Example Mx Output

Multivariate ACE Twin Model

```

** Mx startup successful **

**MX-Linux version 1.47c**
! Mx ACE script for twin data

The following MX script lines were read for group  1

#DEFINE NVAR 3
GROUP1: DEFINES MATRICES
DATA CALC NGROUPS=4
BEGIN MATRICES;
X LOWER NVAR NVAR FREE    ! GENETIC STRUCTURE
Y LOWER NVAR NVAR FREE    ! SHARED ENVIRONMENT
Z LOWER NVAR NVAR FREE    ! NON-SHARED PATH CO-EFFICIENTS
H FULL 1 1
I IDEN 4 4
END MATRICES;
MATRIX H .5
BEGIN ALGEBRA;
A= X*X';   ! GENETIC COVARIANCE MATRIX
C= Y*Y';   ! ENVIRONMENTAL COVARIANCE MATRIX
E= Z*Z';   ! NONSHARED ENVIRONMENTAL COVARIANCE MATRIX
END ALGEBRA;
START 0   X 1 1 TO X NVAR NVAR
START 0   Y 1 1 TO Y NVAR NVAR
START 1.7 Z 1 1 TO Z NVAR NVAR
END

The following MX script lines were read for group  2

GROUP2: MZ TWIN PAIRS
DATA NINPUT_VARS=6 NOBSERVATIONS=1500
CMATRIX
4.24756
-.280441  3.39532
2.01213    .05206    2.95854
3.2865    -.243047   2.01504   4.39321
-.210246  2.38388     .096846  -.202754  3.42946
2.02091    .050704   2.44859   2.02949    .114946  2.86705
LABELS X1 Y1 Z1 X2 Y2 Z2
MATRICES= GROUP 1
COVARIANCES A + C + E  |    A + C  _
A + C    |  A + C + E /
OPTION RS
END

The following MX script lines were read for group  3

GROUP3: DZ TWIN PAIRS
DATA NINPUT_VARS=6 NOBSERVATIONS=2000
CMATRIX
4.35496
-.354591  3.68418
2.04503    .097915  3.17886
2.12497    .329648  1.41837   4.15677
.241837  1.64101    .430632  -.216949  3.43144
1.34426    .501343  1.70592   2.01647    .139561   3.12658
LABELS X1 Y1 Z1 X2 Y2 Z2
MATRICES= GROUP 1
COVARIANCES A + C + E  |   H@A + C  _
H@A + C   |  A + C + E /
OPTION RS
END

The following MX script lines were read for group  4

GROUP4: STANDARDISED SOLUTION
CALCULATION
MATRICES = GROUP 1
BEGIN ALGEBRA;
! PHENOTYPIC COVARIANCE MATRIX

P = A + C + E;
! DIAGONAL MATRIX OF PHENOTYPIC STANDARD DEVIATIONS

D = \SQRT(\V2D(\D2V(P)));
! PHENOTYPICALLY STANDARDISED GENETIC COVARIANCE MATRIX

T = D~ * A * D~;
! PHENOTYPICALLY STANDARDISED SHARED ENVIRONMENTAL COVARIANCE MATRIX

U = D~ * C * D~;
! PHENOTYPICALLY STANDARDISED NONSHARED ENVIRONMENTAL COVARIANCE MATRIX

V = D~ * E * D~;
! GENETIC CORRELATION MATRIX

G = \STND(T);
How am I supposed to take the square root of  0.?
Diagonal elements are:
0.  0.
Matrix is
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
Matrix not fully standardized
! SHARED ENVIRONMENTAL CORRELATION MATRIX

S = \STND(U);
How am I supposed to take the square root of  0.?
Diagonal elements are:
0.  0.
Matrix is
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
Matrix not fully standardized
! NONSHARED ENVIRONMENTAL CORRELATION MATRIX

N = \STND(V);
How am I supposed to take the square root of  0.?
Diagonal elements are:
0.  0.
Matrix is
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
Matrix not fully standardized
END ALGEBRA;
END
How am I supposed to take the square root of  0.?
Diagonal elements are:
0.  0.
Matrix is
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
Matrix not fully standardized
How am I supposed to take the square root of  0.?
Diagonal elements are:
0.  0.
