Summarizing DataPractical ExampleRaw Dataset ozbmi.recDat File: ozbmi.datEstimating Variance by MLSaturated Model! Estimate means and variances - Saturated model ! OZ BMI data - young femalesSaturated Model MZ & DZEquality of means, variancesTestsEquality TestsSpecific Equality TestsACE ModelACE Model + MeansSlide 15! Estimate variance components - ACED model ! OZ BMI data - younger females! Estimate variance components - ACED model ! OZ BMI data - younger females II! Estimate variance components - ACED model ! OZ BMI data - younger females IIISummarizing DataHGEN619 class 2006Practical ExampleDataset: NH&MRC Twin Register1981 questionnaireBMI: weight/ height squaredYoung cohort: 18-30 yearsN MZFY: 534, DZFY: 328Raw Dataset ozbmi.rec115 21 1 2 58 57 1.7000 1.7000 20.0692 19.7232 20.9943 20.8726121 24 1 2 54 53 1.6299 1.6299 20.3244 19.9481 21.0828 20.9519158 21 1 2 55 50 1.6499 1.6799 20.2020 17.7154 21.0405 20.1210172 21 1 2 66 76 1.5698 1.6499 26.7759 27.9155 23.0125 23.3043182 19 1 2 50 48 1.6099 1.6299 19.2894 18.0662 20.7169 20.2583199 26 1 2 60 60 1.5999 1.5698 23.4375 24.3418 22.0804 22.3454221 23 1 2 65 65 1.7500 1.7698 21.2245 20.7476 21.3861 21.2270239 29 1 2 40 39 1.5598 1.5298 16.4366 16.6603 19.5966 19.6912246 24 1 2 60 57 1.7598 1.7698 19.3698 18.1940 20.7460 20.3076251 28 1 2 76 64 1.7000 1.7300 26.2976 21.3839 22.8863 21.4385262 29 1 2 48 51 1.5198 1.5698 20.7756 20.6905 21.2365 21.2077284 19 1 2 70 67 1.6799 1.6799 24.8016 23.7387 22.4764 22.1697524 20 1 2 53 50 1.6199 1.6299 20.1951 18.8189 21.0381 20.5440535 22 1 2 57 55 1.5798 1.5999 22.8329 21.4844 21.8974 21.4713582 26 1 2 62 61 1.6799 1.6399 21.9671 22.6800 21.6268 21.8504587 28 1 2 60 58 1.6299 1.6399 22.5827 21.5645 21.8203 21.4974588 19 1 2 55 55 1.5698 1.5698 22.3133 22.3133 21.7363 21.7363621 21 1 2 46 49 1.5698 1.5498 18.6620 20.3954 20.4854 21.1072630 27 1 1 54 55 1.7698 . 17.2364 . 19.9292 .631 28 1 2 58 60 1.6899 1.6899 20.3074 21.0077 21.0769 21.3142Dat File: ozbmi.dat#include ozbmi.datData NInput=12 Rectangular File=ozbmi.rec Labels fam age zyg part wt1 wt2 ht1 ht2 htwt1 htwt2 bmi1 bmi2Zyg MZF MZM DZF DZM DZFMYoung 1 2 3 4 5Old 6 7 8 9 10Estimating Variance by MLMxGui InterfaceDatamapDrawRunPath InspectorManagerMx Script LanguageSaturated ModelT2T1v1covv21m1m2! Estimate means and variances - Saturated model! OZ BMI data - young females#NGroups 2#define nvar2 2Title 1: MZ data #include ozbmi.dat Select if zyg =1 Select bmi1 bmi2 ; Begin Matrices; M Full 1 nvar2 Free X Symm nvar2 nvar2 Free End Matrices; Start 20 M 1 1 - M 1 nvar2 Start 1 X 1 1 X 2 2 Means M; Covariance X; Option RSidualsEndTitle 2: DZ data #include ozbmi.dat Select if zyg =3 Select bmi1 bmi2 ; Begin Matrices; M Full 1 nvar2 Free X Symm nvar2 nvar2 