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ACE
Problems
Greg Carey
BGA, 2009
Minneapolis, MN
Thought Experiment 1:
• Future technology identifies all loci and alleles
that contribute to a phenotype.
• Genotype a very large sample for all these
loci.
• Code the alleles for additive effects.
• Regress the phenotypes on the additive codes.
• Predicted values of the phenotypes are the
additive genetic values = numerical estimates
of latent variable A.
Locus 2
Locus 1
A11

A1i
A21

^
P
A2j

Locus n
An1

Ank
Assumption 1:
• Phenotypes are influenced by concrete
environmental events or Xs.
Thought Experiment 2:
• Measure all the Xs for a large sample of
individuals.
• Regress the phenotype on all the Xs.
• Predicted values equal the total
environmental values = numerical estimates of
the sum of latent variables C + E.
X1
X2
^
P
Xn
Problem at Hand:
• If (C + E) = SbiXi, we should be able to find
weights for C and weights for E so that:
(1) C and E are uncorrelated in an individual;
(2) the Es for siblings are uncorrelated.
X11
X12
E1
C1
P1
Necessary Condition 1:
• Every X variable can be placed into one of two
mutually exclusive classes—those predicting E
and those predicting C.
• (X variables can be either green or red).
X1e
X1c
E1
C1
P1
Necessary Condition 2:
• X variables predicting the unique environment
cannot be correlated with X variables
predicting the common environment within
an individual.
• (No magenta correlations).
X1e
X1c
X2c
X2e
E1
C1
C2
E2
P1
P2
Necessary Condition 3:
• No sibling correlations among the Xs for the
unique environment.
• (Green Xs cannot correlate across siblings or
no green correlational paths).
X1e
X1c
X2c
X2e
E1
C1
C2
E2
P1
P2
Necessary Condition 4:
• No X for sib 1’s unique environment can
correlate with any X for sib 2’s common
environment.
• (No magenta correlational paths)
X1e
X1c
X2c
X2e
E1
C1
C2
E2
P1
P2
Necessary Condition 5:
• When C1 = C2,
Necessary Condition 5:
• When C1 = C2,
• (With some algebra), a red X for sib 1 and its
counterpart for sib 2 must correlate 1.0.
X1ke
X11e
XXjc12
X1c
E1
X21e
E2
C
P1
X2ke
P2
ACE Model Assumption:
• Select any X variable.
ACE Model Assumption:
• Select any X variable.
• That X must correlate either 0.0 or 1.0 for the
relatives.
ACE Model Assumption:
• Select any X variable.
• That X must correlate either 0.0 or 1.0 for the
relatives.
• It is not possible to have an X that correlates,
say, .43 between sibs.
ACE Model Assumption:
• Conversely, if peer substance abuse correlates
.38 among sibs, then
ACE Model Assumption:
• Conversely, if peer substance abuse correlates
.38 among sibs, then
• Peer substance abuse can NOT be an
environmental influence on substance abuse.
What Happened?
• In the beginning,
What Happened?
• In the beginning, there was G1, G2, E1, and E2
(Jinks & Fulker, 1970).
What Happened?
• In the beginning, there was G1, G2, E1, and E2
(Jinks & Fulker, 1970).
• E2 variance component morphed into variable
C in path analysis.
What Happened?
• In the beginning, there was G1, G2, E1, and E2
(Jinks & Fulker, 1970).
• E2 variance component morphed into variable
C in path analysis.
• E1 variance component morphed into variable
E in path analysis.
What Happened?
• In the beginning, there was G1, G2, E1, and E2
(Jinks & Fulker, 1970).
• E2 variance component morphed into variable
C in path analysis.
• E1 variance component morphed into variable
E in path analysis.
• Variance components G1 and G2 were
eliminated and replaced with variable A.
What Happened?
• In the process, we overlooked the fact that
correlation (variance components) does not
necessarily imply causality.
Res1
Pupil1
School
Res2
Pupil2
Can legitimately calculate:
• Variance component for School.
Can legitimately calculate:
• Variance component for School.
• Orthogonal variance component for Error.
Can legitimately calculate:
• Variance component for School.
• Orthogonal variance component for Error.
• Test of significance of the variance component
for School.
Can legitimately calculate:
• Variance component for School.
• Orthogonal variance component for Error.
• Test of significance of the variance component
for School.
• Intraclass correlation for School.
But is this causal?
But is this causal?
• Not necessarily!
Family1
Res1
Pupil1
Family2
School
Res2
Pupil2
How Important Is This?
• For the simple analysis of a single phenotype,
no problem.
• For some models of GE correlation, how does
a variable (G) correlate with a variance
component?
• What about multivariate models?
Solution?
Solution?
Common and
Unique
Environment
Solution?
Shared and
Nonshared
Environment
Solution?
Use Total Environment
=C+E
a
Ab 1
Eb 1
e
a
P1
h
Eb 2
A
b 2
a
e
P2
$5,000 prize
$5,000 prize
Bouchard Prize
$5,000 prize
Bouchard Prize
Prove me wrong or irrelevant
$5,000 prize
Bouchard Prize
Prove me wrong or irrelevant
Equations, not words