Genetic Growth Curve Models

PracticaBoulder, March 2008

Irene Rebollo & Gitta Lubke & Mike Neale

VU Amsterdam NL & Notre Dame, US & VCU, US

Agg911 Agg951 Agg971 Agg001

is

Agg912 Agg952 Agg972 Agg002

is

Ei Ci Ai1 1 1

aiciei

Es Cs As1 1 1

es cs as

eis cis

ais

Ai Ci Ei As Cs Es

1 1 1 1 11

eiciai

eis

cis

ais

as cs es

0.5/1

0.5/1

1

1

Genetic Growth Curve Model

Agg912 Agg952 Agg972 Agg002

i

1 1 1 1

Vi

s

0 2 3 4.5

Vs

ris

0 0 0 0

αi

αs

e1 e2 e3 e4

1. Phenotypic Growth Curve Model

1. Phenotypic Growth Curve Model: Matrices

Agg912 Agg952 Agg972 Agg002

i

1 1 1 1

Vi

s

0 2 3 4.5

Vs

ris

0 0 0 0

αi

αs

e1 e2 e3e4

phenLingrow_lib08.mx

RUN

1. Phenotypic Growth Curve Model: Matrices

5.41

31

21

01

F

sis

isi

Vr

rVM

4

3

2

1

e

e

e

e

R

Agg912 Agg952 Agg972 Agg002

i

1 1 1 1

Vi

s

0 2 3 4.5

Vs

ris

0 0 0 0

αi

αs

e1 e2 e3e4

s

iQ 4321 N

4321 AgeAgeAgeAgeK

COVARIANCES

MEANS

44332211 5.432

)'*(

AgeAgeAgeAge

NKQFMEANS

sisisii

RMFCOV &

RFMFCOV '**

1. Phenotypic Growth Curve Model: Run!

Agg912 Agg952 Agg972 Agg002

i

1 1 1 1

12.3

s

0 2 3 4.5

0.4

-1.18

10.03

-.38

9.9 7.4 5.4 5.8

FIT: Δχ2 (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 (αs)?

All significant!

phenLingrow_lib08.mx

2. Twin Correlations on the Growth Curve Model

i1 s1 i2 s2

i1 vi

s1 ris vs

i2 vi

s2 ris vs

Agg911 Agg951 Agg971 Agg001

isViVs

ris

Agg912 Agg952 Agg972 Agg002

i sVsVi

ris

(Co)Variance matrix between Intercept & Slope:

1. Phenotypic, within twin co(variances)

2. Twin Correlations on the Growth Curve Model

i1 s1 i2 s2

i1 vi

s1 ris vs

i2 rii vi

s2 rss ris vs

Agg911 Agg951 Agg971 Agg001

isViVs

ris

Agg912 Agg952 Agg972 Agg002

i sVsVi

ris

(Co)Variance matrix between Intercept & Slope:

2. Cross twin-within trait:

i1-i2 & s1-s2

i1 s1 i2 s2

i1 vi

s1 ris vs

i2 rii vi

s2 rss ris vs

MZ DZ

2. Twin Correlations on the Growth Curve Model

i1 s1 i2 s2

i1 vi

s1 ris vs

i2 rii rsi vi

s2 ris rss ris vs

Agg911 Agg951 Agg971 Agg001

isViVs

ris

Agg912 Agg952 Agg972 Agg002

i sVsVi

ris

(Co)Variance matrix between Intercept & Slope:

3. Cross twin-cross trait:

i1-s2 & s1-i2

i1 s1 i2 s2

i1 vi

s1 ris vs

i2 rii rsi vi

s2 ris rss ris vs

MZ DZ

2. Twin Correlations on the Growth Curve Model

TWLingrow_lib08.mx

RUN

Agg911 Agg951 Agg971 Agg001

isViVs

Agg912 Agg952 Agg972 Agg002

i sVsVi

2. Twin Correlations: Matrices (for covariance structure)

5.41

31

21

01

F

4

3

2

1

4

3

2

1

@

e

e

e

e

e

e

e

e

RI

COMMON MATRICES

UncorrelatedResiduals

ZYGOSITY SPECIFIC

Residuals Tw1

Residuals Tw2

1

1I

5.4100

3100

2100

0100

005.41

0031

0021

0001

@FI

4

3

2

1

e

e

e

e

R

sisssMZisMZ

iisMZiiMZ

sis

i

Vrrr

Vrr

Vr

V

M

MZ

Sym

sisssDZisDZ

iisDZiiDZ

sis

i

Vrrr

Vrr

Vr

V

S

DZ

Sym

COVARIANCE (I@F)&M + (I@R) ;

COVARIANCE (I@F)&S + (I@R) ;

2. Twin Correlations: Script & Output

sisssMZisMZ

iisMZiiMZ

sis

i

Vrrr

Vrr

Vr

V

M

MZ

Sym

sisssDZisDZ

iisDZiiDZ

sis

i

Vrrr

Vrr

Vr

V

S

DZ

Sym

154.52.35.

135.55.

154.

1

)(\1 MstndASym

154.48.35.

135.52.

154.

1

)(\3 SstndASym

CORRELATIONS

FOR MODEL SELECTION

2. Twin Correlations: Script & Output

sisssMZisMZ

iisMZiiMZ

sis

i

Vrrr

Vrr

Vr

V

M

MZ

Sym

sisssDZisDZ

iisDZiiDZ

sis

i

Vrrr

Vrr

Vr

V

S

DZ

Sym

43.28.123.83.

05.1383.21.7

43.28.1

05.13

MSym

Sym

COVARIANCES

FOR STARTING VALUES

43.28.121.84.

05.1384.80.6

43.28.1

05.13

S

Agg911 Agg951 Agg971 Agg001

is

Agg912 Agg952 Agg972 Agg002

is

Ei Ci Ai1 1 1

aiciei

Es Cs As1 1 1

es cs as

eis cis

ais

Ai Ci Ei As Cs Es

1 1 1 1 11

eiciai

eis

cis

ais

as cs es

0.5/1

0.5/1

1

1

3. Genetic Growth Curve Model

Lingrow_lib08.mx

RUN

3. Genetic Growth Curve Model

3. Genetic Growth Curve Model: Matrices

5.0H

sis

i

aa

aX

sis

i

cc

cY

sis

i

ee

eZ

'XXA

M = A+C+E | A+C _ A+C | A+C+E;

MZ

'YYC 'ZZE

DZ

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) ;

3. Genetic Growth Curve Model: Script & Output

In Matrix K: %Vi %Vs %Sis

A 6 8 0

C 48 44 65

E 45 47 35

Exercise:

Use the option Multiple to Test for genetic effects on:

-Covariance i-s

-Variance I

-Variance S

3. Genetic Growth Curve Model: Model Fitting Results

MODEL -2LL DF vs χ2 df p

FULL 73945.473 13626

asi =0 73945.473 13627 1 0 1 .986

ai =0 73946.068 13628 2 .595 1 .440

as =0 73947.284 13629 3 1.216 1 .270