. do "C:\Users\hstryhn\AppData\Local\Temp\STD3c8_000000.tmp"

. * do-file for lecture 10 of VHM 802, Winter 2024
. version 18 /* works also with versions 14-17 */

. set more off

. set scheme stcolor_alt

. 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% con f. 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% con f. 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       s14       s15       s16       s17       s18       s19       s20       s21       s22       s23       s24
---------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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  3.588235  3.176471         3  2.941176  2.823529  2.764706  2.705882  2.647059  2.647059  2.470588  2.411765
Min   |         0         0         0         0         0         0         0         0         0         0         0         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        10        15        18        16         9        12         9         9        10        16         8
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  3.985267  5.126345  5.689903  5.018349  3.339822  4.008264  2.931823  3.081014  3.444945  4.638395  2.895229
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  15.88235  26.27941    32.375  25.18382  11.15441  16.06618  8.595588  9.492647  11.86765  21.51471  8.382353
---------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

   Stats |       s25
---------+----------
Mean   |  2.411765
Min   |         0
Max   |        19
SD   |  5.579637
Variance   |  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    Comp10    Comp11    Comp12    Comp13    Comp14    Comp15    Comp16   | Unexplained
    -------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------
    s1   |  -0.2984      0.0048     -0.0653     -0.2825     -0.0472     -0.0449      0.0023      0.1522      0.0422     -0.2297      0.0297     -0.1433      0.0057      0.1227      0.1378      0.3413   |           0
    s2   |   0.2499      0.0176     -0.1849      0.2426      0.1190     -0.2435     -0.0298      0.4761     -0.0501      0.1380     -0.1206     -0.0960     -0.0455      0.1203     -0.2622      0.1699   |           0
    s3   |   0.2008      0.2026     -0.1933      0.1048     -0.0931      0.4313      0.1706      0.0939      0.1062     -0.0028     -0.1654     -0.0838     -0.0841      0.1289      0.3940      0.1590   |           0
    s4   |  -0.1730      0.2432      0.0068      0.0271      0.0698      0.4728      0.3278      0.0534     -0.2510      0.0039     -0.0818      0.1530     -0.1031     -0.1439     -0.1000      0.1298   |           0
    s5   |   0.1077     -0.3159     -0.0723      0.3085      0.0426      0.1811     -0.1457      0.1591      0.3219      0.0617      0.2677     -0.0428      0.0212      0.2524     -0.1464     -0.0883   |           0
    s6   |   0.0813     -0.3122      0.0179      0.2645      0.0978      0.0649      0.3008      0.4140      0.1248     -0.3116      0.0824      0.0795      0.1659     -0.2130      0.3129      0.0377   |           0
    s7   |   0.1139      0.3152     -0.1115     -0.0463     -0.2338     -0.0393      0.3090     -0.0450      0.3580      0.3377     -0.0590     -0.1883      0.2372      0.0155     -0.1041      0.0048   |           0
    s8   |   0.0067      0.3364      0.2274      0.1539      0.0345      0.0158     -0.0877     -0.1021      0.2878     -0.5287     -0.2951      0.0910      0.1592     -0.0096     -0.1252      0.0594   |           0
    s9   |   0.1456      0.3559     -0.0566      0.0695      0.0829     -0.0776     -0.0079      0.0427      0.1190     -0.0896      0.4060      0.1639      0.2252     -0.3766     -0.0139     -0.0913   |           0
    s10   |   0.2342      0.1458      0.1827     -0.0871     -0.3939     -0.0039     -0.0852      0.0190      0.2508      0.0631      0.0162      0.0441      0.0451      0.2195      0.0613     -0.0424   |           0
    s11   |   0.2550     -0.1110      0.1681     -0.0855      0.2218      0.2684     -0.0789     -0.2713      0.2808      0.2053      0.1611      0.0030     -0.0755     -0.0483      0.2233      0.0654   |           0
    s12   |  -0.1298      0.2433      0.2261      0.2504      0.3127      0.1271     -0.1109     -0.0360      0.0329      0.0263      0.2661     -0.4371     -0.2870     -0.1885     -0.0728     -0.0876   |           0
    s13   |   0.0492      0.1170     -0.4448     -0.0450      0.2837     -0.3404      0.1320     -0.1939      0.1322      0.0692      0.0355      0.1233     -0.0501     -0.1909      0.1298     -0.0760   |           0
    s14   |  -0.2807      0.0928      0.0034     -0.1398      0.1552     -0.3003      0.0189      0.1035      0.3583     -0.0926      0.1336      0.1412     -0.1736      0.1664      0.2419      0.2104   |           0
    s15   |  -0.2661      0.1052      0.2553      0.1330      0.1757     -0.0590     -0.0185      0.0424      0.1655     -0.0304     -0.1046     -0.2388      0.1209      0.2735     -0.0680     -0.1104   |           0
    s16   |   0.0267      0.2269      0.1923      0.3268     -0.3751     -0.2106      0.1834     -0.0004     -0.2362     -0.0452      0.4193      0.2391     -0.3099      0.2048      0.0562      0.0326   |           0
    s17   |  -0.2707     -0.0209      0.0477     -0.3216     -0.0962      0.1741      0.0812      0.1999     -0.0222      0.0999      0.4668     -0.0846      0.4132      0.0006     -0.1014      0.0297   |           0
    s18   |   0.2026     -0.1791      0.2872     -0.1034      0.1703     -0.0121      0.3216     -0.1036      0.0832     -0.0815     -0.0157      0.3166      0.1239      0.0048     -0.4556      0.1210   |           0
    s19   |   0.1471      0.2571     -0.1904     -0.1717      0.3259      0.0358      0.2491      0.1610     -0.1325     -0.0665      0.0588     -0.1522     -0.0272      0.3618     -0.1849     -0.1084   |           0
    s20   |   0.2057      0.1767      0.0702     -0.1947      0.3393      0.1376     -0.3209      0.0764     -0.1651      0.0234      0.1047      0.3886      0.0667      0.3557      0.1620     -0.0025   |           0
    s21   |   0.2347      0.1646      0.1077     -0.1817     -0.0909     -0.0208     -0.4061      0.3399     -0.0340      0.0477     -0.0373     -0.0764     -0.0608     -0.3643     -0.1076      0.3666   |           0
