A C E model fitted to the Heath (1989) data ! on alcohol consumption. ! Group 1.... Monozygotic twin pairs ! Anything after a '!' is a comment DAta NGroups=2 NInput_variables=2 NObservations=171 LAbels Alc_t1 Alc_t2 CMatrix 1.28 0.766 1.194 MATrices A FUll 2 6 B SYmmetric 6 6 COvariance_model A*B*A' / SPecification A 1 2 3 0 0 0 0 0 0 1 2 3 LAbels Col A At1 Ct1 Et1 At2 Ct2 Et2 LAbels Row A Pt1 Pt2 MAtrix B 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 LAbels Row B At1 Ct1 Et1 At2 Ct2 Et2 LAbels Col B At1 Ct1 Et1 At2 Ct2 Et2 OUtput RSiduals Group 2.... Dizygotic twin pairs DAta NInput_variables=2 NObservations=101 CMatrix 1.077 0.463 0.962 LAbels Alc_t1 Alc_t2 MATrices A FUll 2 6 =A(1) B SYmm 6 6 COvariance_model A*B*A' / MAtrix B 1 0 1 0 0 1 .5 0 0 1 0 1 0 0 1 0 0 0 0 0 1 LAbels row B At1 Ct1 Et1 At2 Ct2 Et2 LAbels col B At1 Ct1 Et1 At2 Ct2 Et2 STart .6 ALL OUtput RSidual Phenotypic interaction model, fit to Heath 1989 data. ! Female MZ Twins DAta NGroups=2 NInput_vars=2 NObservations=171 CMatrix 1.28 0.766 1.194 LAbels Alc_t1 Alc_t2 MATrices G FUll 2 6 P SYmm 6 6 B FUll 2 2 I IDentity 2 2 COvariance_model (I-B)~*(G*P*G')*(I-B)~'/ LAbels row G B4int_t1 B4int_t2 LAbels col G At1 Ct1 Et1 At2 Ct2 Et2 SPecification G 1 2 3 0 0 0 0 0 0 1 2 3 LAbels row P At1 Ct1 Et1 At2 Ct2 Et2 LAbels col P At1 Ct1 Et1 At2 Ct2 Et2 MAtrix P 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 LAbels col B B4int_t1 B4int_t2 LAbels row B Alc_t1 Alc_t2 SPecification B 0 4 4 0 OUtput RS Phenotypic interaction model, Heath alcohol data ! Female DZ twins DAta NInput_vars=2 NObservations=101 CM SY 1.077 0.463 0.962 MATrices G FUll 2 6 =G(1) P SYmm 6 6 B FUll 1 2 =b1 I IDentity 2 2 COvariance_model (I-B)~*(G*P*G')*(I-B)~'/ LAbels row P At1 Ct1 Et1 At2 Ct2 Et2 LAbels col P At1 Ct1 Et1 At2 Ct2 Et2 MAtrix P 1 0 1 0 0 1 .5 0 0 1 0 1 0 0 1 0 0 0 0 0 1 STart .6 g 1 1 - g(2,6) STart .1 b 1 2 BOundaries -.99 .99 4 BOundaries 0 5 1 2 3 OUtput RSiduals Age correction Sex limitation model MZ FEMALES DAta NGroups=5 NInput_vars=7 NObservations=43 CM FI=/home/ftp/pub/mx/examples/manual/drunkmzf.cov SElect 1 2 5 / MATrices F FUll 3 7 P SYmm 7 7 MOdel F*P*F' / SPecification F 1 2 3 0 0 0 4 0 0 0 3 2 1 4 0 0 0 0 0 0 9 MA P 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 OUtput RSiduals Age correction Sex limitation model MZ MALES DAta NInput_vars=7 NObservations=42 CM FI=/home/ftp/pub/mx/examples/manual/drunkmzm.cov SElect 1 2 5 / MATrices P SYmm 7 7 = P1 M FUll 3 7 MO M*P*M' / SPecification M 5 6 7 0 0 0 4 0 0 0 7 6 5 4 0 0 0 0 0 0 9 OUtput RSiduals Age correction Sex limitation model DZ FEMALES DAta NObservations=44 CM FI=/home/ftp/pub/mx/examples/manual/drunkdzf.cov SElect 1 2 5 / MATrices F FUll 3 7 =F1 P SYmm 7 7 MOdel F*P*F' / MA P 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 .5 0 0 0 0 1 0 0 0 0 0 0 1 OUtput RSiduals Age correction Sex limitation model DZ MALES DAta NObservations=38 CM FI=/home/ftp/pub/mx/examples/manual/drunkdzm.cov SElect 1 2 5 / MATrices M FUll 3 7 =M2 P SYmm 7 7 =P3 MO M*P*M' / OUtput RS Age correction Sex limitation