Categorical DataUnivariate Genetic AnalysisPractical ExampleContingency TablesRaw Dataset usmdd.ordFrequency Data: usmdd?.ctfSaturated Model! Estimate thresholds & correlations – Saturated ! US MDD data – females contingency tables! Estimate thresholds & correlations – Saturated ! US MDD data – females raw ordinal data! Estimate thresholds & correlations – Saturated ! US MDD data – females frequency dataDat File: usmdd.datSubmodels: Equality of ThresholdsACE Model! Estimate variance components - ACED model ! US MDD data - females! Estimate variance components - ACED model ! US MDD data - females II! Estimate variance components - ACED model ! US MDD data - females IIISubmodelsGoodness-of-FitThresholds: A quick reviewThresholds for Multiple Level VariablesCategorical DataHGEN619 2006Univariate Genetic AnalysisSaturated ModelsFree thresholdsUnivariate ModelsVariances partitioned in a, c/d and eFree thresholds (or not)Practical ExampleDataset: VTRFF1 interviewMDD (DSM-IIIR)Adults: 18-60 yearsN individuals MZF (zyg=1): 1180DZF (zyg=2): 880Contingency TablesMZF DZF T2T1- + T2T1- +- 329 83 - 201 94+ 95 83 + 82 63-: unaffected +: affectedRaw Dataset usmdd.ord 1 0 0 2 0 0 1 0 0 2 0 0 1 0 0 2 0 0 1 0 0 2 0 1 1 0 0 2 0 1 1 0 1 2 0 1 1 0 1 2 1 0 1 1 0 2 1 0 1 1 0 2 1 0 1 1 0 2 1 0 1 1 1 2 1 0 1 1 1 2 1 1 1 1 1 2 1 1Frequency Data: usmdd?.ctfMZ0 0 3290 1 831 0 951 1 83DZ0 0 2010 1 941 0 821 1 63Saturated ModelT2T11cor11t1t2! Estimate thresholds & correlations – Saturated! US MDD data – females contingency tables#NGroups 2#define nvar2 2Title 1: MZ data Data NInput=2 CTable 2 2 329 83 95 83 Begin Matrices; T Full nvar2 1 Free X Stnd nvar2 nvar2 Free End Matrices; Start 1 T 1 1 - T nvar2 1 Threshold T; Correlation X; Option RSidualsEndTitle 2: DZ data Data NInput=2 CTable 2 2 201 94 82 63 Begin Matrices; T Full nvar2 1 Free X Stnd nvar2 nvar2 Free End Matrices; Start 1 T 1 1 - T nvar2 1 Threshold T; Correlation X; Option RSiduals Option Multiple IssatEndusmddsatct.mx! Estimate thresholds & correlations – Saturated! US MDD data – females raw ordinal data#NGroups 2#define nvar2 2Title 1: MZ dataData NInput=3 Ordinal File=usmdd.ord Labels zyg mdd1 mdd2Select if zyg=1Select mdd1 mdd2 ; Begin Matrices; T Full 1 nvar2 Free X Stnd nvar2 nvar2 Free End Matrices; Start 1 T 1 1 - T 1 nvar2 Threshold T; Correlation X; Options RSidualsEndTitle 2: DZ dataData NInput=3 Ordinal File=usmddmz.ord Labels zyg mdd1 mdd2Select if zyg=2Select mdd1 mdd2 ; Begin Matrices; T Full 1 nvar2 Free X Stnd nvar2 nvar2 Free End Matrices; Start 1 T 1 1 - T 1 nvar2 Threshold T; Correlation X; Options RSidualsEndusmddsatord.mx! Estimate thresholds & correlations – Saturated! US MDD data – females frequency data#NGroups 2#define nvar2 2Title 1: MZ data Data NInput=3 Ordinal File=usmddmz.ctf Labels mdd1 mdd2 frq Definition frq ; Begin Matrices; T Full 1 nvar2 Free X Stnd nvar2 nvar2 Free F Full 1 1 End Matrices; Start 1 T 1 1 - T 1 nvar2 Specify F frq Threshold T; Correlation X; Frequency F;EndTitle 2: DZ data Data NInput=3 Ordinal File=usmdddz.ctf Labels mdd1 mdd2 frq Definition frq ; Begin Matrices; T Full 1 nvar2 Free X Stnd nvar2 nvar2 Free F Full 1 1 End Matrices; Start 1 T 1 1 - T 1 nvar2 Specify F frq Threshold T; Correlation X; Frequency F;Endusmddsatfrq.mxDat File: usmdd.dat Data NInput=3 Rectangular File=usmdd.ord Labels zyg mdd1 mdd2Submodels: Equality of ThresholdsMZ (group 1) DZ (group 2) part1 t2 v1 cor v2 t3 t4 v3 cor v4Full 1 2 0 3 0 4 5 0 6 0 6II 1 1 0 3 0 4 4 0 6 0 4III 1 1 0 3 0 1 1 0 6 0 3ACE ModelT2AEA Ca ac eT11 111Ee1Cc11 or .51! Estimate variance components - ACED model! US MDD data - 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;Endusmddaces.mx! Estimate variance components - ACED model! US MDD data - females II Title 2: MZ data #include usmdd.dat Select if zyg =1 Select mdd1 mdd2 ; Begin Matrices =Group 1; T Full 1 nvar2 Free End Matrices; Thresholds T; Covariance A+C+E+D | A+C+D _ A+C+D | A+C+E+D; Option RSiduals;EndTitle 3: DZ data #include usmdd.dat Select if zyg =2 Select mdd1 mdd2 ; Begin Matrices =Group 1; T Full 1 nvar2 Free End Matrices; Thresholds T; Covariance A+C+E+D |H@A+C+Q@D _ H@A+C+Q@D|A+C+E+D; Option RSidualsEndusmddaces.mx! Estimate variance components - ACED model! US MDD data - females IIITitle 4: Constrain var=1 Constraint Begin Matrices =Group 1; I Iden 1 1 End Matrices; Start .5 all St 1 T 2 1 1-T 2 1 nvar2 St 1 T 3 1 1-T 3 1 nvar2 Begin Algebra; P=A|C|E|D; End Algebra; Constraint A+C+E+D=I;!ADE model Option NDecimals=4 Option Sat=2508.004,2054 Option MultipleEnd!AE model Drop W 1 1 1End!ACE model Free Y 1 1 1End!CE model Drop X 1 1 1End!E model Drop Y 1 1 1Endusmddaces.mxSubmodelsMatrix / ModelX (a) Y (c) Z (e) W (d) Cor NPMean NPNP DFSat 2 4 6+1*ADE Free Free Free 4 7 0AE Free Free Drop 4 6 1ACE Free Free Free 4 7 0CE Drop Free Free 4 6 1E Drop Free 4 5 2*1 constraint: A+C+D+E=1Goodness-of-Fit-2LL df2df p AICSatADE 0AE 1ACE 0CE 1E 2Thresholds: A quick reviewWhen using raw ordinal data, it is necessary to give Mx starting values for thresholdsThresholds indicate the point at which the variable transitions from one level to the next For a variable with n categories, there will always be n – 1 thresholdsThresholds for Multiple Level
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