    s22   |   0.2133      0.0274      0.3352     -0.2637      0.0102     -0.1656      0.1426      0.2659     -0.1360     -0.0665     -0.1205     -0.1724      0.0224     -0.0806      0.2874     -0.5566   |           0
    s23   |  -0.2878      0.0259      0.0966     -0.1147     -0.0004      0.1075      0.0424      0.3534      0.3218      0.3103     -0.1740      0.3759     -0.3949     -0.1346     -0.1252     -0.2470   |           0
    s24   |   0.1800     -0.1203      0.3641     -0.1210      0.1476     -0.1896      0.3265     -0.0824     -0.0077      0.1671      0.0226     -0.1893     -0.1918     -0.0109      0.0833      0.4041   |           0
    s25   |  -0.2056      0.1123      0.2161      0.3439      0.1671     -0.1272     -0.0366      0.0421     -0.1724      0.4584     -0.1857      0.1564      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    Comp10    Comp11    Comp12    Comp13    Comp14    Comp15    Comp16
    -------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------
    s1   |  -0.2984      0.0048     -0.0653     -0.2825     -0.0472     -0.0449      0.0023      0.1522      0.0422     -0.2297      0.0297     -0.1433      0.0057      0.1227      0.1378      0.3413
    s2   |   0.2499      0.0176     -0.1849      0.2426      0.1190     -0.2435     -0.0298      0.4761     -0.0501      0.1380     -0.1206     -0.0960     -0.0455      0.1203     -0.2622      0.1699
    s3   |   0.2008      0.2026     -0.1933      0.1048     -0.0931      0.4313      0.1706      0.0939      0.1062     -0.0028     -0.1654     -0.0838     -0.0841      0.1289      0.3940      0.1590
    s4   |  -0.1730      0.2432      0.0068      0.0271      0.0698      0.4728      0.3278      0.0534     -0.2510      0.0039     -0.0818      0.1530     -0.1031     -0.1439     -0.1000      0.1298
    s5   |   0.1077     -0.3159     -0.0723      0.3085      0.0426      0.1811     -0.1457      0.1591      0.3219      0.0617      0.2677     -0.0428      0.0212      0.2524     -0.1464     -0.0883
    s6   |   0.0813     -0.3122      0.0179      0.2645      0.0978      0.0649      0.3008      0.4140      0.1248     -0.3116      0.0824      0.0795      0.1659     -0.2130      0.3129      0.0377
    s7   |   0.1139      0.3152     -0.1115     -0.0463     -0.2338     -0.0393      0.3090     -0.0450      0.3580      0.3377     -0.0590     -0.1883      0.2372      0.0155     -0.1041      0.0048
    s8   |   0.0067      0.3364      0.2274      0.1539      0.0345      0.0158     -0.0877     -0.1021      0.2878     -0.5287     -0.2951      0.0910      0.1592     -0.0096     -0.1252      0.0594
    s9   |   0.1456      0.3559     -0.0566      0.0695      0.0829     -0.0776     -0.0079      0.0427      0.1190     -0.0896      0.4060      0.1639      0.2252     -0.3766     -0.0139     -0.0913
    s10   |   0.2342      0.1458      0.1827     -0.0871     -0.3939     -0.0039     -0.0852      0.0190      0.2508      0.0631      0.0162      0.0441      0.0451      0.2195      0.0613     -0.0424
    s11   |   0.2550     -0.1110      0.1681     -0.0855      0.2218      0.2684     -0.0789     -0.2713      0.2808      0.2053      0.1611      0.0030     -0.0755     -0.0483      0.2233      0.0654
    s12   |  -0.1298      0.2433      0.2261      0.2504      0.3127      0.1271     -0.1109     -0.0360      0.0329      0.0263      0.2661     -0.4371     -0.2870     -0.1885     -0.0728     -0.0876
    s13   |   0.0492      0.1170     -0.4448     -0.0450      0.2837     -0.3404      0.1320     -0.1939      0.1322      0.0692      0.0355      0.1233     -0.0501     -0.1909      0.1298     -0.0760
    s14   |  -0.2807      0.0928      0.0034     -0.1398      0.1552     -0.3003      0.0189      0.1035      0.3583     -0.0926      0.1336      0.1412     -0.1736      0.1664      0.2419      0.2104
    s15   |  -0.2661      0.1052      0.2553      0.1330      0.1757     -0.0590     -0.0185      0.0424      0.1655     -0.0304     -0.1046     -0.2388      0.1209      0.2735     -0.0680     -0.1104
    s16   |   0.0267      0.2269      0.1923      0.3268     -0.3751     -0.2106      0.1834     -0.0004     -0.2362     -0.0452      0.4193      0.2391     -0.3099      0.2048      0.0562      0.0326
    s17   |  -0.2707     -0.0209      0.0477     -0.3216     -0.0962      0.1741      0.0812      0.1999     -0.0222      0.0999      0.4668     -0.0846      0.4132      0.0006     -0.1014      0.0297
    s18   |   0.2026     -0.1791      0.2872     -0.1034      0.1703     -0.0121      0.3216     -0.1036      0.0832     -0.0815     -0.0157      0.3166      0.1239      0.0048     -0.4556      0.1210
    s19   |   0.1471      0.2571     -0.1904     -0.1717      0.3259      0.0358      0.2491      0.1610     -0.1325     -0.0665      0.0588     -0.1522     -0.0272      0.3618     -0.1849     -0.1084
    s20   |   0.2057      0.1767      0.0702     -0.1947      0.3393      0.1376     -0.3209      0.0764     -0.1651      0.0234      0.1047      0.3886      0.0667      0.3557      0.1620     -0.0025
    s21   |   0.2347      0.1646      0.1077     -0.1817     -0.0909     -0.0208     -0.4061      0.3399     -0.0340      0.0477     -0.0373     -0.0764     -0.0608     -0.3643     -0.1076      0.3666
    s22   |   0.2133      0.0274      0.3352     -0.2637      0.0102     -0.1656      0.1426      0.2659     -0.1360     -0.0665     -0.1205     -0.1724      0.0224     -0.0806      0.2874     -0.5566
    s23   |  -0.2878      0.0259      0.0966     -0.1147     -0.0004      0.1075      0.0424      0.3534      0.3218      0.3103     -0.1740      0.3759     -0.3949     -0.1346     -0.1252     -0.2470
    s24   |   0.1800     -0.1203      0.3641     -0.1210      0.1476     -0.1896      0.3265     -0.0824     -0.0077      0.1671      0.0226     -0.1893     -0.1918     -0.0109      0.0833      0.4041
    s25   |  -0.2056      0.1123      0.2161      0.3439      0.1671     -0.1272     -0.0366      0.0421     -0.1724      0.4584     -0.1857      0.1564      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
. /* to install the package, use:
> net describe polychoric, from(https://staskolenikov.net/stata)
> net install polychoric
> */
. 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
. drop if missing(age+sex+attd+dehy+eye+jnts+post+pulse+resp+temp+umb+sepsis)==1
(41 observations deleted)

