 2: log likelihood = -32.035688 Iteration 3: log likelihood = -32.035688 Logistic regression Number of obs = 49 LR chi2(5) = 2.85 Prob > chi2 = 0.7225 Log likelihood = -32.035688 Pseudo R2 = 0.0426 -------------------------------------------------------------------------------- surv | Coefficient Std. err. z P>|z| [95% conf. interval] ---------------+---------------------------------------------------------------- total_length | -.1625675 .1396369 -1.16 0.244 -.4362508 .1111159 alar_extent | -.0276413 .1060235 -0.26 0.794 -.2354436 .1801609 l_beak_head | -.0837496 .628623 -0.13 0.894 -1.315828 1.148329 l_humerous | 1.061744 1.023129 1.04 0.299 -.9435529 3.067041 l_keel_sternum | .0715755 .4166297 0.17 0.864 -.7450037 .8881547 _cons | 13.58231 15.86496 0.86 0.392 -17.51244 44.67706 -------------------------------------------------------------------------------- . logit surv scor1-scor5 Iteration 0: log likelihood = -33.462497 Iteration 1: log likelihood = -32.041086 Iteration 2: log likelihood = -32.035688 Iteration 3: log likelihood = -32.035688 Logistic regression Number of obs = 49 LR chi2(5) = 2.85 Prob > chi2 = 0.7225 Log likelihood = -32.035688 Pseudo R2 = 0.0426 ------------------------------------------------------------------------------ surv | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- scor1 | -.0528091 .1565831 -0.34 0.736 -.3597064 .2540881 scor2 | -.0150206 .4274524 -0.04 0.972 -.8528119 .8227707 scor3 | .6865037 .5071386 1.35 0.176 -.3074697 1.680477 scor4 | -.4508785 .5489788 -0.82 0.411 -1.526857 .6251002 scor5 | -.2517201 .7326623 -0.34 0.731 -1.687712 1.184272 _cons | -.3048856 .2979983 -1.02 0.306 -.8889515 .2791804 ------------------------------------------------------------------------------ . . * Manly Table 9.7 - Steneryd data . import delimited steneryd.csv, clear varnames(1) (encoding automatically selected: UTF-8) (30 vars, 17 obs) . * include code to relabel spec1-spec25 as s1-s25 . foreach j of numlist 1(1)25 { 2. rename spec`j' s`j' 3. } . tabstat s1-s25, statistics( mean min max sd var ) Stats | s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 > s11 s12 s13 ---------+-------------------------------------------------------------------------------------------------------- > -------------------------- Mean | 12.11765 11.17647 9.764706 7.647059 6.588235 6 5.647059 4.941176 4.882353 4.411765 > 4 3.588235 3.588235 Min | 0 0 0 0 0 0 0 0 0 0 > 0 0 0 Max | 43 21 39 28 37 45 15 10 11 14 > 9 12 30 SD | 16.22067 7.443414 11.42656 8.358687 11.40756 14.91643 5.049024 3.831948 4.029304 4.912469 3. > 640055 3.74264 7.778647 Variance | 263.1103 55.40441 130.5662 69.86765 130.1324 222.5 25.49265 14.68382 16.23529 24.13235 > 13.25 14.00735 60.50735 ------------------------------------------------------------------------------------------------------------------ > -------------------------- Stats | s14 s15 s16 s17 s18 s19 s20 s21 s22 s23 > s24 s25 ---------+-------------------------------------------------------------------------------------------------------- > ---------------- Mean | 3.588235 3.176471 3 2.941176 2.823529 2.764706 2.705882 2.647059 2.647059 2.470588 2. > 411765 2.411765 Min | 0 0 0 0 0 0 0 0 0 0 > 0 0 Max | 10 15 18 16 9 12 9 9 10 16 > 8 19 SD | 3.985267 5.126345 5.689903 5.018349 3.339822 4.008264 2.931823 3.081014 3.444945 4.638395 2. > 895229 5.579637 Variance | 15.88235 26.27941 32.375 25.18382 11.15441 16.06618 8.595588 9.492647 11.86765 21.51471 8. > 382353 31.13235 ------------------------------------------------------------------------------------------------------------------ > ---------------- . pwcorr s1-s25 | s1 s2 s3 s4 s5 s6 s7 -------------+--------------------------------------------------------------- s1 | 1.0000 s2 | -0.7171 1.0000 s3 | -0.5363 0.4980 1.0000 s4 | 0.4106 -0.4540 0.2366 1.0000 s5 | -0.4408 0.3896 0.0059 -0.5614 1.0000 s6 | -0.3182 0.3304 -0.0708 -0.3910 0.7974 1.0000 s7 | -0.2444 0.2812 0.6918 0.2605 -0.4704 -0.4747 1.0000 s8 | -0.1055 -0.0500 0.2923 0.4169 -0.5239 -0.4647 0.4576 s9 | -0.3976 0.4404 0.6374 0.2195 -0.4186 -0.4316 0.7567 s10 | -0.5662 0.3209 0.5129 -0.2611 -0.0994 -0.2004 0.6009 s11 | -0.7187 0.3137 0.2960 -0.4355 0.4530 0.3096 -0.0408 s12 | 0.1398 -0.2485 -0.0404 0.5984 -0.3746 -0.3672 0.0580 s13 | -0.0442 0.4266 0.2724 -0.0485 -0.1654 -0.1928 0.3812 s14 | 0.8458 -0.5536 -0.5595 0.3762 -0.5071 -0.3722 -0.1195 s15 | 0.5845 -0.5856 -0.5114 0.5150 -0.3802 -0.2648 -0.2124 s16 | -0.2404 0.1033 0.2249 0.2181 -0.3235 -0.2253 0.4764 s17 | 0.8869 -0.7945 -0.4929 0.4703 -0.3596 -0.2505 -0.2278 s18 | -0.5580 0.2201 -0.0257 -0.4345 0.3490 0.5269 -0.1596 s19 | -0.2524 0.4665 0.6387 0.2567 -0.3699 -0.2917 0.6071 s20 | -0.4763 0.3920 0.4437 -0.0555 -0.1533 -0.2801 0.2459 s21 | -0.5006 0.4825 0.4502 -0.2721 -0.1378 -0.2693 0.4093 s22 | -0.4511 0.2707 0.1216 -0.3215 -0.1328 0.0839 0.1936 s23 | 0.7859 -0.6687 -0.4695 0.5381 -0.3268 -0.2276 -0.2033 s24 | -0.4882 0.1907 -0.1046 -0.4172 0.1512 0.3618 -0.0664 s25 | 0.2715 -0.2983 -0.3807 0.4455 -0.2652 -0.1847 -0.1409 | s8 s9 s10 s11 s12 s13 s14 -------------+--------------------------------------------------------------- s8 | 1.0000 s9 | 0.6755 1.0000 s10 | 0.3865 0.5015 1.0000 s11 | -0.0851 0.0852 0.4369 1.0000 s12 | 0.6780 0.3530 -0.1806 -0.1927 1.0000 s13 | -0.0805 0.4430 -0.2128 -0.1369 -0.1350 1.0000 s14 | 0.1620 -0.1239 -0.5335 -0.6721 0.4111 0.1434 1.0000 s15 | 0.4301 -0.1411 -0.4324 -0.5091 0.7663 -0.3037 0.7594 s16 | 0.5676 0.4771 0.4897 -0.2625 0.3346 -0.1920 -0.0551 s17 | -0.1789 -0.4207 -0.4376 -0.5201 0.1384 -0.2873 0.6675 s18 | -0.1376 -0.1224 0.3171 0.7660 -0.3112 -0.2604 -0.5035 s19 | 0.2920 0.7296 0.2084 0.1628 0.1140 0.6241 -0.1199 s20 | 0.3544 0.6106 0.4516 0.5798 0.1421 0.1725 -0.3320 s21 | 0.3422 0.5905 0.7865 0.4514 -0.0568 -0.0351 -0.4605 s22 | 0.1782 0.2445 0.6554 0.5532 -0.1429 -0.2553 -0.3891 s23 | 0.0298 -0.3513 -0.4644 -0.5627 0.3647 -0.2611 0.7820 s24 | -0.0653 -0.0706 0.3696 0.6761 -0.1506 -0.2778 -0.3690 s25 | 0.3695 -0.0172 -0.3760 -0.4554 0.7269 -0.2119 0.5168 | s15 s16 s17 s18 s19 s20 s21 -------------+--------------------------------------------------------------- s15 | 1.0000 s16 | 0.1736 1.0000 s17 | 0.5373 -0.2167 1.0000 s18 | -0.3522 -0.1217 -0.3698 1.0000 s19 | -0.2838 0.0082 -0.2990 0.0294 1.0000 s20 | -0.2999 -0.0562 -0.4133 0.2816 0.6639 1.0000 s21 | -0.4390 0.1854 -0.4380 0.2062 0.4079 0.7489 1.0000 s22 | -0.2794 0.1626 -0.3050 0.7004 0.2788 0.5213 0.6529 s23 | 0.7296 -0.0924 0.7960 -0.4220 -0.3433 -0.4212 -0.4512 s24 | -0.2031 0.0379 -0.3295 0.9064 0.0358 0.2581 0.2695 s25 | 0.8407 0.3425 0.2643 -0.3413 -0.2777 -0.2328 -0.3655 | s22 s23 s24 s25 -------------+------------------------------------ s22 | 1.0000 s23 | -0.3723 1.0000 s24 | 0.8050 -0.3597 1.0000 s25 | -0.3009 0.5306 -0.1814 1.0000 . pca s1-s25 Principal components/correlation Number of obs = 17 Number of comp. = 16 Trace = 25 Rotation: (unrotated = principal) Rho = 1.0000 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 8.79197 3.20666 0.3517 0.3517 Comp2 | 5.58531 2.63045 0.2234 0.5751 Comp3 | 2.95486 1.02607 0.1182 0.6933 Comp4 | 1.92879 .348271 0.0772 0.7704 Comp5 | 1.58052 .45002 0.0632 0.8337 Comp6 | 1.1305 .137441 0.0452 0.8789 Comp7 | .993059 .448469 0.0397 0.9186 Comp8 | .54459 .143101 0.0218 0.9404 Comp9 | .401489 .0527806 0.0161 0.9564 Comp10 | .348708 .152947 0.0139 0.9704 Comp11 | .195761 .01967 0.0078 0.9782 Comp12 | .176091 .0492475 0.0070 0.9853 Comp13 | .126843 .0110218 0.0051 0.9903 Comp14 | .115821 .0414043 0.0046 0.9950 Comp15 | .074417 .0231439 0.0030 0.9979 Comp16 | .0512731 .0512731 0.0021 1.0000 Comp17 | 0 0 0.0000 1.0000 Comp18 | 0 0 0.0000 1.0000 Comp19 | 0 0 0.0000 1.0000 Comp20 | 0 0 0.0000 1.0000 Comp21 | 0 0 0.0000 1.0000 Comp22 | 0 0 0.0000 1.0000 Comp23 | 0 0 0.0000 1.0000 Comp24 | 0 0 0.0000 1.0000 Comp25 | 0 . 0.0000 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) -------------------------------------------------------------------------------------------------------------- > ------------------------ Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 Com > p10 Comp11 Comp12 -------------+------------------------------------------------------------------------------------------------ > ------------------------ s1 | -0.2984 0.0048 -0.0653 -0.2825 -0.0472 -0.0449 0.0023 0.1522 0.0422 -0.2 > 297 0.0297 -0.1433 s2 | 0.2499 0.0176 -0.1849 0.2426 0.1190 -0.2435 -0.0298 0.4761 -0.0501 0.1 > 380 -0.1206 -0.0960 s3 | 0.2008 0.2026 -0.1933 0.1048 -0.0931 0.4313 0.1706 0.0939 0.1062 -0.0 > 028 -0.1654 -0.0838 s4 | -0.1730 0.2432 0.0068 0.0271 0.0698 0.4728 0.3278 0.0534 -0.2510 0.0 > 039 -0.0818 0.1530 s5 | 0.1077 -0.3159 -0.0723 0.3085 0.0426 0.1811 -0.1457 0.1591 0.3219 0.0 > 617 0.2677 -0.0428 s6 | 0.0813 -0.3122 0.0179 0.2645 0.0978 0.0649 0.3008 0.4140 0.1248 -0.3 > 116 0.0824 0.0795 s7 | 0.1139 0.3152 -0.1115 -0.0463 -0.2338 -0.0393 0.3090 -0.0450 0.3580 0.3 > 377 -0.0590 -0.1883 s8 | 0.0067 0.3364 0.2274 0.1539 0.0345 0.0158 -0.0877 -0.1021 0.2878 -0.5 > 287 -0.2951 0.0910 s9 | 0.1456 0.3559 -0.0566 0.0695 0.0829 -0.0776 -0.0079 0.0427 0.1190 -0.0 > 896 0.4060 0.1639 s10 | 0.2342 0.1458 0.1827 -0.0871 -0.3939 -0.0039 -0.0852 0.0190 0.2508 0.0 > 631 0.0162 0.0441 s11 | 0.2550 -0.1110 0.1681 -0.0855 0.2218 0.2684 -0.0789 -0.2713 0.2808 0.2 > 053 0.1611 0.0030 s12 | -0.1298 0.2433 0.2261 0.2504 0.3127 0.1271 -0.1109 -0.0360 0.0329 0.0 > 263 0.2661 -0.4371 s13 | 0.0492 0.1170 -0.4448 -0.0450 0.2837 -0.3404 0.1320 -0.1939 0.1322 0.0 > 692 0.0355 0.1233 s14 | -0.2807 0.0928 0.0034 -0.1398 0.1552 -0.3003 0.0189 0.1035 0.3583 -0.0 > 926 0.1336 0.1412 s15 | -0.2661 0.1052 0.2553 0.1330 0.1757 -0.0590 -0.0185 0.0424 0.1655 -0.0 > 304 -0.1046 -0.2388 s16 | 0.0267 0.2269 0.1923 0.3268 -0.3751 -0.2106 0.1834 -0.0004 -0.2362 -0.0 > 452 0.4193 0.2391 s17 | -0.2707 -0.0209 0.0477 -0.3216 -0.0962 0.1741 0.0812 0.1999 -0.0222 0.0 > 999 0.4668 -0.0846 s18 | 0.2026 -0.1791 0.2872 -0.1034 0.1703 -0.0121 0.3216 -0.1036 0.0832 -0.0 > 815 -0.0157 0.3166 s19 | 0.1471 0.2571 -0.1904 -0.1717 0.3259 0.0358 0.2491 0.1610 -0.1325 -0.0 > 665 0.0588 -0.1522 s20 | 0.2057 0.1767 0.0702 -0.1947 0.3393 0.1376 -0.3209 0.0764 -0.1651 0.0 > 234 0.1047 0.3886 s21 | 0.2347 0.1646 0.1077 -0.1817 -0.0909 -0.0208 -0.4061 0.3399 -0.0340 0.0 > 477 -0.0373 -0.0764 s22 | 0.2133 0.0274 0.3352 -0.2637 0.0102 -0.1656 0.1426 0.2659 -0.1360 -0.0 > 665 -0.1205 -0.1724 s23 | -0.2878 0.0259 0.0966 -0.1147 -0.0004 0.1075 0.0424 0.3534 0.3218 0.3 > 103 -0.1740 0.3759 s24 | 0.1800 -0.1203 0.3641 -0.1210 0.1476 -0.1896 0.3265 -0.0824 -0.0077 0.1 > 671 0.0226 -0.1893 s25 | -0.2056 0.1123 0.2161 0.3439 0.1671 -0.1272 -0.0366 0.0421 -0.1724 0.4 > 584 -0.1857 0.1564 -------------------------------------------------------------------------------------------------------------- > ------------------------ -------------------------------------------------------------------- Variable | Comp13 Comp14 Comp15 Comp16 | Unexplained -------------+----------------------------------------+------------- s1 | 0.0057 0.1227 0.1378 0.3413 | 0 s2 | -0.0455 0.1203 -0.2622 0.1699 | 0 s3 | -0.0841 0.1289 0.3940 0.1590 | 0 s4 | -0.1031 -0.1439 -0.1000 0.1298 | 0 s5 | 0.0212 0.2524 -0.1464 -0.0883 | 0 s6 | 0.1659 -0.2130 0.3129 0.0377 | 0 s7 | 0.2372 0.0155 -0.1041 0.0048 | 0 s8 | 0.1592 -0.0096 -0.1252 0.0594 | 0 s9 | 0.2252 -0.3766 -0.0139 -0.0913 | 0 s10 | 0.0451 0.2195 0.0613 -0.0424 | 0 s11 | -0.0755 -0.0483 0.2233 0.0654 | 0 s12 | -0.2870 -0.1885 -0.0728 -0.0876 | 0 s13 | -0.0501 -0.1909 0.1298 -0.0760 | 0 s14 | -0.1736 0.1664 0.2419 0.2104 | 0 s15 | 0.1209 0.2735 -0.0680 -0.1104 | 0 s16 | -0.3099 0.2048 0.0562 0.0326 | 0 s17 | 0.4132 0.0006 -0.1014 0.0297 | 0 s18 | 0.1239 0.0048 -0.4556 0.1210 | 0 s19 | -0.0272 0.3618 -0.1849 -0.1084 | 0 s20 | 0.0667 0.3557 0.1620 -0.0025 | 0 s21 | -0.0608 -0.3643 -0.1076 0.3666 | 0 s22 | 0.0224 -0.0806 0.2874 -0.5566 | 0 s23 | -0.3949 -0.1346 -0.1252 -0.2470 | 0 s24 | -0.1918 -0.0109 0.0833 0.4041 | 0 s25 | 0.4452 0.0117 0.2526 0.1363 | 0 -------------------------------------------------------------------- . screeplot . scoreplot, comp(3) mlabel(plot) . loadingplot . predict sco1-sco4, score (12 components skipped) Scoring coefficients sum of squares(column-loading) = 1 -------------------------------------------------------------------------------------------------------------- > ------------------------ Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 Com > p10 Comp11 Comp12 -------------+------------------------------------------------------------------------------------------------ > ------------------------ s1 | -0.2984 0.0048 -0.0653 -0.2825 -0.0472 -0.0449 0.0023 0.1522 0.0422 -0.2 > 297 0.0297 -0.1433 s2 | 0.2499 0.0176 -0.1849 0.2426 0.1190 -0.2435 -0.0298 0.4761 -0.0501 0.1 > 380 -0.1206 -0.0960 s3 | 0.2008 0.2026 -0.1933 0.1048 -0.0931 0.4313 0.1706 0.0939 0.1062 -0.0 > 028 -0.1654 -0.0838 s4 | -0.1730 0.2432 0.0068 0.0271 0.0698 0.4728 0.3278 0.0534 -0.2510 0.0 > 039 -0.0818 0.1530 s5 | 0.1077 -0.3159 -0.0723 0.3085 0.0426 0.1811 -0.1457 0.1591 0.3219 0.0 > 617 0.2677 -0.0428 s6 | 0.0813 -0.3122 0.0179 0.2645 0.0978 0.0649 0.3008 0.4140 0.1248 -0.3 > 116 0.0824 0.0795 s7 | 0.1139 0.3152 -0.1115 -0.0463 -0.2338 -0.0393 0.3090 -0.0450 0.3580 0.3 > 377 -0.0590 -0.1883 s8 | 0.0067 0.3364 0.2274 0.1539 0.0345 0.0158 -0.0877 -0.1021 0.2878 -0.5 > 287 -0.2951 0.0910 s9 | 0.1456 0.3559 -0.0566 0.0695 0.0829 -0.0776 -0.0079 0.0427 0.1190 -0.0 > 896 0.4060 0.1639 s10 | 0.2342 0.1458 0.1827 -0.0871 -0.3939 -0.0039 -0.0852 0.0190 0.2508 0.0 > 631 0.0162 0.0441 s11 | 0.2550 -0.1110 0.1681 -0.0855 0.2218 0.2684 -0.0789 -0.2713 0.2808 0.2 > 053 0.1611 0.0030 s12 | -0.1298 0.2433 0.2261 0.2504 0.3127 0.1271 -0.1109 -0.0360 0.0329 0.0 > 263 0.2661 -0.4371 s13 | 0.0492 0.1170 -0.4448 -0.0450 0.2837 -0.3404 0.1320 -0.1939 0.1322 0.0 > 692 0.0355 0.1233 s14 | -0.2807 0.0928 0.0034 -0.1398 0.1552 -0.3003 0.0189 0.1035 0.3583 -0.0 > 926 0.1336 0.1412 s15 | -0.2661 0.1052 0.2553 0.1330 0.1757 -0.0590 -0.0185 0.0424 0.1655 -0.0 > 304 -0.1046 -0.2388 s16 | 0.0267 0.2269 0.1923 0.3268 -0.3751 -0.2106 0.1834 -0.0004 -0.2362 -0.0 > 452 0.4193 0.2391 s17 | -0.2707 -0.0209 0.0477 -0.3216 -0.0962 0.1741 0.0812 0.1999 -0.0222 0.0 > 999 0.4668 -0.0846 s18 | 0.2026 -0.1791 0.2872 -0.1034 0.1703 -0.0121 0.3216 -0.1036 0.0832 -0.0 > 815 -0.0157 0.3166 s19 | 0.1471 0.2571 -0.1904 -0.1717 0.3259 0.0358 0.2491 0.1610 -0.1325 -0.0 > 665 0.0588 -0.1522 s20 | 0.2057 0.1767 0.0702 -0.1947 0.3393 0.1376 -0.3209 0.0764 -0.1651 0.0 > 234 0.1047 0.3886 s21 | 0.2347 0.1646 0.1077 -0.1817 -0.0909 -0.0208 -0.4061 0.3399 -0.0340 0.0 > 477 -0.0373 -0.0764 s22 | 0.2133 0.0274 0.3352 -0.2637 0.0102 -0.1656 0.1426 0.2659 -0.1360 -0.0 > 665 -0.1205 -0.1724 s23 | -0.2878 0.0259 0.0966 -0.1147 -0.0004 0.1075 0.0424 0.3534 0.3218 0.3 > 103 -0.1740 0.3759 s24 | 0.1800 -0.1203 0.3641 -0.1210 0.1476 -0.1896 0.3265 -0.0824 -0.0077 0.1 > 671 0.0226 -0.1893 s25 | -0.2056 0.1123 0.2161 0.3439 0.1671 -0.1272 -0.0366 0.0421 -0.1724 0.4 > 584 -0.1857 0.1564 -------------------------------------------------------------------------------------------------------------- > ------------------------ ------------------------------------------------------ Variable | Comp13 Comp14 Comp15 Comp16 -------------+---------------------------------------- s1 | 0.0057 0.1227 0.1378 0.3413 s2 | -0.0455 0.1203 -0.2622 0.1699 s3 | -0.0841 0.1289 0.3940 0.1590 s4 | -0.1031 -0.1439 -0.1000 0.1298 s5 | 0.0212 0.2524 -0.1464 -0.0883 s6 | 0.1659 -0.2130 0.3129 0.0377 s7 | 0.2372 0.0155 -0.1041 0.0048 s8 | 0.1592 -0.0096 -0.1252 0.0594 s9 | 0.2252 -0.3766 -0.0139 -0.0913 s10 | 0.0451 0.2195 0.0613 -0.0424 s11 | -0.0755 -0.0483 0.2233 0.0654 s12 | -0.2870 -0.1885 -0.0728 -0.0876 s13 | -0.0501 -0.1909 0.1298 -0.0760 s14 | -0.1736 0.1664 0.2419 0.2104 s15 | 0.1209 0.2735 -0.0680 -0.1104 s16 | -0.3099 0.2048 0.0562 0.0326 s17 | 0.4132 0.0006 -0.1014 0.0297 s18 | 0.1239 0.0048 -0.4556 0.1210 s19 | -0.0272 0.3618 -0.1849 -0.1084 s20 | 0.0667 0.3557 0.1620 -0.0025 s21 | -0.0608 -0.3643 -0.1076 0.3666 s22 | 0.0224 -0.0806 0.2874 -0.5566 s23 | -0.3949 -0.1346 -0.1252 -0.2470 s24 | -0.1918 -0.0109 0.0833 0.4041 s25 | 0.4452 0.0117 0.2526 0.1363 ------------------------------------------------------ . pwcorr sco1-sco4 light-nitrogen | sco1 sco2 sco3 sco4 light moisture reaction -------------+--------------------------------------------------------------- sco1 | 1.0000 sco2 | 0.0000 1.0000 sco3 | -0.0000 -0.0000 1.0000 sco4 | 0.0000 -0.0000 -0.0000 1.0000 light | -0.6719 0.6339 0.0299 -0.2520 1.0000 moisture | 0.7569 -0.2847 0.0814 0.4686 -0.8648 1.0000 reaction | 0.6830 -0.4116 0.3313 0.3385 -0.8591 0.9204 1.0000 nitrogen | 0.5991 -0.4826 0.2227 0.4562 -0.8820 0.9246 0.9673 | nitrogen -------------+--------- nitrogen | 1.0000 . scatter light sco1, mlabel(plot) . scatter moisture sco1, mlabel(plot) . biplot s1-s25, std xneg yneg alpha(1) stretch(10) Biplot of 17 observations and 25 variables Explained variance by component 1 = 0.3517 Explained variance by component 2 = 0.2234 Total explained variance = 0.5751 . . * added code to demonstrate equivalence with mds (without standardization) . pca s1-s25, comp(5) cov Principal components/covariance Number of obs = 17 Number of comp. = 5 Trace = 1257.816 Rotation: (unrotated = principal) Rho = 0.8949 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 537.2 206.849 0.4271 0.4271 Comp2 | 330.351 228.047 0.2626 0.6897 Comp3 | 102.304 6.87169 0.0813 0.7711 Comp4 | 95.4323 35.052 0.0759 0.8469 Comp5 | 60.3802 17.7661 0.0480 0.8949 Comp6 | 42.6141 10.1976 0.0339 0.9288 Comp7 | 32.4165 13.7359 0.0258 0.9546 Comp8 | 18.6805 7.56252 0.0149 0.9694 Comp9 | 11.118 1.61979 0.0088 0.9783 Comp10 | 9.49823 4.04332 0.0076 0.9858 Comp11 | 5.45492 1.4904 0.0043 0.9902 Comp12 | 3.96451 .61508 0.0032 0.9933 Comp13 | 3.34943 1.07295 0.0027 0.9960 Comp14 | 2.27648 .398974 0.0018 0.9978 Comp15 | 1.87751 .978727 0.0015 0.9993 Comp16 | .898785 .898785 0.0007 1.0000 Comp17 | 0 0 0.0000 1.0000 Comp18 | 0 0 0.0000 1.0000 Comp19 | 0 0 0.0000 1.0000 Comp20 | 0 0 0.0000 1.0000 Comp21 | 0 0 0.0000 1.0000 Comp22 | 0 0 0.0000 1.0000 Comp23 | 0 0 0.0000 1.0000 Comp24 | 0 0 0.0000 1.0000 Comp25 | 0 . 0.0000 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) ------------------------------------------------------------------------------ Variable | Comp1 Comp2 Comp3 Comp4 Comp5 | Unexplained -------------+--------------------------------------------------+------------- s1 | -0.6297 -0.3017 0.3624 -0.0313 -0.1928 | 4.28 s2 | 0.2446 0.1117 0.1700 -0.1205 0.3161 | 8.775 s3 | 0.2205 0.4382 0.4183 0.4026 -0.3143 | 1.654 s4 | -0.2065 0.1400 0.1418 0.5964 0.0202 | 4.467 s5 | 0.3560 -0.3587 0.1133 0.0381 -0.0576 | 17.88 s6 | 0.4153 -0.5544 0.1964 0.3715 0.0921 | 10.68 s7 | 0.0049 0.2335 0.0803 0.0434 -0.0262 | 6.594 s8 | -0.0322 0.1282 -0.1358 0.1336 0.1062 | 4.423 s9 | 0.0222 0.1913 0.0209 0.0269 0.1350 | 2.665 s10 | 0.0835 0.1605 -0.1947 -0.0399 -0.2585 | 3.811 s11 | 0.1104 0.0164 -0.0843 -0.0465 -0.1395 | 4.502 s12 | -0.0630 0.0509 -0.1154 0.1801 0.2194 | 3.655 s13 | 0.0114 0.1530 0.5251 -0.3199 0.4510 | 2.447 s14 | -0.1462 -0.0437 0.0380 -0.0175 0.1671 | 1.912 s15 | -0.1535 -0.0566 -0.1660 0.1892 0.2509 | 2.526 s16 | 0.0009 0.1409 -0.2516 0.2052 0.1655 | 13.67 s17 | -0.1757 -0.0982 0.0347 0.0687 -0.1868 | 2.739 s18 | 0.0870 -0.0336 -0.1167 -0.0240 -0.0758 | 4.923 s19 | 0.0205 0.1555 0.1716 -0.0116 0.0639 | 4.58 s20 | 0.0359 0.0957 -0.0312 -0.0536 -0.0225 | 4.474 s21 | 0.0454 0.1019 -0.0789 -0.0808 -0.1032 | 3.051 s22 | 0.0532 0.0462 -0.1589 -0.0556 -0.1094 | 6.041 s23 | -0.1538 -0.0812 -0.0048 0.1361 0.0066 | 4.861 s24 | 0.0580 -0.0142 -0.1427 -0.0366 -0.0299 | 4.245 s25 | -0.1069 -0.0285 -0.2108 0.2287 0.4437 | 3.295 ------------------------------------------------------------------------------ . scoreplot, comp(2) mlabel(plot) . mds s1-s25, config noplot id(plot) Classical metric multidimensional scaling Dissimilarity: L2, computed on 25 variables Number of obs = 17 Eigenvalues > 0 = 16 Mardia fit measure 1 = 0.6897 Retained dimensions = 2 Mardia fit measure 2 = 0.9371 -------------------------------------------------------------------------- | abs(eigenvalue) (eigenvalue)^2 Dimension | Eigenvalue Percent Cumul. Percent Cumul. -------------+------------------------------------------------------------ 1 | 8595.198 42.71 42.71 67.99 67.99 2 | 5285.6133 26.26 68.97 25.71 93.71 -------------+------------------------------------------------------------ 3 | 1636.8631 8.13 77.11 2.47 96.17 4 | 1526.9161 7.59 84.69 2.15 98.32 5 | 966.08343 4.80 89.49 0.86 99.18 6 | 681.82604 3.39 92.88 0.43 99.60 7 | 518.66383 2.58 95.46 0.25 99.85 8 | 298.88865 1.49 96.94 0.08 99.93 9 | 177.88838 0.88 97.83 0.03 99.96 10 | 151.97173 0.76 98.58 0.02 99.98 -------------------------------------------------------------------------- Configuration in 2-dimensional Euclidean space (principal normalization) plot | dim1 dim2 ------+---------------------------- 1 | 28.8934 13.5015 2 | 35.3036 14.6290 3 | 39.3429 14.7996 4 | 29.4377 7.8792 5 | 13.6051 -1.7839 6 | 6.2638 -7.2729 7 | 5.9312 -8.1215 8 | -8.2158 -21.9365 9 | -7.5651 -31.9075 10 | -9.4674 -26.6580 11 | -10.2235 -2.5168 12 | -9.8597 -12.9532 13 | -4.2394 -3.7437 14 | -15.5680 -2.3882 15 | -19.2499 4.3623 16 | -33.5732 30.0218 17 | -40.8156 34.0887 ----------------------------------- . * note: eigenvalues multiplied by (n-1) . mdsconfig, xneg yneg . . * calf data . use calf, clear . * note: polychoric is an add-on command; Stata has a tetrachoric command for binary variables . polychoric age sex-umb /* add verbose option to see lots of details! */ Polychoric correlation matrix age sex attd dehy eye jnts post pulse resp > temp umb age 1 sex .01026004 1 attd -.14081148 -.04479291 1 dehy -.12612086 -.14580851 .38207292 1 eye .0441196 .33056917 .15004459 -.09936422 1 jnts .0008926 .04775808 .08356658 -.03024093 .59635231 1 post -.09964047 -.06227926 .87386637 .39732633 .32318563 .08395814 1 pulse -.18651421 .01407062 -.13078394 -.03287323 .07455487 .2575224 -.10822607 1 resp -.26418451 -.09805846 .17307776 -.0249882 .03454427 -.00540613 .19582088 .16964738 1 temp -.09753186 .06242938 -.3340238 -.30588409 .19888097 .07138087 -.37218583 .23121708 .22578032 > 1 umb -.05512062 .15237046 .14517111 -.08484105 .21072786 .3722088 .04435448 .12997537 .09122346 > .12945084 1 . correlate age sex-umb /* note: comparison is not with pwcorr */ (obs=213) | age sex attd dehy eye jnts post pulse resp temp umb -------------+--------------------------------------------------------------------------------------------------- age | 1.0000 sex | 0.0080 1.0000 attd | -0.1175 -0.0297 1.0000 dehy | -0.1261 -0.1158 0.3201 1.0000 eye | 0.0175 0.0894 0.0412 -0.0341 1.0000 jnts | -0.0104 -0.0071 0.0226 -0.0199 0.2205 1.0000 post | -0.0903 -0.0439 0.6322 0.3516 0.1025 0.0598 1.0000 pulse | -0.1865 0.0112 -0.1084 -0.0329 0.0245 0.1285 -0.0923 1.0000 resp | -0.2642 -0.0768 0.1435 -0.0250 0.0115 -0.0156 0.1738 0.1696 1.0000 temp | -0.0975 0.0505 -0.2839 -0.3059 0.0564 0.0233 -0.3447 0.2312 0.2258 1.0000 umb | -0.0386 0.0876 0.0856 -0.0633 0.0626 0.1468 0.0280 0.0920 0.0653 0.0925 1.0000 . * for display of correlations only . foreach var of varlist age sex-umb { 2. egen s`var'=std(`var') 3. } (1 missing value generated) (2 missing values generated) (6 missing values generated) (14 missing values generated) (18 missing values generated) (11 missing values generated) (6 missing values generated) (9 missing values generated) (19 missing values generated) (7 missing values generated) (11 missing values generated) . sort case . polychoric age sex-umb Polychoric correlation matrix age sex attd dehy eye jnts post pulse resp > temp umb age 1 sex .01026004 1 attd -.14081148 -.04479291 1 dehy -.12612086 -.14580851 .38207292 1 eye .0441196 .33056917 .15004459 -.09936422 1 jnts .0008926 .04775808 .08356658 -.03024093 .59635231 1 post -.09964047 -.06227926 .87386637 .39732633 .32318563 .08395814 1 pulse -.18651421 .01407062 -.13078394 -.03287323 .07455487 .2575224 -.10822607 1 resp -.26418451 -.09805846 .17307776 -.0249882 .03454427 -.00540613 .19582088 .16964738 1 temp -.09753186 .06242938 -.3340238 -.30588409 .19888097 .07138087 -.37218583 .23121708 .22578032 > 1 umb -.05512062 .15237046 .14517111 -.08484105 .21072786 .3722088 .04435448 .12997537 .09122346 > .12945084 1 . matrix define polycorr=r(R) . sort case /* the polychoric command resorts the data, so we have to reset */ . pcamat polycorr, n(213) /* n=number of complete rows */ Principal components/correlation Number of obs = 213 Number of comp. = 11 Trace = 11 Rotation: (unrotated = principal) Rho = 1.0000 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 2.48325 .341845 0.2257 0.2257 Comp2 | 2.1414 .636921 0.1947 0.4204 Comp3 | 1.50448 .489274 0.1368 0.5572 Comp4 | 1.01521 .100485 0.0923 0.6495 Comp5 | .914724 .0820931 0.0832 0.7326 Comp6 | .832631 .155607 0.0757 0.8083 Comp7 | .677024 .0613992 0.0615 0.8699 Comp8 | .615625 .120503 0.0560 0.9259 Comp9 | .495122 .240377 0.0450 0.9709 Comp10 | .254746 .188966 0.0232 0.9940 Comp11 | .0657794 . 0.0060 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) -------------------------------------------------------------------------------------------------------------- > ---------------------------- Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 Com > p10 Comp11 | Unexplained -------------+------------------------------------------------------------------------------------------------ > --------------+------------- age | -0.1121 -0.0940 0.5299 -0.1212 0.4967 0.0424 0.5664 0.3285 0.0306 0.0 > 698 -0.0066 | 0 sex | -0.0561 0.2508 0.3094 0.5392 -0.5986 0.0150 0.2841 0.1018 0.1680 0.2 > 384 0.1129 | 0 attd | 0.5781 0.0125 -0.0264 0.1330 0.0732 -0.0995 0.0892 -0.0347 -0.3456 0.4 > 561 -0.5435 | 0 dehy | 0.3715 -0.1919 -0.0889 -0.3194 -0.3236 0.1206 -0.0873 0.7093 0.2804 -0.0 > 686 -0.0444 | 0 eye | 0.1546 0.5117 0.2799 0.1145 0.0951 0.4031 -0.1842 0.0176 0.0111 -0.5 > 365 -0.3591 | 0 jnts | 0.1048 0.5024 0.1699 -0.4449 0.0937 0.0759 -0.2225 -0.1633 0.3302 0.5 > 183 0.2036 | 0 post | 0.5926 0.0303 0.0104 0.1322 0.1192 0.1243 0.1078 -0.0660 -0.2556 -0.1 > 660 0.7013 | 0 pulse | -0.0932 0.3005 -0.3531 -0.4363 -0.2932 0.2076 0.5994 -0.1106 -0.2720 -0.0 > 906 -0.0569 | 0 resp | 0.1119 0.1640 -0.5561 0.3306 0.3572 0.0184 0.2784 0.0273 0.5774 -0.0 > 029 -0.0502 | 0 temp | -0.3160 0.3185 -0.2702 0.1976 0.1981 0.1521 -0.2238 0.5488 -0.4341 0.2 > 511 0.1466 | 0 umb | 0.0709 0.3968 0.0252 -0.0875 0.0022 -0.8504 0.0313 0.1786 -0.0495 -0.2 > 650 0.0207 | 0 -------------------------------------------------------------------------------------------------------------- > ---------------------------- . mkmat sage-sumb, matrix(sdata) . *matrix list sdata . matrix define load=e(L) . matrix define scomat = sdata*load . *matrix list scomat . svmat scomat . twoway (scatter scomat2 scomat1 if sepsis==0, msymbol(smx)) (scatter scomat2 scomat1 if sepsis==1, msymbol(smcir > cle_hollow)), ytitle(2nd principal component) xtitle(1st principal component) title(Polychoric PCA (x=no sepsis, > o=sepsis), size(medium)) legend(off) . . pca age sex-umb Principal components/correlation Number of obs = 213 Number of comp. = 11 Trace = 11 Rotation: (unrotated = principal) Rho = 1.0000 -------------------------------------------------------------------------- Component | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Comp1 | 2.20632 .557409 0.2006 0.2006 Comp2 | 1.64891 .329284 0.1499 0.3505 Comp3 | 1.31963 .291605 0.1200 0.4704 Comp4 | 1.02802 .0970539 0.0935 0.5639 Comp5 | .930968 .0103964 0.0846 0.6485 Comp6 | .920572 .183806 0.0837 0.7322 Comp7 | .736766 .0253664 0.0670 0.7992 Comp8 | .7114 .106639 0.0647 0.8639 Comp9 | .60476 .0606445 0.0550 0.9188 Comp10 | .544116 .195578 0.0495 0.9683 Comp11 | .348538 . 0.0317 1.0000 -------------------------------------------------------------------------- Principal components (eigenvectors) -------------------------------------------------------------------------------------------------------------- > ---------------------------- Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 Com > p10 Comp11 | Unexplained -------------+------------------------------------------------------------------------------------------------ > --------------+------------- age | -0.0952 -0.4431 0.3102 -0.0506 0.1656 0.3516 0.6483 0.1790 0.2882 -0.0 > 798 0.0534 | 0 sex | -0.0973 0.0219 0.3256 0.7102 -0.1504 -0.4916 0.1574 -0.1972 0.1971 -0.1 > 131 0.0096 | 0 attd | 0.5363 0.1414 0.0534 0.1835 0.0699 0.1255 0.1354 -0.0686 -0.0703 0.4 > 719 0.6201 | 0 dehy | 0.4308 -0.0289 -0.1336 -0.2059 -0.3052 -0.2640 -0.0995 0.3691 0.6485 -0.1 > 481 0.0431 | 0 eye | 0.0242 0.1907 0.5419 -0.1440 0.5037 -0.2939 -0.1886 0.4842 -0.1547 -0.0 > 904 0.0802 | 0 jnts | 0.0093 0.2445 0.5130 -0.4838 -0.1412 0.0249 -0.0343 -0.6049 0.2297 -0.0 > 320 0.0371 | 0 post | 0.5576 0.1350 0.0828 0.0855 0.1441 0.0429 0.2150 -0.0639 -0.0825 0.1 > 467 -0.7453 | 0 pulse | -0.1580 0.4427 -0.0781 -0.2397 -0.3818 -0.2586 0.6011 0.2372 -0.2856 0.0 > 517 0.0320 | 0 resp | 0.0628 0.5115 -0.2982 0.1280 0.3999 0.1947 0.1740 -0.1321 0.1896 -0.5 > 733 0.1375 | 0 temp | -0.4094 0.3514 -0.0902 0.0668 0.2139 0.0737 -0.0325 0.1097 0.5004 0.5 > 977 -0.1559 | 0 umb | -0.0133 0.2946 0.3319 0.2767 -0.4538 0.5918 -0.2259 0.3130 -0.0332 -0.1 > 301 -0.0556 | 0 -------------------------------------------------------------------------------------------------------------- > ---------------------------- . predict sco1-sco6 (score assumed) (5 components skipped) Scoring coefficients sum of squares(column-loading) = 1 -------------------------------------------------------------------------------------------------------------- > -------------- Variable | Comp1 Comp2 Comp3 Comp4 Comp5 Comp6 Comp7 Comp8 Comp9 Com > p10 Comp11 -------------+------------------------------------------------------------------------------------------------ > -------------- age | -0.0952 -0.4431 0.3102 -0.0506 0.1656 0.3516 0.6483 0.1790 0.2882 -0.0 > 798 0.0534 sex | -0.0973 0.0219 0.3256 0.7102 -0.1504 -0.4916 0.1574 -0.1972 0.1971 -0.1 > 131 0.0096 attd | 0.5363 0.1414 0.0534 0.1835 0.0699 0.1255 0.1354 -0.0686 -0.0703 0.4 > 719 0.6201 dehy | 0.4308 -0.0289 -0.1336 -0.2059 -0.3052 -0.2640 -0.0995 0.3691 0.6485 -0.1 > 481 0.0431 eye | 0.0242 0.1907 0.5419 -0.1440 0.5037 -0.2939 -0.1886 0.4842 -0.1547 -0.0 > 904 0.0802 jnts | 0.0093 0.2445 0.5130 -0.4838 -0.1412 0.0249 -0.0343 -0.6049 0.2297 -0.0 > 320 0.0371 post | 0.5576 0.1350 0.0828 0.0855 0.1441 0.0429 0.2150 -0.0639 -0.0825 0.1 > 467 -0.7453 pulse | -0.1580 0.4427 -0.0781 -0.2397 -0.3818 -0.2586 0.6011 0.2372 -0.2856 0.0 > 517 0.0320 resp | 0.0628 0.5115 -0.2982 0.1280 0.3999 0.1947 0.1740 -0.1321 0.1896 -0.5 > 733 0.1375 temp | -0.4094 0.3514 -0.0902 0.0668 0.2139 0.0737 -0.0325 0.1097 0.5004 0.5 > 977 -0.1559 umb | -0.0133 0.2946 0.3319 0.2767 -0.4538 0.5918 -0.2259 0.3130 -0.0332 -0.1 > 301 -0.0556 -------------------------------------------------------------------------------------------------------------- > -------------- . list sco1-sco5 scomat1-scomat5 in 250/254 +------------------------------------------------------------------------------------------------------------ > -----------+ | sco1 sco2 sco3 sco4 sco5 scomat1 scomat2 scomat3 scomat4 > scomat5 | |------------------------------------------------------------------------------------------------------------ > -----------| 250. | 1.326669 -.4072271 -.0941716 .7627372 .1074602 1.130997 -.6607679 .3077689 .7555366 > -.7725231 | 251. | .9534625 .7103059 -.5290972 -.2719495 -1.059138 .8767514 -.0802605 -1.011767 -.8056126 > -.1324275 | 252. | .8450878 1.529826 -1.726462 .1313511 2.096028 .851383 -.1763431 -2.277633 1.427279 > 1.672969 | 253. | -.1032492 .2870813 -1.062035 -.2860836 1.260549 -.1976646 -.4571058 -1.03413 .4784389 > 1.272845 | 254. | -2.13716 .1485368 -1.182741 -1.420211 -.5071669 -2.249265 -.1667564 -1.140397 -1.217268 > -.3986959 | +------------------------------------------------------------------------------------------------------------ > -----------+ . list age sex-umb in 250/254 +-------------------------------------------------------------------------------------+ | age sex attd dehy eye jnts post pulse resp temp umb | |-------------------------------------------------------------------------------------| 250. | 8 male depressed 10.0 no 0 lateral 100 40 37.1 no | 251. | 5 female depressed 15.0 no 0 sternal 100 42 39.1 yes | 252. | 3 female depressed 6.5 no 0 lateral 85 90 39.6 no | 253. | 8 female depressed 5.0 no 0 sternal 100 60 38.8 no | 254. | 5 female bright 7.0 no 0 standing 150 28 39.7 no | +-------------------------------------------------------------------------------------+ . twoway (scatter sco2 sco1 if sepsis==0, msymbol(smx)) (scatter sco2 sco1 if sepsis==1, msymbol(smcircle_hollow)) > , ytitle(2nd principal component) xtitle(1st principal component) title(Ordinary