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.