. * restrict dataset to complete observations (without missing values)
. foreach var of varlist age sex-umb {
  2.   egen s`var'=std(`var')
  3.   }

. sort case

. polychoric age sex-umb /* note: results not completely identical to above */

Polychoric correlation matrix

              age         sex        attd        dehy         eye        jnts        post       pulse        resp        temp         umb
  age           1
  sex   .01010373           1
 attd  -.13950976  -.04479291           1
 dehy  -.12612086  -.14575855   .38192896           1
  eye   .04328154   .33056917   .15004459  -.09958976           1
 jnts    .0007256   .04775808   .08356658  -.03035267   .59635231           1
 post  -.09867841  -.06227926   .87386637   .39701107   .32318563   .08395814           1
pulse  -.18651421   .01399805  -.12854908  -.03287323   .07428001    .2535835  -.10637662           1
 resp  -.26418451  -.09671084   .17053345   -.0249882   .03344114  -.00556296   .19301091   .16964738           1
 temp  -.09753186   .06344047    -.338388  -.30588409   .20261028   .07270049  -.37706664   .23121708   .22578032           1
  umb  -.05461964   .15237046   .14517111  -.08483236   .21072786    .3722088   .04435448   .12807892   .08980629   .13150165           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   |      2.48458      .342874             0.2259       0.2259
    Comp2   |       2.1417       .63795             0.1947       0.4206
    Comp3   |      1.50375      .490978             0.1367       0.5573
    Comp4   |      1.01277     .0992471             0.0921       0.6493
    Comp5   |      .913527     .0805611             0.0830       0.7324
    Comp6   |      .832966      .153287             0.0757       0.8081
    Comp7   |      .679678     .0631407             0.0618       0.8699
    Comp8   |      .616538      .120842             0.0560       0.9260
    Comp9   |      .495695      .242187             0.0451       0.9710
    Comp10   |      .253508      .188227             0.0230       0.9941
    Comp11   |     .0652815            .             0.0059       1.0000
    -------------+------------------------------------------------------------

Principal components (eigenvectors)