model DZ OPP SEX DAta NObservations=39 CM FI=/home/ftp/pub/mx/examples/manual/drunkdzos.cov SElect 1 2 5 / MATrices P SYmm 7 7 O FUll 3 7 MO O*P*O' / SPecification O 1 2 3 0 0 0 4 0 0 0 7 6 5 4 0 0 0 0 0 0 9 MAtrix P 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 .5 0 0 0 0 1 0 0 0 0 0 0 1 !FRee P 6 1 !BOundary 0 0.5 P 6 1 BOundary 0 5 1 2 3 5 6 7 STart 2 ALL STart .1 O 1 7 STart 1 O 3 7 OUtput RS Simulated twin data. Raw ML estimation Data Ni=2 Ngroups=3 No=1000 Raw_data file=/home/ftp/pub/mx/examples/manual/mzasc.dat Matrices M Full 1 2 R Stan 2 2 free Mean M / Covariance R / Matrix M 0 0 Bound -.99 .99 R 1 2 OPtions rs End Dummy group to calculate expected cell proportions Data Ni=2 CTable 2 2 0 0 ! It's full of zeros so it 0 0 ! contributes zero to the function Matrices T Full 2 1 R Stan 2 2 =R1 Thresholds T / Covaraince R / Matrix T 1.282 1.282 Options rs End Calculate ascertainment correction Data ni=0 Matrices I iden 1 1 J izero 1 2 P full 2 2 = %P2 T full 1 1 Compute T*\ln(I-J*P*J') / Matrix T 2000 ! twice the sample size of group 1 Options User-defined rs End Assortative mating: Phillips data, test that d 1 1 is zero DAta NGroups=1 NInput_vars=12 NObservations=334 CM FI=/home/ftp/pub/mx/examples/manual/asmat.cov MATrices h SYmm 6 6 fr w SYmm 6 6 fr d FUll 6 6 fr M2 h | h*d'*w_ w*d*h | w / STart 1. h 1 1 h 2 2 h 3 3 h 4 4 h 5 5 h 6 6 STart 1. w 1 1 w 2 2 w 3 3 w 4 4 w 5 5 w 6 6 FIx d 1 1 OUtput RSidual Categorical data analysis. PACE model DAta Ninput=2 NGroup=3 CTable 2 2 11 8 8 72 MATrices A fu 2 6 B fu 2 2 I id 2 2 P SYmm 6 6 T fu 2 1 THresholds T / COvariances (I-B)~* A*P*A' *(I-B)~ / SPecification A 1 2 3 0 0 0 0 0 0 1 2 3 STart .6 All SPecification T 4 4 SPecification B 0 6 6 0 BOundary -.99 .99 6 MAtrix P 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 OUtput RSidual Test of categorical data analysis. DZ twins in ACE model DAta Ninput=2 CTable 2 2 10 9 9 72 MATrices A fu 2 6 =A1 B fu 2 2 =B1 I id 2 2 P SYmm 6 6 T fu 2 1 =T1 THresholds T / COvariances (I-B)~* A*P*A' *(I-B)~ / MAtrix P 1 0 1 0 0 1 .5 0 0 1 0 1 0 0 1 0 0 0 0 0 1 OUtput RSidual Constraint group to ensure a*a + c*c + e*e = 1 DAta COnstraint Ninput=1 MATrices S FUll 1 3 I IDentity 1 1 COnstraint I - S*S' / SPecification S 1 2 3 OUtput NOne Simple MX example file DAta NGroups=1 NObservations=150 NInput_vars=2 CM 1.2 .8 1.3 MATrices A FUll 2 1 D DIag 2 2 MOdel A*A' + D / SPecification A 1 0 SPecification D 0 3 OUtput RSiduals MU SPecification 1 A 1 2 OU Principal components ABA' with constraints ! to keep A orthogonal DAta NGroups=2 NInput_vars=3 NObservations=100 CM SY 1. .6 .9 .4 .2 .7 MATrices A FUll 3 3 B DIag 3 3 MOdel A*B*A'/ SPecification A 1 2 3 4 5 6 7 8 9 SPecification B 10 11 12 STart 1.0 A(1,1) A(2,2) A(3,3) B(1,1) to B(3,3) OUtput LS Here is the constraint A*A'=I DAta CON NInput_vars=3 MATrices A FUll 3 3 = A(1) I IDentity 3 3 MOdel A*A'-I/ OUtput LS Phenotypic interaction PACE model, Heath 1989 data ! Demonstration of RAM specification and output DATA NG=2 NInput=2 NObs=171 CM SY 1.280 0.766 1.194 MATRICES s SY 8 