Free End Matrices; Start 20 M 1 1 - M 1 nvar2 Start 1 X 1 1 X 2 2 Means M; Covariance X; Option RSidualsEndSaturated Model MZ & DZ MZ twins DZ twins10 parametersT2T1v1MZ covv21m1m2T2T1v3DZ covv41m3m4Equality of means, variances MZ twins DZ twins4 parametersT2T1v1MZ covv11m1m1T2T1v1DZ covv11m1m1TestsSaturated modelEquality of meansIs m1 = m2 ?Is m1MZ = m1DZ = m2MZ = m2DZ ?Equality of variancesIs v1 = v2 ?Is v1MZ = v1DZ = v2MZ = v2DZ ?Equality TestsMain ScriptLast Group.... Option Multiple IssatEndSave ozbmisat.mxs! equate means and variances Equate M 1 1 1 M 1 1 2 M 2 1 1 M 2 1 2 Equate X 1 1 1 X 1 2 2 X 2 1 1 X 2 2 2EndSpecific Equality TestsGet ozbmisat.mxs! equate means within zygosity groups Equate M 1 1 1 M 1 1 2 Equate M 2 1 1 M 2 1 2End! equate means across zygosity groups Equate M 1 1 1 M 1 1 2 M 2 1 1 M 2 1 2End! equate variances within zygosity groups Equate X 1 1 1 X 1 2 2 Equate X 2 1 1 X 2 2 2End! equate variances across zygosity groups Equate X 1 1 1 X 1 2 2 X 2 1 1 X 2 2 2EndACE ModelT2AEA Ca ac eT11 111Ee1Cc11 or .51ACE Model + MeansT2AEA Ca ac eT11 111Ee1Cc11 or .511m1 or m3 m2 or m4TestsACE modelIs a significant ? -> CE modelIs c significant ? -> AE modelIs there significant family resemblance ? -> E modelADE model! Estimate variance components - ACED model! OZ BMI data - younger females#NGroups 4#define nvar 1#define nvar2 2Title 1: Model Parameters Calculation Begin Matrices; X Lower nvar nvar Free ! a Y Lower nvar nvar ! c Z Lower nvar nvar Free ! e W Lower nvar nvar Free ! d H Full 1 1 ! 0.5 Q Full 1 1 ! 0.25 End Matrices; Matrix H .5 Matrix Q .25 Label Row X add_gen Label Row Y com_env Label Row Z spec_env Label Row W dom_genBegin Algebra; A= X*X'; ! a^2 C= Y*Y'; ! c^2 E= Z*Z'; ! e^2 D= W*W'; ! d^2 End Algebra;End! Estimate variance components - ACED model! OZ BMI data - younger females II Title 2: MZ data #include ozbmi.dat Select if zyg =1 Select bmi1 bmi2 ; Begin Matrices = Group 1; M Full 1 nvar2 Free End Matrices; Means M; Covariance A+C+E+D | A+C+D _ A+C+D | A+C+E+D; Option RSiduals;EndTitle 3: DZ data #include ozbmi.dat Select if zyg =3 Select bmi1 bmi2 ; Begin Matrices = Group 1; M Full 1 nvar2 Free End Matrices; Means M; Covariance A+C+E+D | H@A+C+Q@D _ H@A+C+Q@D | A+C+E+D; Option RSidualsEnd! Estimate variance components - ACED model! OZ BMI data - younger females IIITitle 4: Standardization Calculation Begin Matrices = Group 1; End Matrices; Start .6 all Start 20 M 2 1 1 - M 2 1 nvar2 Start 20 M 3 1 1 - M 3 1 nvar2 Begin Algebra; V=A+C+E+D; ! total variance P=A|C|E|D; ! concatenate parameter estimates S=P@V~; ! standardized parameter estimates End Algebra;!ADE model Interval S 1 1 - S 1 4 Option NDecimals=4 Option
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