**************************************************************************; ******* reading in the data ******; **********************************************************************; option validvarname = v6; data readin; input obs EDUHS MEDHHIN PERCAPIT PUBWATER WOOD RESP; cards; 1 70.5 17564 9281 11.2 33.0 -7.30523 2 86.7 40076 14554 74.9 2.2 -7.03289 3 72.9 20920 9889 30.5 23.3 -7.22938 4 75.9 20925 8938 33.1 26.4 -7.08875 5 77.3 26619 11018 63.4 8.1 -7.18195 6 72.3 19408 9575 63.7 4.4 -7.44869 7 82.7 25366 11125 75.2 3.1 -7.45323 8 71.7 25032 11244 76.6 4.5 -7.40105 9 75.1 24900 10878 44.6 15.5 -7.13288 10 84.6 39188 16116 72.1 3.6 -7.61564 11 72.5 18732 8991 11.4 34.8 -6.76724 12 73.7 22227 11067 68.2 3.2 -7.23637 13 80.1 31281 12526 43.7 11.2 -7.00609 14 80.5 25891 10836 82.5 2.8 -7.30800 15 64.9 17752 8359 24.0 38.4 -7.09561 16 84.9 22908 12067 19.8 33.6 -7.47994 17 71.7 21661 10335 68.6 3.3 -7.65552 18 75.7 22250 10911 30.0 16.2 -7.18282 19 90.7 42218 17237 91.8 0.7 -7.19225 20 78.7 29071 11932 58.4 4.5 -7.10267 21 76.1 22067 10264 35.7 10.2 -7.34845 22 74.4 22421 11276 68.1 4.2 -7.20223 23 70.2 22155 10146 56.7 9.4 -7.44400 24 75.5 24764 11452 70.9 2.2 -7.39306 25 78.0 29237 12892 65.9 5.4 -7.12041 26 71.9 19773 9622 55.2 7.3 -7.47303 27 88.2 35659 18496 96.0 0.3 -7.10739 28 75.9 25846 11587 59.3 12.8 -7.18405 29 76.4 20151 9527 17.1 33.1 -6.89004 30 78.2 31308 11909 26.6 13.9 -7.27884 31 77.5 22442 10541 30.4 25.8 -7.04145 32 74.2 23157 11287 56.9 3.0 -7.36740 33 69.9 22495 9887 24.3 25.9 -7.15804 34 76.3 25368 11574 57.4 4.7 -7.26909 35 71.0 23518 11050 78.3 9.5 -6.76117 36 73.0 23411 11732 56.7 16.3 -7.18279 37 72.2 21646 10368 52.5 3.7 -7.52693 38 80.2 23478 11415 41.8 15.5 -6.99737 39 75.2 24383 10623 25.8 28.0 -7.30354 40 76.3 27706 11792 55.1 7.3 -7.33723 41 67.7 19211 9616 74.1 4.1 -7.46321 42 75.9 24689 11121 78.8 1.9 -7.33578 43 64.7 16924 7737 34.9 23.6 -7.48375 44 68.5 21707 9675 54.9 12.1 -7.30616 45 75.2 24414 11387 74.7 2.7 -7.39557 46 75.5 29549 12689 70.4 4.9 -7.37226 47 73.4 24516 10843 45.9 8.9 -7.21550 48 70.1 22689 10167 36.9 15.0 -6.98164 49 67.7 22102 9666 34.1 20.1 -7.33731 50 75.8 23763 11599 76.0 1.2 -7.32566 51 69.7 22673 10871 53.7 1.9 -7.54059 52 81.5 30491 12358 76.5 4.8 -7.67704 53 70.4 22942 10860 73.4 0.9 -7.35685 54 69.7 21238 9948 56.8 9.7 -7.12294 55 88.0 35789 16214 80.2 2.0 -7.22099 56 71.6 21909 10467 32.1 16.3 -7.05172 57 72.3 21571 10426 66.8 6.9 -7.49327 58 69.2 21191 9538 22.9 25.9 -7.30384 59 70.4 20737 10050 80.7 1.4 -7.48056 60 73.0 22559 10199 67.0 5.7 -7.04066 61 72.1 20131 9465 38.3 9.2 -6.95791 62 85.0 32043 15645 97.1 0.3 -7.11884 63 64.3 19926 8963 51.8 17.4 -7.00644 64 71.3 22827 10489 66.7 5.2 -7.31025 65 71.7 23278 10795 63.0 4.4 -7.35995 66 78.7 29596 11936 68.6 4.7 -7.10256 67 69.8 24483 11383 79.6 1.7 -7.62295 68 71.8 25910 10280 41.0 15.4 -7.43372 69 80.3 24093 11833 67.5 8.4 -7.11068 70 84.8 40798 15341 69.4 3.4 -7.19746 71 84.2 35585 13147 38.2 9.1 -6.95286 72 68.2 24957 10899 56.2 7.8 -7.39340 73 78.3 27512 11620 59.2 7.7 -7.38323 74 79.4 30571 12993 75.7 2.0 -7.23823 75 77.0 21921 9814 69.0 2.6 -7.27096 76 68.2 18740 9222 59.4 3.3 -7.39121 77 68.4 18836 8535 30.7 21.6 -7.30260 78 71.2 20746 9882 58.7 2.1 -7.78562 79 76.4 26998 11862 57.2 9.6 -7.26850 80 70.6 17333 8640 47.3 21.6 -6.95717 81 77.5 26992 11514 68.1 4.6 -7.72376 82 90.0 44122 17435 70.3 2.1 -7.12013 83 72.2 22496 10658 68.4 3.4 -7.68397 84 73.8 23081 10108 63.9 4.4 -7.38356 85 77.7 25937 11323 71.6 6.1 -7.35966 86 80.1 33456 12687 44.4 7.9 -7.23051 87 72.6 21537 10513 62.1 3.1 -7.58666 ; ****** For numerical optimization reasons in PROC CALIS we first rescale some of the variables Note if this rescaling is not done, we could not get CALIS to converge properly. Credit for discovering the rescaling trick to obtain convergence goes to Dr. Yasuo Amemiya; data minn2; set readin; eduhs=eduhs/10; medhhin=medhhin/10000; percapit=percapit/1000; pubwater=pubwater/10; run; **** Exploratory factor analysis model for two factors underlying data; proc factor data = minn2 method = ml heywood rotate=promax; var eduhs medhhin percapit pubwater wood resp; run; **** Fit the measurement model for the two factors simultaneously **** with the relation between them and the outcome of interest resp; proc calis ucov method = ml aug data = minn2 outram=parm1 MAXITER=2000 maxfunc=1000 gconv = .0000000001; var eduhs medhhin percapit pubwater wood resp; lineqs eduhs = m1 intercep + b11 f1 + e1, medhhin = m2 intercep + b12 f1 + e2, percapit = meanf1 intercep + f1 + e3, pubwater = m3 intercep + b21 f2 + e4, wood = meanf2 intercep + f2 + e5, resp = mresp intercep + alpha1 f1 + alpha2 f2 + e6; std f1-f2 = ph1-ph2, e1-e6 = th1-th6; cov f1 f2 = ph12; bounds 0<=th1-th6, 0<=ph1-ph2; parameters alpha0; mresp = alpha1*meanf1 + alpha2*meanf2 - alpha0; run; ********The estimate for the intercept is taken as the -alpha0 in the output From the "Manifest Variable Equations with Estimates" output, i.e. the unstandardized estimates, the estimate for the coefficient in front of ruralness (f2) is alpha2 and the estimate for the coefficent in front of SES (f1) is alpha1/1000;