PCA (x=no sepsis, o=sepsis), si > ze(medium)) legend(off) . . tabstat sco1-sco6 scomat1-scomat6, statistics( mean semean ) by(sepsis) Summary statistics: Mean, se(mean) Group variable: sepsis (sepsis (0=no, 1=yes)) sepsis | sco1 sco2 sco3 sco4 sco5 sco6 scomat1 scomat2 scomat3 scomat4 sco > mat5 scomat6 -------+---------------------------------------------------------------------------------------------------------- > -------------- no | -.2813099 -.1836713 -.1133812 .013458 -.027279 -.0472951 -.3649133 -.1695357 .0056898 -.0259087 -.045 > 4369 .0122261 | .1206508 .0919026 .0729616 .0752472 .0710346 .0697055 .1148666 .0742771 .0930896 .0737726 .075 > 8695 .0671289 -------+---------------------------------------------------------------------------------------------------------- > -------------- yes | .7009691 .4576728 .2825236 -.0335347 .0679738 .1178502 .7286027 .270085 -.1526351 -.0543031 .053 > 1672 -.1816857 | .1582304 .1940434 .2029532 .154961 .1489091 .1500943 .1540909 .2072477 .1614268 .151281 .12 > 9867 .1445498 -------+---------------------------------------------------------------------------------------------------------- > -------------- Total | -1.08e-09 -7.00e-11 2.37e-09 2.82e-09 -1.33e-09 1.42e-10 -.0517467 -.0436349 -.0396521 -.0340405 -.017 > 1982 -.0433073 | .1017758 .087985 .0787111 .0694723 .0661116 .0657414 .0989125 .080448 .0808757 .0679854 .065 > 5906 .0634057 ------------------------------------------------------------------------------------------------------------------ > -------------- . foreach var of varlist sco1-sco6 scomat1-scomat6 { 2. ttest `var', by(sepsis) unpaired unequal 3. } Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.2813099 .1206508 1.487483 -.5196917 -.0429282 yes | 61 .7009691 .1582304 1.235819 .3844611 1.017477 ---------+-------------------------------------------------------------------- Combined | 213 -1.08e-09 .1017758 1.485369 -.2006221 .2006221 ---------+-------------------------------------------------------------------- diff | -.982279 .1989811 -1.375875 -.5886825 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -4.9365 H0: diff = 0 Satterthwaite's degrees of freedom = 132.283 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.1836713 .0919026 1.133052 -.3652524 -.0020902 yes | 61 .4576728 .1940434 1.515527 .0695283 .8458173 ---------+-------------------------------------------------------------------- Combined | 213 -7.00e-11 .087985 1.284099 -.1734376 .1734376 ---------+-------------------------------------------------------------------- diff | -.6413441 .2147066 -1.068017 -.2146716 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -2.9871 H0: diff = 0 Satterthwaite's degrees of freedom = 88.1739 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0018 Pr(|T| > |t|) = 0.0036 Pr(T > t) = 0.9982 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.1133812 .0729616 .8995311 -.2575386 .0307763 yes | 61 .2825236 .2029532 1.585115 -.1234432 .6884904 ---------+-------------------------------------------------------------------- Combined | 213 2.37e-09 .0787111 1.14875 -.1551566 .1551566 ---------+-------------------------------------------------------------------- diff | -.3959048 .2156696 -.8254474 .0336379 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -1.8357 H0: diff = 0 Satterthwaite's degrees of freedom = 76.0065 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0352 Pr(|T| > |t|) = 0.0703 Pr(T > t) = 0.9648 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 .013458 .0752472 .9277093 -.1352153 .1621312 yes | 61 -.0335347 .154961 1.210284 -.3435028 .2764335 ---------+-------------------------------------------------------------------- Combined | 213 2.82e-09 .0694723 1.013914 -.1369449 .1369449 ---------+-------------------------------------------------------------------- diff | .0469926 .1722645 -.2952589 .3892442 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = 0.2728 H0: diff = 0 Satterthwaite's degrees of freedom = 89.6508 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.6072 Pr(|T| > |t|) = 0.7856 Pr(T > t) = 0.3928 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.027279 .0710346 .875773 -.167629 .1130711 yes | 61 .0679738 .1489091 1.163018 -.2298888 .3658364 ---------+-------------------------------------------------------------------- Combined | 213 -1.33e-09 .0661116 .964867 -.1303203 .1303203 ---------+-------------------------------------------------------------------- diff | -.0952528 .1649844 -.423094 .2325885 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -0.5773 H0: diff = 0 Satterthwaite's degrees of freedom = 88.5914 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.2826 Pr(|T| > |t|) = 0.5652 Pr(T > t) = 0.7174 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.0472951 .0697055 .859387 -.1850192 .0904289 yes | 61 .1178502 .1500943 1.172274 -.1823831 .4180835 ---------+-------------------------------------------------------------------- Combined | 213 1.42e-10 .0657414 .9594644 -.1295906 .1295906 ---------+-------------------------------------------------------------------- diff | -.1651453 .1654906 -.4940725 .1637819 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -0.9979 H0: diff = 0 Satterthwaite's degrees of freedom = 87.0631 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.1605 Pr(|T| > |t|) = 0.3211 Pr(T > t) = 0.8395 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.3649133 .1148666 1.41617 -.5918665 -.13796 yes | 61 .7286027 .1540909 1.203488 .4203751 1.03683 ---------+-------------------------------------------------------------------- Combined | 213 -.0517467 .0989125 1.443581 -.2467247 .1432313 ---------+-------------------------------------------------------------------- diff | -1.093516 .1921934 -1.473766 -.7132661 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -5.6897 H0: diff = 0 Satterthwaite's degrees of freedom = 129.341 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.1695357 .0742771 .9157492 -.3162922 -.0227791 yes | 61 .270085 .2072477 1.618657 -.1444722 .6846422 ---------+-------------------------------------------------------------------- Combined | 213 -.0436349 .080448 1.174099 -.2022153 .1149455 ---------+-------------------------------------------------------------------- diff | -.4396206 .2201561 -.8781083 -.001133 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -1.9969 H0: diff = 0 Satterthwaite's degrees of freedom = 75.9062 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.0247 Pr(|T| > |t|) = 0.0494 Pr(T > t) = 0.9753 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 .0056898 .0930896 1.147685 -.1782365 .1896161 yes | 61 -.1526351 .1614268 1.260783 -.4755367 .1702666 ---------+-------------------------------------------------------------------- Combined | 213 -.0396521 .0808757 1.180342 -.1990757 .1197715 ---------+-------------------------------------------------------------------- diff | .1583249 .1863445 -.2112861 .5279359 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = 0.8496 H0: diff = 0 Satterthwaite's degrees of freedom = 102.056 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.8012 Pr(|T| > |t|) = 0.3975 Pr(T > t) = 0.1988 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.0259087 .0737726 .9095302 -.1716686 .1198512 yes | 61 -.0543031 .151281 1.181542 -.3569102 .2483039 ---------+-------------------------------------------------------------------- Combined | 213 -.0340405 .0679854 .9922142 -.1680544 .0999735 ---------+-------------------------------------------------------------------- diff | .0283944 .1683103 -.3059879 .3627767 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = 0.1687 H0: diff = 0 Satterthwaite's degrees of freedom = 89.9094 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.5668 Pr(|T| > |t|) = 0.8664 Pr(T > t) = 0.4332 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 -.0454369 .0758695 .9353825 -.1953399 .104466 yes | 61 .0531672 .129867 1.014294 -.2066055 .3129398 ---------+-------------------------------------------------------------------- Combined | 213 -.0171982 .0655906 .957263 -.1464915 .1120951 ---------+-------------------------------------------------------------------- diff | -.0986041 .1504049 -.3968908 .1996826 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = -0.6556 H0: diff = 0 Satterthwaite's degrees of freedom = 103.17 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.2568 Pr(|T| > |t|) = 0.5135 Pr(T > t) = 0.7432 Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- no | 152 .0122261 .0671289 .827621 -.1204072 .1448594 yes | 61 -.1816857 .1445498 1.12897 -.4708284 .1074569 ---------+-------------------------------------------------------------------- Combined | 213 -.0433073 .0634057 .9253751 -.1682936 .081679 ---------+-------------------------------------------------------------------- diff | .1939118 .1593767 -.1228634 .5106871 ------------------------------------------------------------------------------ diff = mean(no) - mean(yes) t = 1.2167 H0: diff = 0 Satterthwaite's degrees of freedom = 87.0618 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.8865 Pr(|T| > |t|) = 0.2270 Pr(T > t) = 0.1135 . logit sepsis sco1-sco6 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -108.69433 Iteration 2: log likelihood = -108.11491 Iteration 3: log likelihood = -108.11277 Iteration 4: log likelihood = -108.11277 Logistic regression Number of obs = 213 LR chi2(6) = 38.90 Prob > chi2 = 0.0000 Log likelihood = -108.11277 Pseudo R2 = 0.1525 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- sco1 | .5396573 .123814 4.36 0.000 .2969863 .7823283 sco2 | .4392358 .1345844 3.26 0.001 .1754553 .7030163 sco3 | .3085128 .1455604 2.12 0.034 .0232196 .593806 sco4 | -.0485172 .1645482 -0.29 0.768 -.3710257 .2739912 sco5 | .0911894 .165198 0.55 0.581 -.2325927 .4149715 sco6 | .2045786 .1697519 1.21 0.228 -.1281291 .5372863 _cons | -1.094847 .1782135 -6.14 0.000 -1.444139 -.7455552 ------------------------------------------------------------------------------ . logit sepsis sco1-sco3 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -109.58412 Iteration 2: log likelihood = -109.02695 Iteration 3: log likelihood = -109.02539 Iteration 4: log likelihood = -109.02539 Logistic regression Number of obs = 213 LR chi2(3) = 37.07 Prob > chi2 = 0.0000 Log likelihood = -109.02539 Pseudo R2 = 0.1453 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- sco1 | .5356338 .1229745 4.36 0.000 .2946082 .7766594 sco2 | .4401884 .1343814 3.28 0.001 .1768057 .7035711 sco3 | .3031327 .1452505 2.09 0.037 .018447 .5878185 _cons | -1.089565 .1770145 -6.16 0.000 -1.436507 -.7426225 ------------------------------------------------------------------------------ . logit sepsis sco1-sco2 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -111.92595 Iteration 2: log likelihood = -111.39927 Iteration 3: log likelihood = -111.39815 Iteration 4: log likelihood = -111.39815 Logistic regression Number of obs = 213 LR chi2(2) = 32.33 Prob > chi2 = 0.0000 Log likelihood = -111.39815 Pseudo R2 = 0.1267 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- sco1 | .5269849 .1218987 4.32 0.000 .2880679 .7659019 sco2 | .4419346 .1308304 3.38 0.001 .1855117 .6983575 _cons | -1.086557 .1751577 -6.20 0.000 -1.42986 -.7432543 ------------------------------------------------------------------------------ . logit sepsis scomat1-scomat6 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -108.94862 Iteration 2: log likelihood = -108.31062 Iteration 3: log likelihood = -108.3086 Iteration 4: log likelihood = -108.3086 Logistic regression Number of obs = 213 LR chi2(6) = 38.51 Prob > chi2 = 0.0000 Log likelihood = -108.3086 Pseudo R2 = 0.1509 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- scomat1 | .6675617 .1330421 5.02 0.000 .4068039 .9283195 scomat2 | .4025592 .1443202 2.79 0.005 .1196968 .6854216 scomat3 | -.0644614 .1431169 -0.45 0.652 -.3449654 .2160426 scomat4 | .0003 .1669568 0.00 0.999 -.3269294 .3275294 scomat5 | .1548837 .1716432 0.90 0.367 -.1815307 .4912981 scomat6 | -.1654206 .1702014 -0.97 0.331 -.4990092 .1681681 _cons | -1.055029 .1770475 -5.96 0.000 -1.402036 -.7080225 ------------------------------------------------------------------------------ . logit sepsis scomat1-scomat3 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -109.76602 Iteration 2: log likelihood = -109.19102 Iteration 3: log likelihood = -109.18951 Iteration 4: log likelihood = -109.18951 Logistic regression Number of obs = 213 LR chi2(3) = 36.75 Prob > chi2 = 0.0000 Log likelihood = -109.18951 Pseudo R2 = 0.1440 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- scomat1 | .6622029 .1318271 5.02 0.000 .4038266 .9205792 scomat2 | .4176903 .1456581 2.87 0.004 .1322057 .7031749 scomat3 | -.0592413 .1413369 -0.42 0.675 -.3362566 .2177739 _cons | -1.040415 .1749272 -5.95 0.000 -1.383266 -.6975643 ------------------------------------------------------------------------------ . logit sepsis scomat1-scomat2 Iteration 0: log likelihood = -127.56209 Iteration 1: log likelihood = -109.82172 Iteration 2: log likelihood = -109.27859 Iteration 3: log likelihood = -109.27734 Iteration 4: log likelihood = -109.27734 