1. Genetic Growth Curve Models Practica Boulder, March 2008 Irene Rebollo & Gitta Lubke & Mike Neale VU Amsterdam NL & Notre Dame, US & VCU, US

2. Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Agg91 2 Agg95 2 Agg97 2 Agg00 2 i s EiEi CiCi AiAi 111 aiai cici eiei EsEs CsCs AsAs 111 eses cscs asas e is c is a is AiAi CiCi EiEi AsAs CsEsEs 1 11111 eiei cici aiai e is c is a is asas cscs eses 0.5/1 1 1 Genetic Growth Curve Model

3. Agg91 2 Agg95 2 Agg97 2 Agg00 2 i 1111 ViVi s 0234.5 VsVs r is 0000 αiαi αsαs e1e1 e2e2 e3e3 e4e4 1. Phenotypic Growth Curve Model

4. 1. Phenotypic Growth Curve Model: Matrices Agg91 2 Agg95 2 Agg97 2 Agg00 2 i 1111 ViVi s 0234.5 VsVs r is 0000 αiαi αsαs e1e1 e2e2 e3e3 e4e4 phenLingrow_lib08.mx RUN

5. 1. Phenotypic Growth Curve Model: Matrices Agg91 2 Agg95 2 Agg97 2 Agg00 2 i 1111 ViVi s 0234.5 VsVs r is 0000 αiαi αsαs e1e1 e2e2 e3e3 e4e4 COVARIANCES MEANS

6. 1. Phenotypic Growth Curve Model: Run! Agg91 2 Agg95 2 Agg97 2 Agg00 2 i 1111 12.3 s 0234.5 0.4 -1.18 10.03 -.38 9.9 7.45.45.8 FIT: Δ χ 2 (5)= 28.78, p<.01 RMSEA =.0364 POSSIBLE SUBMODELS: 1.Sig. Variation on Slope? 2.Sig i-s covariance? 3.Age effect = across surveys? 4.Significant change across time (α s )?  All significant! phenLingrow_lib08.mx

7. 2. Twin Correlations on the Growth Curve Model i1i1 s1s1 i2i2 s2s2 i1i1 vivi s1s1 r is vsvs i2i2 vivi s2s2 vsvs Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Vi Vs r is Agg91 2 Agg95 2 Agg97 2 Agg00 2 is VsVi r is (Co)Variance matrix between Intercept & Slope: 1. Phenotypic, within twin co(variances)

8. 2. Twin Correlations on the Growth Curve Model i1i1 s1s1 i2i2 s2s2 i1i1 vivi s1s1 r is vsvs i2i2 r ii vivi s2s2 r ss r is vsvs Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Vi Vs r is Agg91 2 Agg95 2 Agg97 2 Agg00 2 is VsVi r is (Co)Variance matrix between Intercept & Slope: 2. Cross twin-within trait: i 1 -i 2 & s 1 -s 2 i1i1 s1s1 i2i2 s2s2 i1i1 vivi s1s1 r is vsvs i2i2 r ii vivi s2s2 r ss r is vsvs MZDZ

9. 2. Twin Correlations on the Growth Curve Model i1i1 s1s1 i2i2 s2s2 i1i1 vivi s1s1 r is vsvs i2i2 r ii r si vivi s2s2 r is r ss r is vsvs Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Vi Vs r is Agg91 2 Agg95 2 Agg97 2 Agg00 2 is VsVi r is (Co)Variance matrix between Intercept & Slope: 3. Cross twin-cross trait: i 1 -s 2 & s 1 -i 2 i1i1 s1s1 i2i2 s2s2 i1i1 vivi s1s1 r is vsvs i2i2 r ii r si vivi s2s2 r is r ss r is vsvs MZDZ

10. 2. Twin Correlations on the Growth Curve Model TWLingrow_lib08.mx RUN Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Vi Vs Agg91 2 Agg95 2 Agg97 2 Agg00 2 is VsVi

11. 2. Twin Correlations: Matrices (for covariance structure) COMMON MATRICES Uncorrelated Residuals ZYGOSITY SPECIFIC Residuals Tw1 Residuals Tw2 MZ Sym DZ Sym COVARIANCE (I@F)&M + (I@R) ; COVARIANCE (I@F)&S + (I@R) ;

12. 2. Twin Correlations: Script & Output MZ Sym DZ Sym CORRELATIONS FOR MODEL SELECTION

13. 2. Twin Correlations: Script & Output MZ Sym DZ Sym COVARIANCES FOR STARTING VALUES

14. Agg91 1 Agg95 1 Agg97 1 Agg00 1 i s Agg91 2 Agg95 2 Agg97 2 Agg00 2 i s EiEi CiCi AiAi 111 aiai cici eiei EsEs CsCs AsAs 111 eses cscs asas e is c is a is AiAi CiCi EiEi AsAs CsEsEs 1 11111 eiei cici aiai e is c is a is asas cscs eses 0.5/1 1 1 3. Genetic Growth Curve Model

15. Lingrow_lib08.mx RUN 3. Genetic Growth Curve Model

16. 3. Genetic Growth Curve Model: Matrices M = A+C+E | A+C _ A+C | A+C+E; MZDZ S = A+C+E | H@A+C _ H@A+C | A+C+E; COVARIANCE (I@F)&M + (I@R) ;COVARIANCE (I@F)&S + (I@R) ;

17. 3. Genetic Growth Curve Model: Script & Output In Matrix K: %V i %V s %S is A680 C484465 E454735 Exercise: Use the option Multiple to Test for genetic effects on: -Covariance i-s -Variance I -Variance S

18. 3. Genetic Growth Curve Model: Model Fitting Results MODEL-2LLDFvsχ2χ2 dfp FULL 73945.47313626 a si =0 73945.47313627101.986 a i =0 73946.068136282.5951.440 a s =0 73947.2841362931.2161.270