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Univariate Analysis Hermine Maes TC19 March 2006.

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Presentation on theme: "Univariate Analysis Hermine Maes TC19 March 2006."— Presentation transcript:

1 Univariate Analysis Hermine Maes TC19 March 2006

2 Files to Copy to your Computer Faculty/Maes/tc19/maes/univariate  ozbmi.rec  ozbmi.dat  ozbmiyface(s)(2).mx  Univariate.ppt

3 Univariate Genetic Analysis Saturated Models  Free variances, covariances  Free means Univariate Models  Variances partitioned in a, c/d and e  Free means (or not)

4 ACE Model

5 ACE Model + Means

6 ACE Model MZ twinsDZ twins 7 parameters: 4 means, 3 path coefficients: a, c, e

7 ADE Model MZ twinsDZ twins 7 parameters: 4 means, 3 path coefficients: a, d, e

8 Tests ACE model Is a significant ? -> CE model Is c significant ? -> AE model Is there significant family resemblance ? -> E model ADE model Is d significant ? -> AE model

9 ! Estimate variance components - ACED model ! OZ BMI data - younger females #NGroups 4 #define nvar 1 #define nvar2 2 Title 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_gen Begin Algebra; A= X*X'; ! a^2 C= Y*Y'; ! c^2 E= Z*Z'; ! e^2 D= W*W'; ! d^2 End Algebra; End ozbmiyface.mx

10 ! Estimate variance components - ACED model ! OZ BMI data - younger females #NGroups 4 #define nvar 1 #define nvar2 2 Title 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 ozbmiyface.mx Group Type Values for Fixed Parameters

11 ! Estimate variance components - ACED model ! OZ BMI data - younger females Label Row X add_gen Label Row Y com_env Label Row Z spec_env Label Row W dom_gen Begin Algebra; A= X*X'; ! a^2 C= Y*Y'; ! c^2 E= Z*Z'; ! e^2 D= W*W'; ! d^2 End Algebra; End ozbmiyface.mx Labels for Matrix Rows and Columns Algebra Section Additive genetic variance Shared environmental variance Specific environmental variance Dominance genetic variance

12 ! Estimate variance components - ACED model ! OZ BMI data - younger females II Title 2: MZ data #include ozbmi2.dat Select if zyg =1 Select if agecat =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; End Title 3: DZ data #include ozbmi2.dat Select if zyg =3 Select if agecat =1 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 RSiduals End ozbmiyface.mx

13 ! Estimate variance components - ACED model ! OZ BMI data - younger females II Title 2: MZ data #include ozbmi2.dat Select if zyg =1 Select if agecat =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; End Title 3: DZ data #include ozbmi2.dat Select if zyg =3 Select if agecat =1 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 RSiduals End Model Statements Kronecker product Copy Matrices from Group 1

14 ! Estimate variance components - ACED model ! OZ BMI data - younger females III Title 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 Sat=4055.935,1767 End ozbmiyface.mx

15 ! Estimate variance components - ACED model ! OZ BMI data - younger females III Title 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; P=A|C|E|D; S=P@V~; End Algebra; !ADE model Interval S 1 1 - S 1 4 Option NDecimals=4 Option Sat=4055.935,1767 End Start Values for all free Parameters Overwrite Start Values for Means Calculate Total Variance by adding 4 Variance Components Sticking 4 Variance Components together in 1 Matrix Multiplying each of 4 Variance Components by the Inverse of the Variance, Equivalent to Dividing Variance Components by the Variance to get Standardized Variance Components Calculate 95% Confidence Intervals Compare with Likelihood (-2LL, df) of Saturated model (ozbmiyfsat.mxo), to obtain Chi-square Goodness-of-Fit Statistics

16 ! Estimate variance components - ACED model ! OZ BMI data - younger females IV Title 4: Standardization Calculation Begin Matrices = Group 1; End Matrices; Start.6 all Start 20 M 2 1 1 - M 2 1 2 Start 20 M 3 1 1 - M 3 1 2 Begin Algebra; V=A+C+E+D; P=A|C|E|D; S=P@V~; End Algebra; !ADE model Interval S 1 1 - S 1 4 Option NDecimals=4 Option Sat=4055.935,1767 Option Multiple End !AE model Drop W 1 1 1 End !ACE model Free Y 1 1 1 End !CE model Drop X 1 1 1 End !E model Drop Y 1 1 1 End ozbmifyaces.mx

17 ! Estimate variance components - ACED model ! OZ BMI data - younger females IV Title 4: Standardization Calculation Begin Matrices = Group 1; End Matrices; Start.6 all Start 20 M 2 1 1 - M 2 1 2 Start 20 M 3 1 1 - M 3 1 2 Begin Algebra; V=A+C+E+D; P=A|C|E|D; S=P@V~; End Algebra; !ADE model Interval S 1 1 - S 1 4 Option NDecimals=4 Option Sat=4055.935,1767 Option Multiple End !AE model Drop W 1 1 1 End !ACE model Free Y 1 1 1 End !CE model Drop X 1 1 1 End !E model Drop Y 1 1 1 End Indicates to Mx that you want to fit submodels which will follow, Has to be before the End statement of the Last Group of your Main Script Submodel, just requires Changes compared to Full Script Free previously fixed Parameter Drop fixes Parameter to 0

18 Submodels: ozbmifyaces.mx Matrix / Model X (a)Y (c)Z (e)W (d)Cov NP Mean NP NPDF Sat6410 ADEFree 473 AEFree Drop464 ACEFree 473 CEDropFree 464 EDropFree455

19 ! Estimate variance components - ACED model ! OZ BMI data - younger females IV..... !ADE model Interval S 1 1 - S 1 4 Option NDecimals=4 Option Sat=4055.935,1767 Option Multiple End !Save ozbmiyf.mxs Option Issat End !AE model Drop W 1 1 1 End !ACE model Free Y 1 1 1 Option Sat=4055.935,1767 End Option Issat End !CE model Drop X 1 1 1 End !E model Drop Y 1 1 1 End ozbmiyfaces2.mx Compare with Saturated Model (free means, variances, covariances) Make current Model the Saturated Model (ADE) to compare submodels with Expect submodels

20 Submodels: ozbmifyaces2.mx Matrix / Model X (a)Y (c)Z (e)W (d)Cov NP Mean NP NPSat NP DF Sat #6410 ADE $Free 4710#3 AEFree Drop467 $1 ACE &Free 4710#3 CEDropFree 467 &1 EDropFree457 &2 NP: number of parameters, Sat: saturated, DF: degrees of freedom

21 Goodness-of-Fit for BMI yf -2LLdfP2P2 pAIC)P2)P2 dfp Sat ADE AE ACE CE E

22 Parameter Estimates for BMI yf Path coefficientsVariance compStand var comp aceda2a2 c2c2 e2e2 d2d2 a2a2 c2c2 e2e2 d2d2 Sat ADE AE ACE CE E

23 Goodness-of-Fit for BMI yf -2LLdfP2P2 pAIC)P2)P2 dfp Sat4055.931767 ADE4059.2117703.283.35-2.72 AE4063.6117717.684.10-0.324.401.04 ACE4063.6117707.683.051.68 CE4216.291771160.4.00152 1.00 E4585.591772529.5.005195212.00

24 Parameter Estimates for BMI yf Path coefficientsVariance compStand var comp aceda2a2 c2c2 e2e2 d2d2 a2a2 c2c2 e2e2 d2d2 Sat ADE.56.41.54.31.17.29.40.22.38 AE.78.42.61.17.78.22 ACE.78.00.42.61.00.17.78.00.22 CE.67.56.47.32.59.41 E.88.771.0

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