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Modeling Interaction Between Family Members

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?.

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Modeling Interaction Between Family Members

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

  2. Thank Tim York

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

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

  5. 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.

  6. Two Examples • Twin and sibling Interaction • Assortative mating and spousal interaction

  7. 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. ActaGenetica 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.

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

  9. Cooperation and competition in twins

  10. Structure BEFORE interaction S= A+C+E | gA+C gA+C | A+C+E

  11. b12 b21

  12. What is structure after interaction?

  13. What is structure AFTER interaction? S*= (I-B)-1S(I-B)’-1 Where B= ( 0 b12 ) b210 Note: Compare this with the LISREL model

  14. RUN AN EXAMPLE…BRAD!!!!

  15. 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?

  16. 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!!!!

  17. Spousal Interaction: S

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

  19. 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

  20. What does this model assume?

  21. 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.

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