! Phenotypic Simplex Model Neale & Cardon (1992) Example
 
 
 The following MX script lines were read for group  1
 
 #DEFINE NVAR 6
 G1: SIMPLEX STRUCTURE
 DATA NINPUT_VARS=6 NOBSERVATIONS=66 NGROUPS=1
 LABELS
 WEIGHT1 WEIGHT2 WEIGHT3 WEIGHT4 WEIGHT5 WEIGHT6
 CMATRIX
 51.470
 53.867 58.150
 55.399 59.709 63.658
 58.573 63.124 67.071 72.820
 56.597 60.644 65.104 70.421 71.634
 52.222 55.930 60.485 66.239 67.360 66.855
 BEGIN MATRICES;
 A DIAG NVAR NVAR FREE      ! INNOVATIONS
 B LOWER NVAR NVAR FREE   ! BETA TRANSMISSIONS
 U DIAG NVAR NVAR FREE     ! MEASUREMENT ERROR VARIANCES
 I IDEN NVAR NVAR               ! IDENTITY MATRIX
 END MATRICES;
 SPECIFY B
 0
 101 0
 0 102 0
 0 0 103 0
 0 0 0 104 0
 0 0 0 0 105 0
 EQ U 1 1 U 2 2 U 3 3 U 4 4 U 5 5 U 6 6 !MEASUREMENT ERROR EQUATED ACROSS OCCASIONS
 BEGIN ALGEBRA;
 C = (I-B)~*(A*A')*(I-B)~'+U*U';   !PHENOTYPIC COVARIANCE MATRIX
 D = (I-B)~*(A*A')*(I-B)~';    !COVARIANCE DUE TO SIMPLEX PROCESS
 E = U*U';       !MEASUREMENT ERROR VARIANCE
 F = \D2V(C);       !PHENOTYPIC VARIANCE AT EACH TIME POINT
 G = \D2V(D);       !VARIANCE DUE TO SIMPLEX PROCESS AT EACH TIME POINT
 H = \D2V(E);       !ERROR VARIANCE
 J = \D2V(A*A');      !INNOVATION VARIANCE AT EACH TIME POINT
 END ALGEBRA;
 LABELS ROW F TOTAL_VARIANCE
 LABELS COL F VAR1 VAR2 VAR3 VAR4 VAR5 VAR6
 LABELS ROW G LATENT_VARIANCE
 LABELS COL G VAR(ETA1) VAR(ETA2) VAR(ETA3) VAR(ETA4) VAR(ETA5) VAR(ETA6)
 LABELS ROW H MEASUREMENT_ERROR_VARIANCE
 LABELS COL H ERROR1 ERROR2 ERROR3 ERROR4 ERROR5 ERROR6
 LABELS ROW J INNOVATION_VARIANCE
 LABELS COL J INNOV1 INNOV2 INNOV3 INNOV4 INNOV5 INNOV6
 COVARIANCES C /
 OPTIONS RS
 OPTIONS MULTIPLE
 START 7 ALL
 END
 
 
 PARAMETER SPECIFICATIONS
 
 GROUP NUMBER:           1
 
G1: Simplex structure                                                                                                           
 
 MATRIX A
 This is a DIAGONAL matrix of order    6 by    6
    1 2 3 4 5 6
 1  1
 2  0 2
 3  0 0 3
 4  0 0 0 4
 5  0 0 0 0 5
 6  0 0 0 0 0 6
 
 MATRIX B
 This is a LOWER TRIANGULAR matrix of order    6 by    6
      1   2   3   4   5   6
 1    0
 2  101   0
 3    0 102   0
 4    0   0 103   0
 5    0   0   0 104   0
 6    0   0   0   0 105   0
 
 MATRIX C
 This is a computed FULL matrix of order    6 by    6
 It has no free parameters specified
 
 MATRIX D
 This is a computed FULL matrix of order    6 by    6
 It has no free parameters specified
 
 MATRIX E
 This is a computed FULL matrix of order    6 by    6
 It has no free parameters specified
 
 MATRIX F
 This is a computed FULL matrix of order    1 by    6
 It has no free parameters specified
 
 MATRIX G
 This is a computed FULL matrix of order    1 by    6
 It has no free parameters specified
 
