modeling interaction between family members
DESCRIPTION
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?. - PowerPoint PPT PresentationTRANSCRIPT
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 cross-sectional twin data. Acta Genetica Med. et Gemellol. 36:5-20.
• 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 T1 T2 S2S1T1T2S2
What is B?
S1 T1 T2 S2S1 0 b 0 0T1 b 0 0 0T2 0 0 0 bS2 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.