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)

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11 Marital Separation: Selected Results

12 Competing Risks

13 Discrete-time Competing Risks Model

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

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17 Years to Partnership Transitions: Quartiles 25%50%75% Marriage  Separation Cohab  Separation Cohab  Marriage

18 Cohabitation Outcomes: Selected Results

19 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.

20 Multiple States: Episode-based File

21 Multiple States: Discrete-time File

22 Multiple States: Estimation Include c ij, m ij, c ij *age ij and m ij *age ij as explanatory variables. Coefficients of m ij and m ij *age ij are intercept and effect of age on marital separation. Allow coefficient of m ij to vary randomly across individuals. c ij and c ij *age ij will each have two coefficients for r=1 and r=2, and c ij will have two random effects. Estimation in MLwiN (see Steele et al. 2004), or aML.

23 Multiple States: Random Effects Covariance Matrix

24 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

25 Multiprocess Model of Partnership Transitions and Fertility h P (t): Hazard of partnership transition at time t h F (t): Hazard of conception at time t F(t): Children born before t X P (t) (Observed) X F (t) (Observed) u F (Unobserved) u P (Unobserved)

26 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

27 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*

28 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

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

30 Some References on Discrete-time Event History Analysis Competing risks –Steele, Diamond and Wang (1996). Demography, 33: Multiple states –Goldstein, Pan and Bynner (2004). Understanding Statistics, 3: –Steele, Goldstein and Browne (2004). Journal of Statistical Modelling, 4: Multiple processes –Upchurch, Lillard and Panis (2002). Demography, 39: –Steele, Kallis, Goldstein and Joshi (2004). To appear at