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Modeling Interaction Between Family Members When you are by yourself and have no one to ask.

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Thank Tim York

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So Far: Have assumed people don’t affect each other May not be true

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Examples Do sibs (twins) affect each other? Peer effects? Spousal interaction? Mother-child interaction?

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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.

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Two Examples Twin and sibling Interaction Assortative mating and spousal interaction

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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.

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Approach Start without interaction Figure out covariances between relatives “Include interaction” Use OpenMx to figure out what happens if….

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Cooperation and competition in twins

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Structure BEFORE interaction = A+C+E | gA+C gA+C | A+C+E

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b 12 b 21

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What is structure after interaction?

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What is structure AFTER interaction? ’ Where = ( 0 b 12 ) b 21 0 Note: Compare this with the LISREL model

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RUN AN EXAMPLE… BRAD!!!!

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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?

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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!!!!

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Spousal Interaction:

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What is B? S1 T1 T2 S2 S1 T1 T2 S2

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What is B? S1 T1 T2 S2 S1 0 b 0 0 T1 b 0 0 0 T2 0 0 0 b S2 0 0 b 0

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What does this model assume?

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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.

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