1Categorical DataHGEN619 2006Univariate Genetic Analysisn Saturated Models¨ Free thresholdsn Univariate Models¨ Variances partitioned in a, c/d and e¨ Free thresholds (or not)2Practical Examplen Dataset: VTRn FF1 interviewn MDD (DSM-IIIR)n Adults: 18-60 yearsn N individuals MZF (zyg=1): 1180DZF (zyg=2): 880Contingency Tables6382+8395+94201-83329-+-T2T1+-T2T1DZFMZF-: unaffected +: affected3Raw Dataset usmdd.ord1 0 0 2 0 01 0 0 2 0 01 0 0 2 0 01 0 0 2 0 11 0 0 2 0 11 0 1 2 0 11 0 1 2 1 01 1 0 2 1 01 1 0 2 1 01 1 0 2 1 01 1 1 2 1 01 1 1 2 1 11 1 1 2 1 1Frequency Data: usmdd?.ctfMZ0 0 3290 1 831 0 951 1 83DZ0 0 2010 1 941 0 821 1 634Saturated ModelT2T11cor11t1t2! Estimate thresholds & correlations – Saturated! US MDD data – females contingency tablesn #NGroups 2n #define nvar2 2n Title 1: MZ datan Data NInput=2n CTable 2 2n 329 83 95 83n Begin Matrices;n T Full nvar2 1 Freen X Stnd nvar2 nvar2 Freen End Matrices;n Start 1 T 1 1 - T nvar2 1n Threshold T;n Correlation X;n Option RSidualsn Endn Title 2: DZ datan Data NInput=2n CTable 2 2n 201 94 82 63n Begin Matrices;n T Full nvar2 1 Freen X Stnd nvar2 nvar2 Freen End Matrices;n Start 1 T 1 1 - T nvar2 1n Threshold T;n Correlation X;n Option RSidualsn Option Multiple Issatn Endusmddsatct.mx5! Estimate thresholds & correlations – Saturated! US MDD data – females raw ordinal datan #NGroups 2n #define nvar2 2n Title 1: MZ datan Data NInput=3n Ordinal File=usmdd.ordn Labels zyg mdd1 mdd2n Select if zyg=1n Select mdd1 mdd2 ;n Begin Matrices;n T Full 1 nvar2 Freen X Stnd nvar2 nvar2 Freen End Matrices;n Start 1 T 1 1 - T 1 nvar2n Threshold T;n Correlation X;n Options RSidualsn Endn Title 2: DZ datan Data NInput=3n Ordinal File=usmddmz.ordn Labels zyg mdd1 mdd2n Select if zyg=2n Select mdd1 mdd2 ;n Begin Matrices;n T Full 1 nvar2 Freen X Stnd nvar2 nvar2 Freen End Matrices;n Start 1 T 1 1 - T 1 nvar2n Threshold T;n Correlation X;n Options RSidualsn Endusmddsatord.mx! Estimate thresholds & correlations – Saturated! US MDD data – females frequency datan #NGroups 2n #define nvar2 2n Title 1: MZ datan Data NInput=3n Ordinal File=usmddmz.ctfn Labels mdd1 mdd2 frqn Definition frq ;n Begin Matrices;n T Full 1 nvar2 Freen X Stnd nvar2 nvar2 Freen F Full 1 1n End Matrices;n Start 1 T 1 1 - T 1 nvar2n Specify F frqn Threshold T;n Correlation X;n Frequency F;n Endn Title 2: DZ datan Data NInput=3n Ordinal File=usmdddz.ctfn Labels mdd1 mdd2 frqn Definition frq ;n Begin Matrices;n T Full 1 nvar2 Freen X Stnd nvar2 nvar2 Freen F Full 1 1n End Matrices;n Start 1 T 1 1 - T 1 nvar2n Specify F frqn Threshold T;n Correlation X;n Frequency F;n Endusmddsatfrq.mx6Dat File: usmdd.datn Data NInput=3n Rectangular File=usmdd.ordn Labels zyg mdd1 mdd2Submodels: Equality of Thresholds346parDZ (group 2)MZ (group 1)v4corv3t4t3v2corv1t2t10601103011III0604403011II0605403021Full7ACE ModelT2AEA Ca ac eT11 111Ee1Cc11 or .51! Estimate variance components - ACED model! US MDD data - femalesn #NGroups 4n #define nvar 1n #define nvar2 2n Title 1: Model Parametersn Calculationn Begin Matrices;n X Lower nvar nvar Free !an Y Lower nvar nvar !cn Z Lower nvar nvar Free !en W Lower nvar nvar Free !dn H Full 1 1 !0.5n Q Full 1 1 !0.25n End Matrices;n Matrix H .5n Matrix Q .25n Label Row X add_genn Label Row Y com_envn Label Row Z spec_envn Label Row W dom_genn Begin Algebra;n A= X*X'; !a^2n C= Y*Y'; !c^2n E= Z*Z'; !e^2n D= W*W'; !d^2n End Algebra;n Endusmddaces.mx8! Estimate variance components - ACED model! US MDD data - females IIn Title 2: MZ datan #include usmdd.datn Select if zyg =1n Select mdd1 mdd2 ;n Begin Matrices =Group 1;n T Full 1 nvar2 Freen End Matrices;n Thresholds T;n Covariancen A+C+E+D | A+C+D _n A+C+D | A+C+E+D;n Option RSiduals;n Endn Title 3: DZ datan #include usmdd.datn Select if zyg =2n Select mdd1 mdd2 ;n Begin Matrices =Group 1;n T Full 1 nvar2 Freen End Matrices;n Thresholds T;n Covariancen A+C+E+D |H@A+C+Q@D _n H@A+C+Q@D|A+C+E+D;n Option RSidualsn Endusmddaces.mx! Estimate variance components - ACED model! US MDD data - females IIIn Title 4: Constrain var=1n Constraintn Begin Matrices =Group 1;n I Iden 1 1n End Matrices;n Start .5 alln St 1 T 2 1 1-T 2 1 nvar2n St 1 T 3 1 1-T 3 1 nvar2n Begin Algebra;n P=A|C|E|D; n End Algebra;n Constraint A+C+E+D=I;n !ADE modeln Option NDecimals=4n Option Sat=2508.004,2054n Option Multiplen End!AE modeln Drop W 1 1 1n Endn !ACE modeln Free Y 1 1 1n Endn !CE modeln Drop X 1 1 1n Endn !E modeln Drop Y 1 1 1n Endusmddaces.mx9Submodels567676+1*NP21010DF444444Mean NP2CorNPSatFreeDropEFreeFreeDropCEFreeFreeFreeACEDropFreeFreeAEFreeFreeFreeADEW (d)Z (e)Y (c)X (a)Matrix / Model*1 constraint:
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