8 i id 8 8 a FU 8 8 f zi 2 8 MODEL F*(I-A)~*S*(I-A)~'*F'/ MA s 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 label row a a1 c1 e1 a2 c2 e2 p1 p2 label col a a1 c1 e1 a2 c2 e2 p1 p2 label row s a1 c1 e1 a2 c2 e2 p1 p2 label col s a1 c1 e1 a2 c2 e2 p1 p2 specify a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 4 ! This is where the parameters are 0 0 0 1 2 3 4 0 start .6 a 7 1 a 7 3 OU RS draw=mz.ram Group 2.... DZ twins DATA NI=2 NO=101 CM SY 1.077 0.463 0.962 MATRICES s SY 8 8 i id 8 8 a FU 8 8 = a1 f zi 2 8 MODEL F*(I-A)~*S*(I-A)~'*F'/ ma s 1 0 1 0 0 1 .5 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 label row s a1 c1 e1 a2 c2 e2 p1 p2 label col s a1 c1 e1 a2 c2 e2 p1 p2 BOund -.99 .99 3 BOund 0 5 1 2 OU RS draw=dz.ram ! ! ML fitting to raw data simulated ! with SAS, whose PROC COR COV gave: ! ! VARIABLE N MEAN STANDARD ! DEVIATION ! P1 1000 0.00182388 0.98499439 ! P2 1000 -0.98608262 1.40083917 ! P3 1000 2.05400385 1.79139557 ! ! COVARIANCE MATRIX ! P1 P2 P3 ! P1 0.970214 0.506058 0.620529 ! P2 0.506058 1.96235 0.807754 ! P3 0.620529 0.807754 3.2091 ! ! Cholesky for covariance structure ! ML example, calculation of likelihood for each observation. DAta NInput_vars=3 NObservations=1000 NGroups=1 RAw_data FIle=/home/ftp/pub/mx/examples/manual/mlped.raw MATrices M FUll 1 3 FRee S LOwer 3 3 FRee MEans M / COvariances S*S' / MAtrix_start_values S 1 .6 .8 .6 .0 .8 OUtput RM ! ! ML fitting to raw variable length data. ! ! Cholesky decomposition for the expected covariance matrix ! ! Also matrix expression for means, M1 ! - in this case just a simple vector with free parameters. ! Variable pedigree size ML example. DAta NInput_vars=3 NObservations=1000 NGroups=1 VL FI=/home/ftp/pub/mx/examples/manual/unbalanced.raw MATrices M FUll 1 3 FRee S LOwer 3 3 FRee M1 M / M2 S*S' / STart 1 s 1 1 s 2 2 s 3 3 OUtput RM Simple MX example file DAta NGroups=1 NObservations=150 NInput_variables=2 CMatrix 1.2 .8 1.3 MATRICES A FUll 2 1 D DIag 2 2 COvariance_model A*A' + D / SPecification A 1 2 SPecification D 0 3 OUtput ! ! Trivariate Cholesky 'Independent Pathways' model. ! ! Additive Genetic factors are group 1 matrix H ! Random Environ. factors are group 2 matrix E ! Common Environ. factors are group 3 matrix C ! ! Data are Extraversion, Neuroticism and CESD Depression ! This group JUST calculates, no fitting is done. ! Genetic factors DAta CAlculation NGroups=9 MATrices H Lower 3 3 FRee MOdel H*H' / OUtput Title 2nd Group also for calculation ! Specific Envt. DAta CAlculation MATrices E Lower 3 3 FRee MOdel E*E' / OUtput Title 3rd Group also for calculation ! Shared Envt. DAta CAlculation MATrices C Lower 3 3 FRee MOdel C*C' / OUtput ! ! Now get to the actual data, and use the results of ! groups 1, 2 and 3 (%E1 %E2 & %E3) ! Unmatched twins DAta NInput_vars=3 NObservations=449 CM SY .102216 -.021648 .0827805 -.005792 .0177622 .0138577 MAtrices G SYmm 3 3 = %E1 E SYmm 3 3 = %E2 C SYmm 3 3 = %E3 MOdel (G + E + C) / OUtput MZ twins with cotwins Extraversion Neuroticism and Depression DAta NInput_vars=6 no=456 cm .0887349 -.018651 0.08036 -.001031 .0185154 .0139989 .0366848 -.008858 -.002873 0.097803 .0013777 .0291787 .0110424 -.014907 .0818947 -0.00122 .0103675 .0050655 -.005258 .0172896 0.013687 MAtrices G SYmm 3 3 = %E1 E SYmm 3 3 = %E2 C SYmm 3 3 = %E3 MOdel (G + E + C| G + C _ G + C| G + E + C ) / OUtput RSiduals ! ! DZ twins with cotwins Extraversion Neuroticism and Depression DAta NInput_vars=6 NObservations=357 CM 0.100808 -0.02249 .0785764 -.003347 .0173292 .0150047 -0.00471 .0025537 -.002045 0.102181 .0032861 .0081708 .0078504 -.023836 .0808707 -.001514 .0053548 .0036505 -.005488 .0164667 .0143083 MATrices G SYmm 3 3 = %E1 E SYmm 3 3 = %E2 C SYmm 3 3 = %E3 h DIag 1 1 MOdel ! ! Covariance matrix bit. Note H as diag matrix of .5's ! that models DZ genet cov. By using the Kron operator, ! every element of G is multiplied by .5, in accordance with ! genetic theory that DZ twins share only half their genes. ! (G + E + C| H @ G + C _ H @ G + C| G + E + C ) / MA Half .5 STart .5 ALL BOundary -1 1 ALL OUtput RSiduals Calculation of standardized solution - Additive Genetic DAta ca MATrices A SYmm 3 3 =%e1 P SYmm 3 3 = %E4 MOdel A%P / OUtput RS Calculation of standardized solution - Shared Environment DAta ca MATrices C SYmm 3 3 =%e3 P SYmm 3 3 = %E4 MOdel C%P / OUtput RS Calculation of standardized solution - Random Environment DAta ca MATrices E SYmm 3 3 =%e2 P SYmm 3 3 = %E4 MOdel E%P / OUtput RS ! ! Rose Fear data: Social phobia on twins and parents ! ! Twins and parents: Genetic and cultural transmission model. ! P--P assortment ! Reduced P-C genetic correlation is ! commented out group 7 ! Group 1 - Assortative mating constraints DAta CAlculation NGroups=10 MATrices A FUll 1 3 D STandardized 3 3 M FUll 1 1 COmpute (A*D)'*M*(A*D) / LAbels Column A A C E LAbels Row A P SPecification A 1 2 3 MAtrix A .7 .5 .5 LAbels Row D A C E LAbels Col D A C E SPecification D 4 0 0 SPecification M 5 OUtput Group 2 - construct the overall covariance matrix of parents' ! latent variables DAta CAlculate MATrices D STan 3 3 = D1 E FUll 3 3 = %E1 COmpute (D|E _E|D) / LAbels row E Ah Ch Eh LAbels col E Aw Cw Ew OUtput Group 3 - precalculate parents model DAta CAlculate MATrices P SYmmetric 6 6 = %E2 G FUll 4 6 R DIagonal 4 4 COmpute G*P*G' + R/ ! For reduced genetic correlation between parent & child model ! parts commented out with ! are needed SPecification G 1 2 3 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 !99 0 0 0 0 0 0 0 0 0 0 0 !0 0 0 99 0 0 LAbels row G PH PW AH' AW' LAbels column G AH CH EH AW CW EW VAlue 1 G 3 1 G 4 4 ! SPecification r ! 0 0 100 100 OUtput Group 4 - precalculate middle of model DAta CAlculate MATrices P SYmmetric 4 4 = %E3 F FUll 5 4 S SYmmetric 5 5 COmpute F*P*F'+S / LAbels row F PH PW AC1 AC2 CT LAbels col F PH PW AH' AW' SPecification F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 0 0 VAlue 1 F 1 1 F 2 2 VAlue .5 F 3 3 F 3 4 F 4 3 F 4 4 LAbels row S PH PW AC1 AC2 CT LAbels col S PH PW AC1 AC2 CT SPecification S 0 0 0 0 0 8 0 0 0 8 0 0 0 0 9 STart .5 S 3 3 S 4 4 STart 1 s 5 5 OUtput G5 - Constraints on