    -------------+--------------------------------------------------------------------------------------------------------------+-------------
    Variable   | Comp1    Comp2    Comp3    Comp4    Comp5    Comp6    Comp7    Comp8    Comp9    Comp10    Comp11   | Unexplained
    -------------+--------------------------------------------------------------------------------------------------------------+-------------
    age   |  -0.1101     -0.0949      0.5312     -0.1278      0.4912      0.0490      0.5629      0.3375      0.0324      0.0695     -0.0061   |           0
    sex   |  -0.0573      0.2510      0.3077      0.5485     -0.5920      0.0104      0.2792      0.1068      0.1724      0.2361      0.1135   |           0
    attd   |   0.5778      0.0169     -0.0270      0.1316      0.0757     -0.0988      0.0929     -0.0375     -0.3414      0.4624     -0.5402   |           0
    dehy   |   0.3723     -0.1888     -0.0912     -0.3134     -0.3286      0.1162     -0.1019      0.7121      0.2710     -0.0695     -0.0446   |           0
    eye   |   0.1511      0.5140      0.2777      0.1128      0.0930      0.4044     -0.1852      0.0175      0.0017     -0.5345     -0.3614   |           0
    jnts   |   0.1021      0.5027      0.1691     -0.4464      0.0873      0.0760     -0.2209     -0.1648      0.3391      0.5128      0.2041   |           0
    post   |   0.5923      0.0348      0.0096      0.1307      0.1197      0.1256      0.1098     -0.0670     -0.2537     -0.1661      0.7015   |           0
    pulse   |  -0.0941      0.2972     -0.3550     -0.4316     -0.3025      0.2072      0.6037     -0.1061     -0.2638     -0.0876     -0.0562   |           0
    resp   |   0.1081      0.1641     -0.5569      0.3286      0.3646      0.0216      0.2717      0.0407      0.5760     -0.0082     -0.0514   |           0
    temp   |  -0.3207      0.3178     -0.2675      0.1901      0.1983      0.1505     -0.2273      0.5387     -0.4423      0.2577      0.1505   |           0
    umb   |   0.0682      0.3972      0.0257     -0.0889      0.0077     -0.8504      0.0333      0.1766     -0.0536     -0.2652      0.0194   |           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(smcircle_hollow)), ytitle(2nd principal component) xtitle(1st principal component) title(Polychoric PCA (x=no sepsis, o=sepsis), size(medium)) legend(off)

. drop __POLY* /* two variables created by polychoric with unclear use */

.
. 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    Comp10    Comp11   | Unexplained
    -------------+--------------------------------------------------------------------------------------------------------------+-------------
    age   |  -0.0952     -0.4431      0.3102     -0.0506      0.1656      0.3516      0.6483      0.1790      0.2882     -0.0798      0.0534   |           0
    sex   |  -0.0973      0.0219      0.3256      0.7102     -0.1504     -0.4916      0.1574     -0.1972      0.1971     -0.1131      0.0096   |           0
    attd   |   0.5363      0.1414      0.0534      0.1835      0.0699      0.1255      0.1354     -0.0686     -0.0703      0.4719      0.6201   |           0
    dehy   |   0.4308     -0.0289     -0.1336     -0.2059     -0.3052     -0.2640     -0.0995      0.3691      0.6485     -0.1481      0.0431   |           0
    eye   |   0.0242      0.1907      0.5419     -0.1440      0.5037     -0.2939     -0.1886      0.4842     -0.1547     -0.0904      0.0802   |           0
    jnts   |   0.0093      0.2445      0.5130     -0.4838     -0.1412      0.0249     -0.0343     -0.6049      0.2297     -0.0320      0.0371   |           0
    post   |   0.5576      0.1350      0.0828      0.0855      0.1441      0.0429      0.2150     -0.0639     -0.0825      0.1467     -0.7453   |           0
    pulse   |  -0.1580      0.4427     -0.0781     -0.2397     -0.3818     -0.2586      0.6011      0.2372     -0.2856      0.0517      0.0320   |           0
    resp   |   0.0628      0.5115     -0.2982      0.1280      0.3999      0.1947      0.1740     -0.1321      0.1896     -0.5733      0.1375   |           0
    temp   |  -0.4094      0.3514     -0.0902      0.0668      0.2139      0.0737     -0.0325      0.1097      0.5004      0.5977     -0.1559   |           0
    umb   |  -0.0133      0.2946      0.3319      0.2767     -0.4538      0.5918     -0.2259      0.3130     -0.0332     -0.1301     -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    Comp10    Comp11
    -------------+--------------------------------------------------------------------------------------------------------------
    age   |  -0.0952     -0.4431      0.3102     -0.0506      0.1656      0.3516      0.6483      0.1790      0.2882     -0.0798      0.0534
    sex   |  -0.0973      0.0219      0.3256      0.7102     -0.1504     -0.4916      0.1574     -0.1972      0.1971     -0.1131      0.0096
    attd   |   0.5363      0.1414      0.0534      0.1835      0.0699      0.1255      0.1354     -0.0686     -0.0703      0.4719      0.6201
    dehy   |   0.4308     -0.0289     -0.1336     -0.2059     -0.3052     -0.2640     -0.0995      0.3691      0.6485     -0.1481      0.0431
    eye   |   0.0242      0.1907      0.5419     -0.1440      0.5037     -0.2939     -0.1886      0.4842     -0.1547     -0.0904      0.0802
    jnts   |   0.0093      0.2445      0.5130     -0.4838     -0.1412      0.0249     -0.0343     -0.6049      0.2297     -0.0320      0.0371
    post   |   0.5576      0.1350      0.0828      0.0855      0.1441      0.0429      0.2150     -0.0639     -0.0825      0.1467     -0.7453
    pulse   |  -0.1580      0.4427     -0.0781     -0.2397     -0.3818     -0.2586      0.6011      0.2372     -0.2856      0.0517      0.0320
    resp   |   0.0628      0.5115     -0.2982      0.1280      0.3999      0.1947      0.1740     -0.1321      0.1896     -0.5733      0.1375
    temp   |  -0.4094      0.3514     -0.0902      0.0668      0.2139      0.0737     -0.0325      0.1097      0.5004      0.5977     -0.1559
    umb   |  -0.0133      0.2946      0.3319      0.2767     -0.4538      0.5918     -0.2259      0.3130     -0.0332     -0.1301     -0.0556
    -------------+--------------------------------------------------------------------------------------------------------------

