Univariate Analysis in Mx

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 ltnumber of groupsgt
• define ltnamegt ltnumbergt
• e.g. define nvar 1
• define ltnamegt ltstringgt
• include filename

4
Reading Data

• Data NInputvarsltngt NObsltngt
• Rectangular File
• Missing
• Labels
• Select if
• Select if zyg 1
• Select
• Summarized in filename.dat

5
Matrices Declaration

• Begin Matrices
• ltNamegt lttypegt ltrowsgt ltcolumnsgt
• End Matrices
• Matrix Types Mx manual p. 56
• Begin Matrices Group ltnumbergt

6
Matrix Algebra

• Begin Algebra
• ltmatrix namegt ltmatrix formulagt
• ltmatrix namegt ltmatrix formulagt
• End Algebra
• Matrix Operations Mx Manual p. 59
• Matrix Functions Mx Manual p. 64

7
Means/Covariances

• Means ltformulagt
• e.g. Means M
• dimensions of expected matrix must equal
  dimensions of observed means
• Covariances ltformulagt
• 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_vars5
• Missing-1.00
• Rectangular FileAgg10.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 _at_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 _at_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
A2
C2
E2
D1
D2
a
c
e
a
c
e
d
d
P1
P2
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MZ Twins
Observed Covariance Variance Twin 1 Covariance
Covariance Variance Twin 2
Expected Covariance a2c2e2d2 a2c2d2
a2c2d2 a2c2e2d2
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DZ Twins
Observed Covariance Variance Twin 1 Covariance
Covariance Variance Twin 2
Expected Covariance a2c2e2d2 .5a2c2.25d2
.5a2c2.25d2 a2c2e2d2
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 _at_ .5 for DZ cov of
  A
• Q Full 1 1 ! scalar fixed _at_ .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
A2
C2
E2
D1
D2
a X
c Y
e Z
a X
c Y
e Z
d W
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 XX' ! additive genetic variance
• C YY' ! common environmental variance
• E ZZ' ! unique environmental variance
• D WW ! dominance variance
• V ACED ! total variance
• P ACED ! put parameters in one matrix
• S P_at_V ! standardized variance components
• End Algebra
• Interval _at_95 S 1 1 S 1 3 ! confidence
  intervals
• End

18
Univariate Mx Script III

• G2 male MZ twins, datagroup
• Data NInput_vars5
• 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
  
• ACED ACD _
• AC D ACED
• 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
  
• ACED H_at_ACQ_at_D _
• H_at_ACQ_at_D ACED
• Option RSiduals
• End

20
Path Diagram to Matrices
Path Coefficient a c e d
Matrix Name X Y Z W
Variance Component a2 c2 e2 d2
Matrix Name A C E D
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