Genetic simplex model: practical

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Presentation transcript:

Genetic simplex model: practical Sanja Franic, Conor Dolan

Practical: estimate the genetic and environmental contributions to temporal stability and change in full-scale IQ measured at four time points (mean ages 5.5, 6.8, 9.7, 12.2, SDs .3, .19, .43, .24) N = 562 twin pairs (261 MZ, 301 DZ) The proportions of observed FSIQ data: 0.812, 0.295, 0.490, 0.828 (MZ twin 1) 0.812, 0.295, 0.490, 0.828 (MZ twin 2) 0.774, 0.379, 0.598, 0.797 (DZ twin1) 0.774, 0.379, 0.598, 0.797 (DZ twin 2)

Models Saturated Model - estimate means (subject to twin1-twin2 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4

Models Saturated Model - estimate means (subject to twin1-twin1 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4 How many parameters?

Models Saturated Model - estimate means (subject to twin1-twin1 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 ( 8*(8-1)/2 + 8 ) * 2 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4 How many parameters?

Models Saturated Model - estimate means (subject to twin1-twin1 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 ( 8*(8-1)/2 + 8 ) * 2 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4 How many parameters? 4

Models Saturated Model - estimate means (subject to twin1-twin1 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 ( 8*(8-1)/2 + 8 ) * 2 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4 How many parameters? 76 4

Models Saturated Model - estimate means (subject to twin1-twin1 equality constraints), variances and covariances IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 var1 cov21 var2 cov31 cov32 var3 cov41 cov42 cov43 var4 cov51 cov52 cov53 cov54 var5 cov61 cov62 cov63 cov64 cov65 var6 IQ23 cov71 cov72 cov73 cov74 cov75 cov76 var7 IQ24 cov81 cov82 cov83 cov84 cov85 cov86 cov87 var8 ( 8*(8-1)/2 + 8 ) * 2 different over MZ & DZ IQ11 IQ21 IQ31 IQ41 IQ12 IQ22 IQ32 IQ42 mean m1 m2 m3 m4 How many parameters? 76 4

Models SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC 2) ACE Cholesky Model - depicting only A component to avoid clutter - means subject to same equality constraints as in the saturated model SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC .5SA+SC SA+SC+SE

Models SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 2) ACE Cholesky Model - depicting only A component to avoid clutter - means subject to same equality constraints as in the saturated model SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 d41 d42 d43 d44

Models SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 2) ACE Cholesky Model - depicting only A component to avoid clutter - means subject to same equality constraints as in the saturated model SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 d41 d42 d43 d44 How many parameters?

Models SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 2) ACE Cholesky Model - depicting only A component to avoid clutter - means subject to same equality constraints as in the saturated model SA = DADAt DA = d11 0 0 0 d21 d22 0 0 d31 d32 d33 0 d41 d42 d43 d44 How many parameters? 34

Models SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC 3) Simplex Model - the genetic A simplex: 3 + 4 = 7 parameters SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC .5SA+SC SA+SC+SE SA = (I-BA) YA (I-BA) t + QA

Models SA = (I-BA) YA (I-BA) t + QA 3) Simplex Model s2z1 s2z2 s2z3 s2z2 s2z3 s2z4 bA21 bA32 bA43 s2a1 s2a2 s2a3 s2a4 SA = (I-BA) YA (I-BA) t + QA

Models SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC 3) Simplex Model - the genetic C simplex: 3 + 4 = 7 parameters SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC .5SA+SC SA+SC+SE SC = (I-BC) YC (I-BC) t + QC

Models SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC 3) Simplex Model - the genetic E model: 4 parameters SMZ = SA+SC+SE SA+SC SA+SC SA+SC+SE SDZ = SA+SC+SE .5SA+SC .5SA+SC SA+SC+SE SE = QE

faculty/sanja/2016/Simplex/Practical/simplexPractical.R

Saturated model: Rmz [1,] 1.000 0.650 0.523 0.409 0.769 0.510 0.482 0.455 [2,] 0.650 1.000 0.748 0.608 0.655 0.696 0.665 0.582 [3,] 0.523 0.748 1.000 0.775 0.609 0.745 0.840 0.757 [4,] 0.409 0.608 0.775 1.000 0.549 0.723 0.747 0.799 [5,] 0.769 0.655 0.609 0.549 1.000 0.572 0.550 0.613 [6,] 0.510 0.696 0.745 0.723 0.572 1.000 0.782 0.658 [7,] 0.482 0.665 0.840 0.747 0.550 0.782 1.000 0.760 [8,] 0.455 0.582 0.757 0.799 0.613 0.658 0.760 1.000 Rdz [1,] 1.000 0.603 0.475 0.471 0.641 0.397 0.201 0.248 [2,] 0.603 1.000 0.661 0.673 0.298 0.481 0.317 0.396 [3,] 0.475 0.661 1.000 0.737 0.283 0.374 0.483 0.469 [4,] 0.471 0.673 0.737 1.000 0.258 0.346 0.368 0.501 [5,] 0.641 0.298 0.283 0.258 1.000 0.481 0.361 0.345 [6,] 0.397 0.481 0.374 0.346 0.481 1.000 0.627 0.635 [7,] 0.201 0.317 0.483 0.368 0.361 0.627 1.000 0.707 [8,] 0.248 0.396 0.469 0.501 0.345 0.635 0.707 1.000 5.5y 6.8y 9.7y 12.2y 0.769 0.696 0.840 0.799 MZ FSIQ correlation (FIML estimates) 0.641 0.481 0.483 0.501 DZ FSIQ correlation (FIML estimates)