. list sco1-sco5 scomat1-scomat5 in 1/5

     +-----------------------------------------------------------------------------------------------------------------------+
     |      sco1        sco2        sco3        sco4        sco5     scomat1     scomat2     scomat3     scomat4     scomat5 |
     +-----------------------------------------------------------------------------------------------------------------------+
  1. |  -2.44531   -.8043134   -.7452768   -.8335332    .3806761   -2.610665   -.4952926   -.1272509   -.2516125    .4102666 |
  2. |  .5995948   -1.179423   -.3471844   -1.023328   -.1128355    .3270429   -1.216479    .4410701   -1.056379    .3552441 |
  3. | -1.182303   -.7322186   -.4973935   -.8034819    .1122511   -1.308873   -.5795658    .0396257   -.6177249    .4194184 |
  4. |  .4215459   -2.548945    .9689444    .7864367    .0941712    .0930695   -1.340782    2.476868    .5437759   -.2081751 |
  5. |  1.893089   -1.843985    1.772735    1.865979   -.6890295    1.749807   -.7147474    2.585642    .7578143    .0399886 |
     +-----------------------------------------------------------------------------------------------------------------------+

. list age sex-umb in 1/5

     +-------------------------------------------------------------------------------------+
     | age      sex        attd   dehy   eye   jnts       post   pulse   resp   temp   umb |
     +-------------------------------------------------------------------------------------+
  1. |   6   female      bright    3.0    no      0   standing     100     20   40.0    no |
  2. |  14   female   depressed    9.0    no      0    sternal     120     28   36.5    no |
  3. |  10   female   depressed    4.5    no      0   standing     120     20   39.0    no |
  4. |  17     male   depressed    5.0    no      0    sternal      80     16   35.0    no |
  5. |  17     male    comatose    7.0    no      0    sternal      60     22   34.5   yes |
     +-------------------------------------------------------------------------------------+

. 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), size(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   scomat5   scomat6
-------+------------------------------------------------------------------------------------------------------------------------
no   | -.2813099 -.1836713 -.1133812   .013458  -.027279 -.0472951 -.3212777 -.1427129  .0403154  .0026226 -.0330248  .0438504
       |  .1206508  .0919026  .0729616  .0752472  .0710346  .0697055  .1169062  .0748924  .0947006  .0742237  .0763126  .0680037
-------+------------------------------------------------------------------------------------------------------------------------
yes   |  .7009691  .4576728  .2825236 -.0335347  .0679738  .1178502  .8005608  .3556125 -.1004579 -.0065351  .0822913 -.1092667
       |  .1582304  .1940434  .2029532   .154961  .1489091  .1500943  .1576926  .2253974   .167468  .1523248  .1309676  .1544467
-------+------------------------------------------------------------------------------------------------------------------------
Total   | -1.08e-09 -7.00e-11  2.37e-09  2.82e-09 -1.33e-09  1.42e-10 -8.50e-09  9.13e-09  6.93e-09  3.46e-09  3.95e-09 -9.13e-09
       |  .1017758   .087985  .0787111  .0694723  .0661116  .0657414  .1008735  .0849003  .0827686  .0684174  .0660538  .0656244
-------+------------------------------------------------------------------------------------------------------------------------

. 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   -.3212777    .1169062    1.441316   -.5522608   -.0902946
     yes |      61    .8005608    .1576926    1.231619    .4851286    1.115993
---------+--------------------------------------------------------------------
Combined |     213   -8.50e-09    .1008735    1.472201   -.1988436    .1988436
---------+--------------------------------------------------------------------
    diff |           -1.121838    .1963008               -1.510235   -.7334421
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =  -5.7149
H0: diff = 0                     Satterthwaite's degrees of freedom =  128.637

    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   -.1427129    .0748924    .9233357   -.2906852    .0052595
     yes |      61    .3556125    .2253974     1.76041   -.0952494    .8064744
---------+--------------------------------------------------------------------
Combined |     213    9.13e-09    .0849003    1.239079   -.1673569    .1673569
---------+--------------------------------------------------------------------
    diff |           -.4983254    .2375139               -.9716224   -.0250283
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =  -2.0981
H0: diff = 0                     Satterthwaite's degrees of freedom =   73.623

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0197         Pr(|T| > |t|) = 0.0393          Pr(T > t) = 0.9803

Two-sample t test with unequal variances
---------+--------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
      no |     152    .0403154    .0947006    1.167548   -.1467941    .2274248
     yes |      61   -.1004579     .167468    1.307967   -.4354438     .234528
---------+--------------------------------------------------------------------
Combined |     213    6.93e-09    .0827686    1.207968   -.1631549    .1631549
---------+--------------------------------------------------------------------
    diff |            .1407733    .1923896               -.2409022    .5224488
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =   0.7317
H0: diff = 0                     Satterthwaite's degrees of freedom =  100.428

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.7670         Pr(|T| > |t|) = 0.4660          Pr(T > t) = 0.2330

Two-sample t test with unequal variances
---------+--------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
      no |     152    .0026226    .0742237    .9150917   -.1440285    .1492738
     yes |      61   -.0065351    .1523248    1.189695     -.31123    .2981599
---------+--------------------------------------------------------------------
Combined |     213    3.46e-09    .0684174    .9985186   -.1348655    .1348655
---------+--------------------------------------------------------------------
    diff |            .0091577    .1694462               -.3274838    .3457992
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =   0.0540
H0: diff = 0                     Satterthwaite's degrees of freedom =  89.8617

