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Discrete-time Event History Analysis

Discrete-time Event History Analysis. Fiona Steele Centre for Multilevel Modelling Institute of Education. Discrete-time EHA for …. Repeated events Multiple states Competing risks Multiple processes. Application: Partnership Outcomes and Childbearing in Britain.

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Discrete-time Event History Analysis

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  1. Discrete-time Event History Analysis Fiona Steele Centre for Multilevel Modelling Institute of Education

  2. Discrete-time EHA for … • Repeated events • Multiple states • Competing risks • Multiple processes

  3. Application: Partnership Outcomes and Childbearing in Britain • Data from National Child Development Study (NCDS) – 1958 birth cohort. Women only. • Partnership defined as co-resident relationship of  1 month. • Interested in durations of partnerships and intervals between conceptions (leading to live births) within partnerships.

  4. Features of NCDS Data • Repeated events • Women with > 1 partnership and/or birth • Multiple states • Marriage and cohabitation • Competing risks • Outcomes of cohabitation: separation or marriage • Multiple processes • Partnership durations and conception intervals

  5. Discrete-time Data Structure

  6. Example of Data Structure

  7. Standard Discrete-time Model

  8. Model for Repeated Events

  9. Example: Marital Separation • Duration of marriage episode – time between start of marriage and separation/interview • (t) a cubic polynomial • Covariates include age at start of marriage, education (time-varying)

  10. Marital Separation: Selected Results

  11. Competing Risks

  12. Discrete-time Competing Risks Model

  13. Competing Risks: Example • Outcomes of cohabitation • Separation (r=1) • Marriage to cohabiting partner (r=2) • (r)(t) cubic polynomials

  14. Years to Partnership Transitions:Quartiles

  15. Cohabitation Outcomes: Selected Results

  16. Multiple States • Estimate equations for marital separation and outcomes of cohabitation jointly. • State-specific intercepts and covariate effects are fitted by including dummy variables for each state and their interactions with covariates. • Equations are linked by allowing random effects to correlate across equations.

  17. Multiple States: Episode-based File

  18. Multiple States: Discrete-time File

  19. Multiple States: Estimation • Include cij, mij, cij*ageijand mij*ageijas explanatory variables. • Coefficients of mijand mij*ageijare intercept and effect of age on marital separation. Allow coefficient of mijto vary randomly across individuals. cijand cij*ageijwill each have two coefficients for r=1 and r=2, and cijwill have two random effects. • Estimation in MLwiN (see Steele et al. 2004), or aML.

  20. Multiple States: Random Effects Covariance Matrix

  21. Multiple Processes • Interested in impact of no. and age of children at time t ,F(t), on hazard of partnership transition • F(t) are prior outcomes of another, related, dynamic process - fertility • Partnership and childbearing decisions may be affected by similar unobserved characteristics  F(t) may be endogenous

  22. uP (Unobserved) XP(t) (Observed) hP(t): Hazard of partnership transition at time t F(t): Children born beforet hF(t): Hazard of conception at time t XF(t) (Observed) uF (Unobserved) Multiprocess Model of Partnership Transitions and Fertility

  23. Multiprocess Modelling • Estimate multistate model for transitions from marriage and cohabitation jointly with model for childbearing within marriage and cohabitation • Leads to a total of 5 equations, with individual-level random effect in each • In multiprocess model random effects are correlated across equations, so equations must be estimated simultaneously

  24. Selected Random Effect Residual Correlations Across Processes • Separation from marriage and marital conception r = -0.28* (*sig. at 5% level) • Separation from cohabitation and cohabiting conception r = 0.19 • Cohabitation to marriage and cohabiting conception r = 0.59*

  25. Example of Interpretation • Cohabitation to marriage and cohabiting conception, r = 0.59* • Women with a high propensity to move from cohabitation to marriage tend also to have a high propensity to conceive during cohabitation. • If this correlation is ignored, hazard of marriage for women who had a child with their partner will be overstated

  26. Effects of Fertility Variables on Log-odds of Marrying vs. Staying Cohabiting

  27. Some References on Discrete-time Event History Analysis • Competing risks • Steele, Diamond and Wang (1996). Demography, 33: 12-33. • Multiple states • Goldstein, Pan and Bynner (2004). Understanding Statistics, 3: 85-99. • Steele, Goldstein and Browne (2004). Journal of Statistical Modelling, 4: 145-159. • Multiple processes • Upchurch, Lillard and Panis (2002). Demography, 39: 311-329. • Steele, Kallis, Goldstein and Joshi (2004). To appear at www.mlwin.com/team/mmmpceh

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