Matrix is
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
0.0000E+00   0.0000E+00   0.0000E+00
Matrix not fully standardized

PARAMETER SPECIFICATIONS

GROUP NUMBER: 1

Group1: Defines Matrices

MATRIX A
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX C
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX E
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX H
This is a FULL matrix of order    1 by    1
It has no free parameters specified

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1 2 3
1  1
2  2 3
3  4 5 6

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1   7
2   8  9
3  10 11 12

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1  13
2  14 15
3  16 17 18

GROUP NUMBER: 2

Group2: MZ twin pairs

MATRIX A
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX C
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX E
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX H
This is a FULL matrix of order    1 by    1
It has no free parameters specified

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1 2 3
1  1
2  2 3
3  4 5 6

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1   7
2   8  9
3  10 11 12

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1  13
2  14 15
3  16 17 18

GROUP NUMBER: 3

Group3: DZ twin pairs

MATRIX A
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX C
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX E
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX H
This is a FULL matrix of order    1 by    1
It has no free parameters specified

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1 2 3
1  1
2  2 3
3  4 5 6

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1   7
2   8  9
3  10 11 12

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1  13
2  14 15
3  16 17 18

GROUP NUMBER: 4

Group4: Standardised solution

MATRIX A
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX C
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX D
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX E
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX G
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX H
This is a FULL matrix of order    1 by    1
It has no free parameters specified

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX N
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX P
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX S
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX T
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX U
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX V
This is a computed FULL matrix of order    3 by    3
It has no free parameters specified

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1 2 3
1  1
2  2 3
3  4 5 6

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1   7
2   8  9
3  10 11 12

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1  2  3
1  13
2  14 15
3  16 17 18

*** WARNING! ***

I am not sure I have found a solution that satisfies
Kuhn-Tucker conditions for a minimum.
NAG's IFAIL parameter is  1

We probably have a minimum here, but you might consider trying different
starting values.  You can randomize these with TH=n on  the OU line, where
n is the number of times you wish to do this.
I STRONGLY recommend BOundaries to be set if you use TH

MX PARAMETER ESTIMATES

GROUP NUMBER: 1

Group1: Defines Matrices

MATRIX A
This is a computed FULL matrix of order    3 by    3
[=X*X']
1          2          3
1      2.1760    -1.0631     1.2854
2     -1.0631     1.6775    -0.6641
3      1.2854    -0.6641     1.8815

MATRIX C
This is a computed FULL matrix of order    3 by    3
[=Y*Y']
1          2          3
1      1.0759     0.8058     0.7510
2      0.8058     0.7914     0.7540
3      0.7510     0.7540     0.7195

MATRIX E
This is a computed FULL matrix of order    3 by    3
[=Z*Z']
1          2          3
1      1.0355    -0.0177    -0.0010
2     -0.0177     1.0384     0.0083
3     -0.0010     0.0083     0.4697

MATRIX H
This is a FULL matrix of order    1 by    1
1
1   0.5000