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.5215         Pr(|T| > |t|) = 0.9570          Pr(T > t) = 0.4785

Two-sample t test with unequal variances
---------+--------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
      no |     152   -.0330248    .0763126    .9408445   -.1838031    .1177535
     yes |      61    .0822913    .1309676     1.02289    -.179683    .3442655
---------+--------------------------------------------------------------------
Combined |     213    3.95e-09    .0660538    .9640239   -.1302064    .1302064
---------+--------------------------------------------------------------------
    diff |            -.115316    .1515788               -.4159388    .1853067
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =  -0.7608
H0: diff = 0                     Satterthwaite's degrees of freedom =  102.943

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.2243         Pr(|T| > |t|) = 0.4485          Pr(T > t) = 0.7757

Two-sample t test with unequal variances
---------+--------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
      no |     152    .0438504    .0680037    .8384065   -.0905113    .1782121
     yes |      61   -.1092667    .1544467    1.206267   -.4182061    .1996728
---------+--------------------------------------------------------------------
Combined |     213   -9.13e-09    .0656244    .9577568     -.12936    .1293599
---------+--------------------------------------------------------------------
    diff |            .1531171    .1687551               -.1824559      .48869
---------+--------------------------------------------------------------------
    diff = mean(no) - mean(yes)                                   t =   0.9073
H0: diff = 0                     Satterthwaite's degrees of freedom =   84.261

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.8166         Pr(|T| > |t|) = 0.3668          Pr(T > t) = 0.1834

. 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% con f. 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% con f. 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% con f. 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 = -108.75811
Iteration 2:  Log likelihood = -108.13007
Iteration 3:  Log likelihood = -108.12793
Iteration 4:  Log likelihood = -108.12793

 Logistic regression                                    Number of obs    = 213
                                                        LR chi2(6)    = 38.87
                                                        Prob > chi2    = 0.0000
 Log likelihood    = -108.12793                         Pseudo R2     = 0.1524

-------------+----------------------------------------------------------------
       sepsis | Coefficient   Std. err.       z    P>|z|      [95% con f. interval]
-------------+----------------------------------------------------------------
     scomat1 |    .6476041    .1298367      4.99    0.000      .3931289     .9020794
     scomat2 |      .38853    .1351751      2.87    0.004      .1235916     .6534683
     scomat3 |   -.0755895    .1378584     -0.55    0.583      -.345787     .1946081
     scomat4 |   -.0084634    .1651533     -0.05    0.959     -.3321579     .3152311
     scomat5 |    .1518494    .1703247      0.89    0.373     -.1819808     .4856796
     scomat6 |   -.1815719    .1627748     -1.12    0.265     -.5006047     .1374609
       _cons |   -1.100297    .1783789     -6.17    0.000     -1.449913    -.7506807
-------------+----------------------------------------------------------------

. logit sepsis scomat1-scomat3

Iteration 0:  Log likelihood = -127.56209
Iteration 1:  Log likelihood = -109.66913
Iteration 2:  Log likelihood = -109.12697
Iteration 3:  Log likelihood = -109.12551
Iteration 4:  Log likelihood = -109.12551

 Logistic regression                                    Number of obs    = 213
                                                        LR chi2(3)    = 36.87
                                                        Prob > chi2    = 0.0000
 Log likelihood    = -109.12551                         Pseudo R2     = 0.1445

-------------+----------------------------------------------------------------
       sepsis | Coefficient   Std. err.       z    P>|z|      [95% con f. interval]
-------------+----------------------------------------------------------------
     scomat1 |    .6390479    .1284708      4.97    0.000      .3872497      .890846
     scomat2 |    .3932847    .1395737      2.82    0.005      .1197252     .6668442
     scomat3 |   -.0754824    .1374788     -0.55    0.583     -.3449359     .1939711
       _cons |   -1.087493    .1767718     -6.15    0.000      -1.43396     -.741027
-------------+----------------------------------------------------------------

. logit sepsis scomat1-scomat2

Iteration 0:  Log likelihood = -127.56209
Iteration 1:  Log likelihood = -109.77408
Iteration 2:  Log likelihood = -109.27714
Iteration 3:  Log likelihood = -109.27603
Iteration 4:  Log likelihood = -109.27603

 Logistic regression                                    Number of obs    = 213
                                                        LR chi2(2)    = 36.57
                                                        Prob > chi2    = 0.0000
 Log likelihood    = -109.27603                         Pseudo R2     = 0.1434

-------------+----------------------------------------------------------------
       sepsis | Coefficient   Std. err.       z    P>|z|      [95% con f. interval]
-------------+----------------------------------------------------------------
     scomat1 |    .6381828    .1282141      4.98    0.000      .3868877     .8894778
     scomat2 |    .4023098    .1405466      2.86    0.004      .1268436      .677776
       _cons |   -1.080515    .1758392     -6.14    0.000     -1.425154    -.7358767
-------------+----------------------------------------------------------------

.
. * technical, for demonstration purposes
. polychoricpca age sex-umb, score(polysco) nscore(6) /* same as with pcamat above */