ACE Cholesky model: RA_est 5.5y 6.8y 9.7y 12.2y 1.000 0.939 0.909 0.802 0.939 1.000 0.997 0.959 0.909 0.997 1.000 0.978 0.802 0.959 0.978 1.000 RC_est 5.5y 6.8y 9.7y 12.2y 1.000 0.610 0.295 0.388 0.610 1.000 0.609 0.651 0.295 0.609 1.000 0.767 0.388 0.651 0.767 1.000 RE_est 5.5y 6.8y 9.7y 12.2y 1.000 0.107 -.057 0.020 0.107 1.000 0.233 0.150 -.057 0.233 1.000 0.126 0.020 0.150 0.126 1.000

SA = (I-BA) YA (I-BA) t + QA Simplex model: YA [1,] 62.926 0.000 0 0 [2,] 0.000 32.775 0 0 [3,] 0.000 0.000 0 0 [4,] 0.000 0.000 0 0 BA [1,] 0.000 0.000 0.000 0 [2,] 1.191 0.000 0.000 0 [3,] 0.000 1.058 0.000 0 [4,] 0.000 0.000 0.913 0 QA (fixed) [1,] 0 0 0 0 [2,] 0 0 0 0 [3,] 0 0 0 0 [4,] 0 0 0 0 SA = (I-BA) YA (I-BA) t + QA

SC = (I-BC) YC (I-BC) t + QC Simplex model: YC [1,] 103.218 0.000 0.00 0.000 [2,] 0.000 15.587 0.00 0.000 [3,] 0.000 0.000 38.31 0.000 [4,] 0.000 0.000 0.00 23.119 BC [1,] 0.000 0.000 0.000 0 [2,] 0.468 0.000 0.000 0 [3,] 0.000 0.614 0.000 0 [4,] 0.000 0.000 0.691 0 QC (fixed) [1,] 0 0 0 0 [2,] 0 0 0 0 [3,] 0 0 0 0 [4,] 0 0 0 0 SC = (I-BC) YC (I-BC) t + QC

SE = QE Simplex model: YE (fixed) [1,] 0 0 0 0 [2,] 0 0 0 0 [1,] 0 0 0 0 [2,] 0 0 0 0 [3,] 0 0 0 0 [4,] 0 0 0 0 BE (fixed) QE [1,] 48.95 0.000 0.000 0.000 [2,] 0.00 56.691 0.000 0.000 [3,] 0.00 0.000 44.331 0.000 [4,] 0.00 0.000 0.000 44.897 SE = QE

Simplex model: Standardized variance components 5.5y 6.8y 9.7y 12.2y h2 0.293 0.562 0.584 0.550 Increasing c2 0.480 0.176 0.226 0.233 Decreasing e2 0.228 0.261 0.190 0.217 About constant

Simplex model: Phenotypic covariance between age 9.7 and 12.2 equals 123.271 Contributions of A to 123.271 is 77.4% Contributions of A to 123.271 is 22.6% Contributions of E to 123.271 is 0% Conclude? > round(SA_est/Sph_est,3) [1,] 0.293 0.608 0.728 0.779 [2,] 0.608 0.562 0.846 0.879 [3,] 0.728 0.846 0.584 0.774 [4,] 0.779 0.879 0.774 0.550 > round(SC_est/Sph_est,3) [1,] 0.480 0.392 0.272 0.221 [2,] 0.392 0.176 0.154 0.121 [3,] 0.272 0.154 0.226 0.226 [4,] 0.221 0.121 0.226 0.233 > round(SE_est/Sph_est,3) [1,] 0.228 0.000 0.00 0.000 [2,] 0.000 0.261 0.00 0.000 [3,] 0.000 0.000 0.19 0.000 [4,] 0.000 0.000 0.00 0.217 Standardized variance components 5.5y 6.8y 9.7y 12.2y h2 0.293 0.562 0.584 0.550 Increasing c2 0.480 0.176 0.226 0.233 Decreasing e2 0.228 0.261 0.190 0.217 About constant