! 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 ______________________________________________________________________________