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### 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 <number of groups>
- #define <name> <number>

e.g. #define nvar 1

- #define <$name> <string>
- #include filename

Reading Data

- Data NInputvars=<n> [NObs=<n>]
- Rectangular File=
- Missing=
- Labels
- Select if
- Select if zyg =1;
- Select

Summarized in filename.dat

Matrices Declaration

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

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

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

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

! Interval @95 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

! Interval @95 P 2 1

Option RSiduals

End

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

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

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;

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

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= [email protected]~; ! standardized variance components

End Algebra;

Interval @95 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 | [email protected][email protected] _

[email protected][email protected] | A+C+E+D ;

Option RSiduals

End

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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