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.4751
2     -0.7207     1.0762
3      0.8714    -0.0336     1.0588

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1            2            3
1    1.0373E+00
2    7.7683E-01   4.3352E-01
3    7.2405E-01   4.4189E-01  -9.1639E-07

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.0176
2     -0.0174     1.0189
3     -0.0010     0.0081     0.6853

GROUP NUMBER: 2

Group2: MZ twin pairs

MATRIX A
This is a computed FULL matrix of order    3 by    3
[=X*X']
1          2          3
1      2.1760    -1.0631     1.2854
2     -1.0631     1.6775    -0.6641
3      1.2854    -0.6641     1.8815

MATRIX C
This is a computed FULL matrix of order    3 by    3
[=Y*Y']
1          2          3
1      1.0759     0.8058     0.7510
2      0.8058     0.7914     0.7540
3      0.7510     0.7540     0.7195

MATRIX E
This is a computed FULL matrix of order    3 by    3
[=Z*Z']
1          2          3
1      1.0355    -0.0177    -0.0010
2     -0.0177     1.0384     0.0083
3     -0.0010     0.0083     0.4697

MATRIX H
This is a FULL matrix of order    1 by    1
1
1   0.5000

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.4751
2     -0.7207     1.0762
3      0.8714    -0.0336     1.0588

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1            2            3
1    1.0373E+00
2    7.7683E-01   4.3352E-01
3    7.2405E-01   4.4189E-01  -9.1639E-07

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.0176
2     -0.0174     1.0189
3     -0.0010     0.0081     0.6853

OBSERVED COVARIANCE MATRIX
X1         Y1         Z1         X2         Y2         Z2
X1      4.2476
Y1     -0.2804     3.3953
Z1      2.0121     0.0521     2.9585
X2      3.2865    -0.2430     2.0150     4.3932
Y2     -0.2102     2.3839     0.0968    -0.2028     3.4295
Z2      2.0209     0.0507     2.4486     2.0295     0.1149     2.8670

EXPECTED COVARIANCE MATRIX
X1         Y1         Z1         X2         Y2         Z2
X1      4.2874
Y1     -0.2751     3.5073
Z1      2.0353     0.0982     3.0708
X2      3.2519    -0.2574     2.0364     4.2874
Y2     -0.2574     2.4690     0.0899    -0.2751     3.5073
Z2      2.0364     0.0899     2.6010     2.0353     0.0982     3.0708

RESIDUAL MATRIX
X1      Y1      Z1      X2      Y2      Z2
X1  -0.0398
Y1  -0.0053 -0.1120
Z1  -0.0232 -0.0462 -0.1122
X2   0.0346  0.0143 -0.0213  0.1058
Y2   0.0471 -0.0851  0.0069  0.0723 -0.0779
Z2  -0.0155 -0.0392 -0.1524 -0.0059  0.0167 -0.2037

Function value of this group:     11.3182
Where the fit function is Maximum Likelihood

GROUP NUMBER: 3

Group3: DZ twin pairs

MATRIX A
This is a computed FULL matrix of order    3 by    3
[=X*X']
1          2          3
1      2.1760    -1.0631     1.2854
2     -1.0631     1.6775    -0.6641
3      1.2854    -0.6641     1.8815

MATRIX C
This is a computed FULL matrix of order    3 by    3
[=Y*Y']
1          2          3
1      1.0759     0.8058     0.7510
2      0.8058     0.7914     0.7540
3      0.7510     0.7540     0.7195

MATRIX E
This is a computed FULL matrix of order    3 by    3
[=Z*Z']
1          2          3
1      1.0355    -0.0177    -0.0010
2     -0.0177     1.0384     0.0083
3     -0.0010     0.0083     0.4697

MATRIX H
This is a FULL matrix of order    1 by    1
1
1   0.5000

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.4751
2     -0.7207     1.0762
3      0.8714    -0.0336     1.0588

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1            2            3
1    1.0373E+00
2    7.7683E-01   4.3352E-01
3    7.2405E-01   4.4189E-01  -9.1639E-07

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.0176
2     -0.0174     1.0189
3     -0.0010     0.0081     0.6853

OBSERVED COVARIANCE MATRIX
X1         Y1         Z1         X2         Y2         Z2
X1      4.3550
Y1     -0.3546     3.6842
Z1      2.0450     0.0979     3.1789
X2      2.1250     0.3296     1.4184     4.1568
Y2      0.2418     1.6410     0.4306    -0.2169     3.4314
Z2      1.3443     0.5013     1.7059     2.0165     0.1396     3.1266