 MATRIX H
 This is a computed FULL matrix of order    1 by    6
 It has no free parameters specified
 
 MATRIX I
 This is an IDENTITY matrix of order    6 by    6
 
 MATRIX J
 This is a computed FULL matrix of order    1 by    6
 It has no free parameters specified
 
 MATRIX U
 This is a DIAGONAL matrix of order    6 by    6
     1  2  3  4  5  6
 1  28
 2   0 28
 3   0  0 28
 4   0  0  0 28
 5   0  0  0  0 28
 6   0  0  0  0  0 28
 
 
 
 
 MX PARAMETER ESTIMATES
 
 GROUP NUMBER:           1
 
G1: Simplex structure                                                                                                           
 
 MATRIX A
 This is a DIAGONAL matrix of order    6 by    6
             1          2          3          4          5          6
 1     -7.1650
 2      0.0000    -1.2246
 3      0.0000     0.0000     1.4396
 4      0.0000     0.0000     0.0000     1.3626
 5      0.0000     0.0000     0.0000     0.0000     1.8095
 6      0.0000     0.0000     0.0000     0.0000     0.0000    -1.8093
 
 MATRIX B
 This is a LOWER TRIANGULAR matrix of order    6 by    6
             1          2          3          4          5          6
 1      0.0000
 2      1.0492     0.0000
 3      0.0000     1.0292     0.0000
 4      0.0000     0.0000     1.0559     0.0000
 5      0.0000     0.0000     0.0000     0.9688     0.0000
 6      0.0000     0.0000     0.0000     0.0000     0.9420     0.0000
 
 MATRIX C
 This is a computed FULL matrix of order    6 by    6
 [=(I-B)~*(A*A')*(I-B)~'+U*U']
             1          2          3          4          5          6
 1     51.4700    53.8650    55.4365    58.5374    56.7132    53.4241
 2     53.8650    58.1504    59.7099    63.0498    61.0849    57.5423
 3     55.4365    59.7099    63.6576    67.0777    64.9873    61.2184
 4     58.5374    63.0498    67.0777    72.8197    70.4213    66.3373
 5     56.7132    61.0849    64.9873    70.4213    71.6344    67.3545
 6     53.4241    57.5423    61.2184    66.3373    67.3545    66.8550
 
 MATRIX D
 This is a computed FULL matrix of order    6 by    6
 [=(I-B)~*(A*A')*(I-B)~']
             1          2          3          4          5          6
 1     51.3368    53.8650    55.4365    58.5374    56.7132    53.4241
 2     53.8650    58.0172    59.7099    63.0498    61.0849    57.5423
 3     55.4365    59.7099    63.5244    67.0777    64.9873    61.2184
 4     58.5374    63.0498    67.0777    72.6865    70.4213    66.3373
 5     56.7132    61.0849    64.9873    70.4213    71.5012    67.3545
 6     53.4241    57.5423    61.2184    66.3373    67.3545    66.7218
 
 MATRIX E
 This is a computed FULL matrix of order    6 by    6
 [=U*U']
          1       2       3       4       5       6
 1   0.1332  0.0000  0.0000  0.0000  0.0000  0.0000
 2   0.0000  0.1332  0.0000  0.0000  0.0000  0.0000
 3   0.0000  0.0000  0.1332  0.0000  0.0000  0.0000
 4   0.0000  0.0000  0.0000  0.1332  0.0000  0.0000
 5   0.0000  0.0000  0.0000  0.0000  0.1332  0.0000
 6   0.0000  0.0000  0.0000  0.0000  0.0000  0.1332
 
 MATRIX F
 This is a computed FULL matrix of order    1 by    6
 [=\D2V(C)]
                       VAR1       VAR2       VAR3       VAR4       VAR5
 TOTAL_VARIANCE     51.4700    58.1504    63.6576    72.8197    71.6344
 
                       VAR6
 TOTAL_VARIANCE     66.8550
 
 MATRIX G
 This is a computed FULL matrix of order    1 by    6
 [=\D2V(D)]
                   VAR(ETA1)  VAR(ETA2)  VAR(ETA3)  VAR(ETA4)  VAR(ETA5)
 LATENT_VARIANCE     51.3368    58.0172    63.5244    72.6865    71.5012
 