Logistic regression Number of obs = 213 LR chi2(2) = 36.57 Prob > chi2 = 0.0000 Log likelihood = -109.27734 Pseudo R2 = 0.1433 ------------------------------------------------------------------------------ sepsis | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- scomat1 | .6624942 .1316674 5.03 0.000 .4044308 .9205576 scomat2 | .4274262 .144854 2.95 0.003 .1435175 .7113348 _cons | -1.033279 .1737881 -5.95 0.000 -1.373898 -.692661 ------------------------------------------------------------------------------ . . * factor analysis . factormat polycorr, n(213) pcf (obs=213) Factor analysis/correlation Number of obs = 213 Method: principal-component factors Retained factors = 4 Rotation: (unrotated) Number of params = 38 -------------------------------------------------------------------------- Factor | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Factor1 | 2.48325 0.34184 0.2257 0.2257 Factor2 | 2.14140 0.63692 0.1947 0.4204 Factor3 | 1.50448 0.48927 0.1368 0.5572 Factor4 | 1.01521 0.10049 0.0923 0.6495 Factor5 | 0.91472 0.08209 0.0832 0.7326 Factor6 | 0.83263 0.15561 0.0757 0.8083 Factor7 | 0.67702 0.06140 0.0615 0.8699 Factor8 | 0.61562 0.12050 0.0560 0.9259 Factor9 | 0.49512 0.24038 0.0450 0.9709 Factor10 | 0.25475 0.18897 0.0232 0.9940 Factor11 | 0.06578 . 0.0060 1.0000 -------------------------------------------------------------------------- LR test: independent vs. saturated: chi2(55) = 801.64 Prob>chi2 = 0.0000 Factor loadings (pattern matrix) and unique variances --------------------------------------------------------------------- Variable | Factor1 Factor2 Factor3 Factor4 | Uniqueness -------------+----------------------------------------+-------------- age | -0.1766 -0.1376 0.6499 -0.1222 | 0.5125 sex | -0.0884 0.3670 0.3796 0.5433 | 0.4183 attd | 0.9109 0.0182 -0.0324 0.1340 | 0.1509 dehy | 0.5854 -0.2808 -0.1091 -0.3218 | 0.4630 eye | 0.2437 0.7489 0.3433 0.1154 | 0.2486 jnts | 0.1652 0.7351 0.2083 -0.4483 | 0.1879 post | 0.9338 0.0444 0.0127 0.1332 | 0.1081 pulse | -0.1468 0.4398 -0.4331 -0.4396 | 0.4042 resp | 0.1764 0.2400 -0.6820 0.3331 | 0.3352 temp | -0.4979 0.4661 -0.3314 0.1991 | 0.3853 umb | 0.1117 0.5807 0.0309 -0.0881 | 0.6416 --------------------------------------------------------------------- . loadingplot . rotate, varimax Factor analysis/correlation Number of obs = 213 Method: principal-component factors Retained factors = 4 Rotation: orthogonal varimax (Kaiser off) Number of params = 38 -------------------------------------------------------------------------- Factor | Variance Difference Proportion Cumulative -------------+------------------------------------------------------------ Factor1 | 2.45570 0.59006 0.2232 0.2232 Factor2 | 1.86563 0.33343 0.1696 0.3928 Factor3 | 1.53220 0.24139 0.1393 0.5321 Factor4 | 1.29081 . 0.1173 0.6495 -------------------------------------------------------------------------- LR test: independent vs. saturated: chi2(55) = 801.64 Prob>chi2 = 0.0000 Rotated factor loadings (pattern matrix) and unique variances --------------------------------------------------------------------- Variable | Factor1 Factor2 Factor3 Factor4 | Uniqueness -------------+----------------------------------------+-------------- age | -0.1523 0.0279 -0.6623 0.1576 | 0.5125 sex | -0.0313 0.1012 -0.0285 0.7548 | 0.4183 attd | 0.9142 0.0574 0.0993 0.0163 | 0.1509 dehy | 0.5549 -0.0293 -0.0948 -0.4682 | 0.4630 eye | 0.2109 0.6679 0.0060 0.5107 | 0.2486 jnts | 0.0571 0.8969 -0.0659 -0.0003 | 0.1879 post | 0.9365 0.0902 0.0692 0.0438 | 0.1081 pulse | -0.2534 0.4970 0.3883 -0.3657 | 0.4042 resp | 0.1695 -0.0481 0.7953 0.0363 | 0.3352 temp | -0.5169 0.1841 0.5085 0.2347 | 0.3853 umb | 0.0548 0.5554 0.1514 0.1548 | 0.6416 --------------------------------------------------------------------- Factor rotation matrix -------------------------------------------------- | Factor1 Factor2 Factor3 Factor4 -------------+------------------------------------ Factor1 | 0.9879 0.1230 0.0228 -0.0918 Factor2 | -0.0785 0.8506 0.3525 0.3822 Factor3 | 0.0414 0.1654 -0.8770 0.4493 Factor4 | 0.1272 -0.4837 0.3258 0.8023 -------------------------------------------------- . loadingplot . . * sparrow data revisited for factor analysis . import delimited sparrow.csv, clear (encoding automatically selected: ISO-8859-1) (6 vars, 49 obs) . factor total_length-l_keel_sternum, pcf /* only one factor */ (obs=49) Factor analysis/correlation Number of obs = 49 Method: principal-component factors Retained factors = 1 Rotation: (unrotated) Number of params = 5 -------------------------------------------------------------------------- Factor | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Factor1 | 3.61598 3.08447 0.7232 0.7232 Factor2 | 0.53150 0.14508 0.1063 0.8295 Factor3 | 0.38642 0.08486 0.0773 0.9068 Factor4 | 0.30157 0.13704 0.0603 0.9671 Factor5 | 0.16453 . 0.0329 1.0000 -------------------------------------------------------------------------- LR test: independent vs. saturated: chi2(10) = 153.49 Prob>chi2 = 0.0000 Factor loadings (pattern matrix) and unique variances --------------------------------------- Variable | Factor1 | Uniqueness -------------+----------+-------------- total_length | 0.8591 | 0.2619 alar_extent | 0.8779 | 0.2293 l_beak_head | 0.8567 | 0.2660 l_humerous | 0.8951 | 0.1987 l_keel_ste~m | 0.7562 | 0.4281 --------------------------------------- . factor total_length-l_keel_sternum, pcf mineigen(0.5) (obs=49) Factor analysis/correlation Number of obs = 49 Method: principal-component factors Retained factors = 2 Rotation: (unrotated) Number of params = 9 -------------------------------------------------------------------------- Factor | Eigenvalue Difference Proportion Cumulative -------------+------------------------------------------------------------ Factor1 | 3.61598 3.08447 0.7232 0.7232 Factor2 | 0.53150 0.14508 0.1063 0.8295 Factor3 | 0.38642 0.08486 0.0773 0.9068 Factor4 | 0.30157 0.13704 0.0603 0.9671 Factor5 | 0.16453 . 0.0329 1.0000 -------------------------------------------------------------------------- LR test: independent vs. saturated: chi2(10) = 153.49 Prob>chi2 = 0.0000 Factor loadings (pattern matrix) and unique variances ------------------------------------------------- Variable | Factor1 Factor2 | Uniqueness -------------+--------------------+-------------- total_length | 0.8591 0.0370 | 0.2605 alar_extent | 0.8779 -0.2184 | 0.1816 l_beak_head | 0.8567 -0.2366 | 0.2100 l_humerous | 0.8951 -0.1346 | 0.1806 l_keel_ste~m | 0.7562 0.6390 | 0.0198 ------------------------------------------------- . end of do-file