EXPECTED COVARIANCE MATRIX
X1         Y1         Z1         X2         Y2         Z2
X1      4.2874
Y1     -0.2751     3.5073
Z1      2.0353     0.0982     3.0708
X2      2.1639     0.2742     1.3937     4.2874
Y2      0.2742     1.6302     0.4220    -0.2751     3.5073
Z2      1.3937     0.4220     1.6603     2.0353     0.0982     3.0708

RESIDUAL MATRIX
X1           Y1           Z1           X2           Y2
X1    6.7568E-02
Y1   -7.9488E-02   1.7684E-01
Z1    9.6869E-03  -3.0825E-04   1.0809E-01
X2   -3.8908E-02   5.5443E-02   2.4665E-02  -1.3062E-01
Y2   -3.2368E-02   1.0833E-02   8.6615E-03   5.8154E-02  -7.5898E-02
Z2   -4.9445E-02   7.9372E-02   4.5648E-02  -1.8873E-02   4.1338E-02

Z2
X1
Y1
Z1
X2
Y2
Z2    5.5810E-02

Function value of this group:     11.0339
Where the fit function is Maximum Likelihood

GROUP NUMBER: 4

Group4: Standardised solution

MATRIX A
This is a computed FULL matrix of order    3 by    3
[=X*X']
1          2          3
1      2.1760    -1.0631     1.2854
2     -1.0631     1.6775    -0.6641
3      1.2854    -0.6641     1.8815

MATRIX C
This is a computed FULL matrix of order    3 by    3
[=Y*Y']
1          2          3
1      1.0759     0.8058     0.7510
2      0.8058     0.7914     0.7540
3      0.7510     0.7540     0.7195

MATRIX D
This is a computed FULL matrix of order    3 by    3
[=\SQRT(\V2D(\D2V(P)))]
1          2          3
1      2.0706     0.0000     0.0000
2      0.0000     1.8728     0.0000
3      0.0000     0.0000     1.7524

MATRIX E
This is a computed FULL matrix of order    3 by    3
[=Z*Z']
1          2          3
1      1.0355    -0.0177    -0.0010
2     -0.0177     1.0384     0.0083
3     -0.0010     0.0083     0.4697

MATRIX G
This is a computed FULL matrix of order    3 by    3
[=\STND(T)]
1       2       3
1   1.0000 -0.5564  0.6353
2  -0.5564  1.0000 -0.3738
3   0.6353 -0.3738  1.0000

MATRIX H
This is a FULL matrix of order    1 by    1
1
1   0.5000

MATRIX I
This is an IDENTITY matrix of order    4 by    4

MATRIX N
This is a computed FULL matrix of order    3 by    3
[=\STND(V)]
1       2       3
1   1.0000 -0.0171 -0.0015
2  -0.0171  1.0000  0.0119
3  -0.0015  0.0119  1.0000

MATRIX P
This is a computed FULL matrix of order    3 by    3
[=A+C+E]
1          2          3
1      4.2874    -0.2751     2.0353
2     -0.2751     3.5073     0.0982
3      2.0353     0.0982     3.0708

MATRIX S
This is a computed FULL matrix of order    3 by    3
[=\STND(U)]
1       2       3
1   1.0000  0.8732  0.8536
2   0.8732  1.0000  0.9992
3   0.8536  0.9992  1.0000

MATRIX T
This is a computed FULL matrix of order    3 by    3
[=D~*A*D~]
1       2       3
1   0.5075 -0.2742  0.3542
2  -0.2742  0.4783 -0.2024
3   0.3542 -0.2024  0.6127

MATRIX U
This is a computed FULL matrix of order    3 by    3
[=D~*C*D~]
1       2       3
1   0.2509  0.2078  0.2070
2   0.2078  0.2256  0.2298
3   0.2070  0.2298  0.2343

MATRIX V
This is a computed FULL matrix of order    3 by    3
[=D~*E*D~]
1            2            3
1    2.4153E-01  -4.5754E-03  -2.8605E-04
2   -4.5754E-03   2.9606E-01   2.5342E-03
3   -2.8605E-04   2.5342E-03   1.5297E-01

MATRIX X
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.4751
2     -0.7207     1.0762
3      0.8714    -0.0336     1.0588

MATRIX Y
This is a LOWER TRIANGULAR matrix of order    3 by    3
1            2            3
1    1.0373E+00
2    7.7683E-01   4.3352E-01
3    7.2405E-01   4.4189E-01  -9.1639E-07

MATRIX Z
This is a LOWER TRIANGULAR matrix of order    3 by    3
1          2          3
1      1.0176
2     -0.0174     1.0189
3     -0.0010     0.0081     0.6853

*** WARNING! ***
Minimization may not be successful.  See above
CODE GREEN - it probably was OK

Your model has   18 estimated parameters and     42 Observed statistics

Chi-squared fit of model >>>>>>>    22.352
Degrees of freedom >>>>>>>>>>>>>        24
Probability >>>>>>>>>>>>>>>>>>>>     0.558
Akaike's Information Criterion >   -25.648
RMSEA >>>>>>>>>>>>>>>>>>>>>>>>>>     0.000

This problem used  0.2% of my workspace