Polychoric correlation matrix

              age         sex        attd        dehy         eye        jnts        post       pulse        resp        temp         umb
  age           1
  sex   .01010373           1
 attd  -.13950976  -.04479291           1
 dehy  -.12612086  -.14575855   .38192896           1
  eye   .04328154   .33056917   .15004459  -.09958976           1
 jnts    .0007256   .04775808   .08356658  -.03035267   .59635231           1
 post  -.09867841  -.06227926   .87386637   .39701107   .32318563   .08395814           1
pulse  -.18651421   .01399805  -.12854908  -.03287323   .07428001    .2535835  -.10637662           1
 resp  -.26418451  -.09671084   .17053345   -.0249882   .03344114  -.00556296   .19301091   .16964738           1
 temp  -.09753186   .06344047    -.338388  -.30588409   .20261028   .07270049  -.37706664   .23121708   .22578032           1
  umb  -.05461964   .15237046   .14517111  -.08483236   .21072786    .3722088   .04435448   .12807892   .08980629   .13150165           1

Principal component analysis

 k  |  Eigenvalues  |  Proportion explained  |  Cum. explained
----+---------------+------------------------+------------------
  1 |    2.484577   |    0.225871            |   0.225871
  2 |    2.141703   |    0.194700            |   0.420571
  3 |    1.503753   |    0.136705            |   0.557276
  4 |    1.012774   |    0.092070            |   0.649346
  5 |    0.913527   |    0.083048            |   0.732394
  6 |    0.832966   |    0.075724            |   0.808118
  7 |    0.679678   |    0.061789            |   0.869907
  8 |    0.616538   |    0.056049            |   0.925956
  9 |    0.495695   |    0.045063            |   0.971019
  10 |    0.253508  |    0.023046            |   0.994065
  11 |    0.065282  |    0.005935            |   1.000000

               Scoring coefficients

    Variable    |  Coeff. 1  |  Coeff. 2  |  Coeff. 3
------------------------------------------------------
 age            | -0.110078  | -0.094856  |  0.531185
 sex
             0  |  0.046860  | -0.205252  | -0.251615
             1  | -0.044290  |  0.193995  |  0.237815
 attd
             0  | -0.994278  | -0.029053  |  0.046519
             1  | -0.057320  | -0.001675  |  0.002682
             2  |  0.854373  |  0.024965  | -0.039973
 dehy           |  0.372261  | -0.188823  | -0.091168
 eye
             0  | -0.009056  | -0.030814  | -0.016649
             1  |  0.347813  |  1.183493  |  0.639463
 jnts
             0  | -0.021443  | -0.105577  | -0.035524
             1  |  0.155110  |  0.763688  |  0.256961
             2  |  0.219958  |  1.082969  |  0.364391
             4  |  0.278263  |  1.370035  |  0.460981
 post
             0  | -0.593876  | -0.034851  | -0.009615
             1  |  0.090762  |  0.005326  |  0.001469
             2  |  0.735721  |  0.043175  |  0.011912
 pulse          | -0.094149  |  0.297249  | -0.354982
 resp           |  0.108061  |  0.164079  | -0.556871
 temp           | -0.320655  |  0.317770  | -0.267468
 umb
             0  | -0.026983  | -0.157247  | -0.010162
             1  |  0.089250  |  0.520126  |  0.033611

. * _tt variables with latent variables values used for score coefficients in table (latent variable*eigenvalue)
. * method behind construction of latent variables not documented, appears to be quite ad-hoc
.
. * 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    |      2.48458      0.34287            0.2259       0.2259
    Factor2    |      2.14170      0.63795            0.1947       0.4206
    Factor3    |      1.50375      0.49098            0.1367       0.5573
    Factor4    |      1.01277      0.09925            0.0921       0.6493
    Factor5    |      0.91353      0.08056            0.0830       0.7324
    Factor6    |      0.83297      0.15329            0.0757       0.8081
    Factor7    |      0.67968      0.06314            0.0618       0.8699
    Factor8    |      0.61654      0.12084            0.0560       0.9260
    Factor9    |      0.49570      0.24219            0.0451       0.9710
    Factor10    |      0.25351      0.18823            0.0230       0.9941
    Factor11    |      0.06528            .            0.0059       1.0000
    -------------+------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(55) =  803.52 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -------------+----------------------------------------+--------------
    Variable   | Factor1    Factor2    Factor3    Factor4   | Uniqueness
    -------------+----------------------------------------+--------------
    age   |  -0.1735     -0.1388      0.6514     -0.1286   |     0.5098
    sex   |  -0.0903      0.3673      0.3773      0.5519   |     0.4100
    attd   |   0.9108      0.0247     -0.0332      0.1324   |     0.1512
    dehy   |   0.5868     -0.2763     -0.1118     -0.3154   |     0.4674
    eye   |   0.2381      0.7522      0.3406      0.1135   |     0.2486
    jnts   |   0.1609      0.7356      0.2074     -0.4493   |     0.1881
    post   |   0.9337      0.0509      0.0118      0.1315   |     0.1082
    pulse   |  -0.1484      0.4350     -0.4353     -0.4343   |     0.4106
    resp   |   0.1703      0.2401     -0.6829      0.3307   |     0.3377
    temp   |  -0.5054      0.4650     -0.3280      0.1913   |     0.3841
    umb   |   0.1074      0.5812      0.0315     -0.0895   |     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    |      2.45781      0.58988            0.2234       0.2234
    Factor2    |      1.86793      0.33618            0.1698       0.3932
    Factor3    |      1.53175      0.24642            0.1392       0.5325
    Factor4    |      1.28533            .            0.1168       0.6493
    -------------+------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(55) =  803.52 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -------------+----------------------------------------+--------------
    Variable   | Factor1    Factor2    Factor3    Factor4   | Uniqueness
    -------------+----------------------------------------+--------------
    age   |  -0.1513      0.0319     -0.6662      0.1500   |     0.5098
    sex   |  -0.0318      0.1004     -0.0260      0.7604   |     0.4100
    attd   |   0.9138      0.0595      0.0995      0.0171   |     0.1512
    dehy   |   0.5562     -0.0335     -0.0885     -0.4629   |     0.4674
    eye   |   0.2078      0.6720      0.0067      0.5066   |     0.2486
    jnts   |   0.0565      0.8969     -0.0655     -0.0053   |     0.1881
    post   |   0.9362      0.0924      0.0694      0.0443   |     0.1082
    pulse   |  -0.2509      0.4893      0.3920     -0.3651   |     0.4106
    resp   |   0.1649     -0.0482      0.7946      0.0374   |     0.3377
    temp   |  -0.5230      0.1901      0.5028      0.2310   |     0.3841
    umb   |   0.0533      0.5566      0.1499      0.1525   |     0.6416
    -------------+----------------------------------------+--------------