                   VAR(ETA6)
 LATENT_VARIANCE     66.7218
 
 MATRIX H
 This is a computed FULL matrix of order    1 by    6
 [=\D2V(E)]
                              ERROR1  ERROR2  ERROR3  ERROR4  ERROR5  ERROR6
 MEASUREMENT_ERROR_VARIANCE   0.1332  0.1332  0.1332  0.1332  0.1332  0.1332
 
 MATRIX I
 This is an IDENTITY matrix of order    6 by    6
 
 MATRIX J
 This is a computed FULL matrix of order    1 by    6
 [=\D2V(A*A')]
                          INNOV1     INNOV2     INNOV3     INNOV4     INNOV5
 INNOVATION_VARIANCE     51.3368     1.4996     2.0725     1.8568     3.2744
 
                          INNOV6
 INNOVATION_VARIANCE      3.2735
 
 MATRIX U
 This is a DIAGONAL matrix of order    6 by    6
          1       2       3       4       5       6
 1   0.3650
 2   0.0000  0.3650
 3   0.0000  0.0000  0.3650
 4   0.0000  0.0000  0.0000  0.3650
 5   0.0000  0.0000  0.0000  0.0000  0.3650
 6   0.0000  0.0000  0.0000  0.0000  0.0000  0.3650
 
 OBSERVED COVARIANCE MATRIX
             WEIGHT1    WEIGHT2    WEIGHT3    WEIGHT4    WEIGHT5    WEIGHT6
 WEIGHT1     51.4700
 WEIGHT2     53.8670    58.1500
 WEIGHT3     55.3990    59.7090    63.6580
 WEIGHT4     58.5730    63.1240    67.0710    72.8200
 WEIGHT5     56.5970    60.6440    65.1040    70.4210    71.6340
 WEIGHT6     52.2220    55.9300    60.4850    66.2390    67.3600    66.8550
 
 
 EXPECTED COVARIANCE MATRIX
             WEIGHT1    WEIGHT2    WEIGHT3    WEIGHT4    WEIGHT5    WEIGHT6
 WEIGHT1     51.4700
 WEIGHT2     53.8650    58.1504
 WEIGHT3     55.4365    59.7099    63.6576
 WEIGHT4     58.5374    63.0498    67.0777    72.8197
 WEIGHT5     56.7132    61.0849    64.9873    70.4213    71.6344
 WEIGHT6     53.4241    57.5423    61.2184    66.3373    67.3545    66.8550
 
 RESIDUAL MATRIX
               WEIGHT1      WEIGHT2      WEIGHT3      WEIGHT4      WEIGHT5
 WEIGHT1   -9.4529E-06
 WEIGHT2    2.0419E-03  -3.7238E-04
 WEIGHT3   -3.7498E-02  -8.5098E-04   4.1583E-04
 WEIGHT4    3.5613E-02   7.4226E-02  -6.6721E-03   2.9321E-04
 WEIGHT5   -1.1617E-01  -4.4093E-01   1.1669E-01  -3.4745E-04  -3.6020E-04
 WEIGHT6   -1.2021E+00  -1.6123E+00  -7.3340E-01  -9.8300E-02   5.5142E-03
 
               WEIGHT6
 WEIGHT1
 WEIGHT2
 WEIGHT3
 WEIGHT4
 WEIGHT5
 WEIGHT6    2.7260E-05
 
 Function value of this group:     12.9946
 Where the fit function is Maximum Likelihood                 
 
 Your model has   12 estimated parameters and     21 Observed statistics

 
 Chi-squared fit of model >>>>>>>    12.995
 Degrees of freedom >>>>>>>>>>>>>         9
 Probability >>>>>>>>>>>>>>>>>>>>     0.163
 Akaike's Information Criterion >    -5.005
 RMSEA >>>>>>>>>>>>>>>>>>>>>>>>>>     0.082



 

 
 

 

 

 
 This problem used  0.0% of my workspace
 
 Task                     Time elapsed (DD:HH:MM:SS)
 Reading script & data      0: 0: 0: 0.06
 Execution                  0: 0: 0: 1.15
 TOTAL                      0: 0: 0: 1.21
 
Total number of warnings issued:           0
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