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Univariate Analysis in Mx: Data Management and Matrix Genetics

This guide details the procedures and scripts for conducting univariate analyses using Mx software in the context of twin studies. It covers data reading, matrix declaration, and operations involved in calculating means and covariances for different groups (MZ and DZ twins). The document includes step-by-step examples for defining variables, selecting data subsets, assigning specifications, and performing matrix algebra. Essential options for residual analysis and confidence intervals are also provided, ensuring a comprehensive understanding of statistical modeling in genetic research.

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Univariate Analysis in Mx: Data Management and Matrix Genetics

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  1. Univariate Analysis in Mx Boulder, 2004

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

  3. Additional Commands • ! Comments • #NGroups <number of groups> • #define <name> <number> e.g. #define nvar 1 • #define <$name> <string> • #include filename

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

  5. Matrices Declaration • Begin Matrices; • <Name> <type> <rows> <columns> • … • End Matrices; • Matrix Types: Mx manual p. 56 • Begin Matrices = Group <number>

  6. Matrix Algebra • Begin Algebra; • <matrix name> = <matrix formula>; • <matrix name> = <matrix formula>; • … • End Algebra; • Matrix Operations: Mx Manual p. 59 • Matrix Functions: Mx Manual p. 64

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

  8. 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

  9. 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 ! Interval @95 O 2 1 Option RSiduals End

  10. 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 ! Interval @95 P 2 1 Option RSiduals End

  11. Mx Script IV ! equate means Equate M 1 1 1 M 1 1 2 N 2 1 1 N 2 1 2 End ! equate means and variances Equate X 1 1 1 X 1 2 2 Y 2 1 1 Y 2 2 2 End

  12. Path Diagram for MZ and DZ twins 1.00 / 0.50 1.00 1.00 / 0.25 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 A1 C1 E1 D1 A2 C2 E2 D2 a c e d a c e d P1 P2

  13. MZ Twins

  14. DZ Twins

  15. 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 fixed @ .5 for DZ cov of A Q Full 1 1 ! scalar fixed @ .25 for DZ cov of D End Matrices;

  16. Declared Matrices 1.00 / 0.50 [H] 1.00 1.00 / 0.25 [Q] 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 A1 C1 E1 D1 A2 C2 E2 D2 a [X] c [Y] e [Z] d [W] a [X] c [Y] e [Z] d [W] P1 P2

  17. 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= P@V~; ! standardized variance components End Algebra; Interval @95 S 1 1 – S 1 3 ! confidence intervals End

  18. 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

  19. 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 | H@A+C+Q@D _ H@A+C+Q@D | A+C+E+D ; Option RSiduals End

  20. Path Diagram to Matrices

  21. Mx Script V Save satm.mxs ! equate means Equate M 1 1 1 M 1 1 2 N 2 1 1 N 2 1 2 End ! equate means and variances Equate X 1 1 1 X 1 2 2 Y 2 1 1 Y 2 2 2 End Get satm.mxs ! equate variances only Equate X 1 1 1 X 1 2 2 Y 2 1 1 Y 2 2 2 End

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