Factor rotation matrix

    -------------+------------------------------------
       | Factor1    Factor2    Factor3    Factor4
    -------------+------------------------------------
    Factor1   |  0.9885     0.1181     0.0208    -0.0923
    Factor2   | -0.0738     0.8527     0.3514     0.3794
    Factor3   |  0.0401     0.1672    -0.8785     0.4457
    Factor4   |  0.1259    -0.4806     0.3229     0.8056
    -------------+------------------------------------

. 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
    -------------+--------------------+--------------

. rotate, varimax normalize

Factor analysis/correlation                      Number of obs    =         49
    Method: principal-component factors          Retained factors =          2
    Rotation: orthogonal varimax (Kaiser on)     Number of params =          9

    -------------+------------------------------------------------------------
         Factor  | Variance     Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
    Factor1    |      2.76996      1.39243            0.5540       0.5540
    Factor2    |      1.37753            .            0.2755       0.8295
    -------------+------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(10) =  153.49 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    -------------+--------------------+--------------
    Variable   | Factor1    Factor2   | Uniqueness
    -------------+--------------------+--------------
    total_length   |   0.7125      0.4814   |     0.2605
    alar_extent   |   0.8623      0.2737   |     0.1816
    l_beak_head   |   0.8538      0.2471   |     0.2100
    l_humerous   |   0.8331      0.3541   |     0.1806
    l_keel_ste~m   |   0.3095      0.9404   |     0.0198
    -------------+--------------------+--------------

Factor rotation matrix

    -------------+------------------
       | Factor1    Factor2
    -------------+------------------
    Factor1   |  0.8519     0.5237
    Factor2   | -0.5237     0.8519
    -------------+------------------

. * normalize option to include Kaiser normalization (default in Minitab)
.
. * added illustration of eigenvalue and eigenvector concepts
. clear

. matrix input a=(9 6\6 16)

. matrix list a

symmetric a[2,2]
    c1  c2
r1   9
r2   6  16

. pcamat a, n(1) names(v1 v2)

Principal components/correlation                 Number of obs    =          1
                                                 Number of comp.  =          2
                                                 Trace             =          2
    Rotation: (unrotated = principal)            Rho              =     1.0000

    -------------+------------------------------------------------------------
       Component |   Eigenvalue   Difference         Proportion   Cumulative
    -------------+------------------------------------------------------------
    Comp1   |          1.5            1             0.7500       0.7500
    Comp2   |           .5            .             0.2500       1.0000
    -------------+------------------------------------------------------------

Principal components (eigenvectors)

    -------------+--------------------+-------------
    Variable   | Comp1    Comp2   | Unexplained
    -------------+--------------------+-------------
    v1   |   0.7071      0.7071   |           0
    v2   |   0.7071     -0.7071   |           0
    -------------+--------------------+-------------

. pcamat a, cov n(1) names(v1 v2)

Principal components/covariance                  Number of obs    =          1
                                                 Number of comp.  =          2
                                                 Trace             =         25
    Rotation: (unrotated = principal)            Rho              =     1.0000

    -------------+------------------------------------------------------------
       Component |   Eigenvalue   Difference         Proportion   Cumulative
    -------------+------------------------------------------------------------
    Comp1   |      19.4462      13.8924             0.7778       0.7778
    Comp2   |      5.55378            .             0.2222       1.0000
    -------------+------------------------------------------------------------

Principal components (eigenvectors)

    -------------+--------------------+-------------
    Variable   | Comp1    Comp2   | Unexplained
    -------------+--------------------+-------------
    v1   |   0.4981      0.8671   |           0
    v2   |   0.8671     -0.4981   |           0
    -------------+--------------------+-------------

. matrix symeigen evect eval = a

. matrix list eval

eval[1,2]
           e1         e2
r1  19.446222   5.553778

. matrix list evect

symmetric evect[2,2]
            e1          e2
r1   .49806073
r2   .86714215  -.49806073

. matrix define c=a*evect

. matrix define d=c-eval[1,1]*evect

. matrix list d /* first column=0 */

d[2,2]
            e1          e2
r1  -1.776e-15  -12.046724
r2           0   6.9192807

. matrix define d=c-eval[1,2]*evect

. matrix list d /* second column=0 */

d[2,2]
            e1          e2
r1   6.9192807           0
r2   12.046724  -8.882e-16

.
end of do-file

. exit, clear