Modeling Interaction Between
Family Members
When you are by yourself and have
no one to ask.
Thank Tim York
So Far:
Have assumed people
don’t affect each other
May not be true
Examples
•
•
•
•
Do sibs (twins) affect each other?
Peer effects?
Spousal interaction?
Mother-child interaction?
THINK!
• How do you think the world works?
• How do you translate “how the world works”
into:
•
design (choice of subjects)
•
measurement
•
model (diagram, algebra)
•
data (expectations for statistics)
•
analysis (code, decision)
OpenMx can help you do the nuts and bolts.
Two Examples
• Twin and sibling Interaction
• Assortative mating and spousal interaction
Some early papers (caveat emptor!)
• Eaves, LJ (1976) A model for sibling effects in man.
Heredity 36:205-214.
• Carey G (1986) Sibling imitation and contrast effects.
Behavior Genetics 38:319-341
• Heath AC (1987) The analysis of marital interaction in crosssectional twin data. Acta Genetica Med. et Gemellol. 36:520.
• Nance WE, Kramer AA, Corey LA, Winter PM, Eaves LJ
(1983) A causal analysis of birthweight in the offspring of
monozygotic twins. Am. J. hum. Genet. 35:1211-1223.
• Lytton H, Martin NG, Eaves LJ (1977) Environmental and
genetical causes of variation in ethological aspects of
behavior in two year old boys. Social Biol. 24:200-211.
Approach
•
•
•
•
Start without interaction
Figure out covariances between relatives
“Include interaction”
Use OpenMx to figure out what happens if….
Cooperation and competition in twins
Structure BEFORE interaction
S=
A+C+E | gA+C
gA+C | A+C+E
b12
b21
What is structure after interaction?
What is structure AFTER interaction?
S*= (I-B)-1S(I-B)-1
Where B=
(
0 b12
b21 0
)
Note: Compare this with the LISREL model
RUN AN EXAMPLE…
BRAD!!!!
•
•
•
•
•
Now Try It Yourself!
Work out expected covariances and
correlations
For different values of b (symmetric)
Use positive and negative values of b
For models with and without A
Try to predict your answers
Summarize the principal implications of social
interaction for the data
• Under what circumstances are you
likely/unlikely to detect interactions?
Now…Think about other worlds
• What would you expect for singletons
• What do you think would happen in larger
sibships (3,4…siblings)?
• How would you model the process?
TRY IT!!!!
Spousal Interaction: S
What is B?
S1
S1
T1
T2
S2
T1
T2
S2
What is B?
S1
S1 0
T1 b
T2 0
S2 0
T1
b
0
0
0
T2
0
0
0
b
S2
0
0
b
0
What does this model assume?
What does this model assume?
• Both twins married
• Mutual effect of husbands and wives
symmetric
• “Phenotypic” assortment for initial trait
• Process has reached developmental
equilibrium - implied by (I-B)-1 - limit of
infinite series of interactions.