genetic environmental variance and ! covariance in children DAta COnstraint NInput=2 MATrices D STandardized 3 3 = D1 !Correlation matrix of AH CH EH H FUll 5 5 = %E4 !Correlation matrix of PH PW AC1 AC2 CE Y IZero 2 3 !Filter matrix to get corr matrix AH CH Z ZIden 2 5 !Filter matrix to get corr matrix AC2 CE COnstraint Y*D*Y' - Z*H*Z' / OUtput NOne G6 - Fourth constraint for standardization DAta COnstraint NInput_vars=1 MATrices H FUll 5 5 = %E4 Z IZ 1 5 I IDentity 1 1 COnstraint I - Z*H*Z' / OUtput NOne Group 7 new constraint for genetic transmission parameter ! The commented out parts of this group are needed if reduced ! genetic correlation between parent and child model is to be ! fitted, and the covariance statement should be commented out DAta CAlculation ni=1 ! Change the above to DAta COnstraint ni=1 for Rg model MATrices A SYmm 1 1 B SYmm 1 1 I IDen 1 1 COnstraint a / ! Delete the above line for Rg model and uncomment ! the next five lines: !constraint (a*a+b)-i / !SPecification a !99 !SPecification b !100 OUtput None Group 8 - Rose fear data: MZ twins & their parents DAta NInput=4 NObservations=144 LAbels Husband Wife MZ_Twin1 MZ_Twin2 CMatrix .903 .113 1.1053 .2547 .0864 .9467 .1602 .2052 .4938 .8947 MATrices C FUll 5 5 = %E4 L FUll 4 5 V DIagonal 4 4 !Matrix of standard deviations E DIagonal 4 4 !Matrix to add random environment for children COvariance_Model V*(L*C*L'+E*E)*V'/ SPecification V 10 10 10 10 MAtrix V 1 1 1 1 LAbels row V PH PW PT1 PT2 LAbels column V PH PW PT1 PT2 LAbels row E Dummy Dummy Et1 Et2 LAbels column E Dummy Dummy Et1 Et2 SPecification E 0 0 3 3 BOundary 1 5 v 1 1 v 2 2 v 3 3 V 4 4 LAbels row L Ph Pw Pmzt1 Pmzt2 LAbels column L Ph Pw At1 At2 Ct SPecification L 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 1 0 2 VAlue 1 L 1 1 L 2 2 OUtput RSiduals Group 9 - Rose social criticism DZ twins & their parents DAta NInput_vars=4 NObservations=106 LAbels Husband Wife DZ_Twin1 DZ_Twin2 CM 1.0811 .2111 .9063 .1443 .2398 1.2079 .1001 .1551 .3246 1.0318 MATrices C FUll 5 5 = %E4 L FUll 4 5 V DIag 4 4 = V8 E DIag 4 4 = E8 COvariances V*(L*C*L'+E*E)*V'/ SPecification L 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 1 2 VAlue 1 L 1 1 L 2 2 LAbels row E Dummy Dummy Et1 Et2 LAbels column E Dummy Dummy Et1 Et2 LAbels row L Ph Pw Pdzt1 Pdzt2 LAbels column L Ph Pw At1 At2 Ct STart 1.5 v 1 1 v 2 2 v 3 3 V 4 4 BOundary .5 2 v 1 1 v 2 2 v 3 3 V 4 4 OUtput RSiduals IT=500 Group 10 - summary printout of parameter estimates DAta CAlculation MATrices P FUll 1 10 COmpute P/ SPecification P 1 2 3 4 5 6 7 8 9 10 LAbels c p a c e s mu zf zm res(a) res(c) vp BOundary -.99 .99 4 5 6 7 BOundary 0 1 1 2 3 8 9 OUtput MUltiple ! ! Re-fit the model with Father-child and Mother-child ! cultural transmission set equal ! EQuate f 4 5 1 f 4 5 2 OUtput ! ! User defined fit function - least squares ! User defined function to fit to a correlation matrix ! by least squares DAta NInput=3 NGroupies=1 CMatrix SYmm 1 .2 1 .3 .4 1 MATrices A SYmm 3 3 = %O1 B STan 3 3 FRee MOdel \tr((a-b)*(a-b))/ OUtput USer RSidjools