Univariate Analysis in Mx Boulder, 2004

Group Structure Title Type: Data/ Calculation/ Constraint Reading Data Matrices Declaration Assigning Specifications/ Values Matrix Algebra and/or Means/ Covariances Options End

Additional Commands ! Comments #NGroups #define e.g. #define nvar 1 #define #include filename

Reading Data Data NInputvars= [NObs= ] Rectangular File= Missing= Labels Select if Select if zyg =1; Select Summarized in filename.dat

Matrices Declaration Begin Matrices; … End Matrices; Matrix Types: Mx manual p. 56 Begin Matrices = Group

Matrix Algebra Begin Algebra; = ; … End Algebra; Matrix Operations: Mx Manual p. 59 Matrix Functions: Mx Manual p. 64

Means/Covariances Means ; e.g. Means M; dimensions of expected matrix must equal dimensions of observed means Covariances ; dimensions of expected covariance matrix must equal the square of the number of variables

Mx Script I #NGroups 2 #define nvar 1 #define nsib 2 G1: male MZ twin pairs Data NInput_vars=5 Missing=-1.00 Rectangular File=Agg10.rec Labels ZYG RB10A AGG10A RB10B AGG10B Select if zyg =1 ; ! select MZM twins Select AGG10A AGG10B ; May be put in agg10.dat and included with #Include filename

Mx Script II Begin Matrices; X Symm nsib nsib Free! covariances I Iden nsib nsib M Full nvar nsib Free! means End Matrices; Start 2 X 1 1 X 2 2! starting values for variances Start 0.5 M 1 1 M 1 2! starting values for means Begin Algebra; O= \sqrt(I.X)~&X;! MZM correlation End Algebra; Means M;! model for MZM means Covariances X;! model for MZM (co)variances ! O 2 1 Option RSiduals End

Mx Script III Begin Matrices; Y Symm nsib nsib Free! covariances I Iden nsib nsib N Full nvar nsib Free! means End Matrices; Start 2 Y 1 1 X 2 2! starting values for variances Start 0.5 N 1 1 N 1 2! starting values for means Begin Algebra; P= \sqrt(I.Y)~&Y;! DZM correlation End Algebra; Means N;! model for DZM means Covariances Y;! model for DZM (co)variances ! P 2 1 Option RSiduals End

Mx Script IV ! equate means Equate M M N N End ! equate means and variances Equate X X Y Y End

Path Diagram for MZ and DZ twins P1 A1C1E1 P2 A2C2E2D1D aceace 1.00 / d d 1.00 / 0.25

MZ Twins Observed Covariance Variance Twin 1 Covariance Variance Twin 2 Expected Covariance a 2+ c 2+ e 2+ d 2 a 2+ c 2+ d 2 a 2+ c 2+ e 2+ d 2

DZ Twins Observed Covariance Variance Twin 1 Covariance Variance Twin 2 Expected Covariance a 2+ c 2+ e 2+ d 2.5a 2+ c 2+.25d 2 a 2+ c 2+ e 2+ d 2

Univariate Mx Script I #NGroups 3 #define nvar 1 ! define nvar as number of variables #define nsib 2 Title G1: Model Parameters Calculation Begin Matrices; X Lower nvar nvar Free! additive genetic structure Y Lower nvar nvar Free! common environmental structure Z Lower nvar nvar Free! unique environmental path struct. W Lower nvar nvar Free! dominance structure H Full 1 1! scalar for DZ cov of A Q Full 1 1! scalar for DZ cov of D End Matrices;

Declared Matrices P1 A1C1E1 P2 A2C2E2D1D a [X]c [Y]e [Z]a [X]c [Y]e [Z] / 0.50 [H]1.00 d [W] 1.00 d [W] 1.00 / 0.25 [Q]

Univariate Mx Script II Matrix H.5 Matrix Q.25 Start.5 all! starting values for free parameters Begin Algebra; A= X*X' ;! additive genetic variance C= Y*Y' ; ! common environmental variance E= Z*Z' ;! unique environmental variance D= W*W’;! dominance variance V= A+C+E+D;! total variance P= A|C|E|D;! put parameters in one matrix S= standardized variance components End Algebra; S 1 1 – S 1 3! confidence intervals End

Univariate Mx Script III G2: male MZ twins, datagroup Data NInput_vars=5 Missing=-1.00 Rectangular File= Agg10.rec Labels ZYG RB10A AGG10A RB10B AGG10B Select if zyg =1;! select MZM twins Select AGG10A AGG10B ; Begin Matrices = Group 1; M Full nsib nvar Free! means End Matrices; Start 0.5 M 1 1 M 1 2! starting values for means Means M;! model for means Covariances! model for MZ variance/covariances A+C+E+D| A+C+D _ A+C+D| A+C+E+D; Options RSiduals End

Univariate Mx Script IV G3: male DZ twins, datagroup Data NInput_vars= Missing=-1.00 Rectangular File= Agg10.rec Labels ZYG RB10A AGG10A RB10B AGG10B Select if zyg =2;! select DZM twins Select AGG10A AGG10B ; Begin Matrices = Group 1; M Full nsib nvar Free! means End Matrices; Start 0.5 M 1 1 M 1 2! starting values for means Means M;! model for means Covariances! model for DZ variance/covariances A+C+E+D| _ A+C+E+D; Option RSiduals End

Path Diagram to Matrices Path Coefficient aced Matrix NameXYZW Variance Component a2a2 c2c2 e2e2 d2d2 Matrix NameACED

Mx Script V Save satm.mxs ! equate means Equate M M N N End ! equate means and variances Equate X X Y Y End Get satm.mxs ! equate variances only Equate X X Y Y End