1. Multilevel Multiprocess Models for Partnership and Childbearing Event Histories Fiona Steele, Constantinos Kallis, Harvey Goldstein and Heather Joshi Institute of Education, University of London

2. 2 Aims of Research Develop methodology for the analysis of correlated event histories Apply in an analysis of the link between partnership stability and childbearing –Examine effect of presence of children on separation and move from cohabitation to marriage, adjusting for correlation between partnership transitions and fertility

3. 3 Previous Research in Britain Most consider 1 st partnership only –Those using NCDS look at transitions for ages 16-33 (e.g. Kiernan & Cherlin 1999; Berrington 2001) Transitions from marriage and (unmarried) cohabitation modelled separately Prior fertility outcomes treated as exogenous

4. 4 Our Methodological Approach Consider all partnerships for ages 16-42 using multilevel modelling Estimate simultaneously models for 3 types of partnership transition: –Marriage Separation –Cohabitation Separation; Cohabitation Marriage Estimate these transitions jointly with model for fertility to allow for potential endogeneity of fertility outcomes

5. 5 Endogeneity of Prior Fertility Outcomes Interested in effect of presence of children on partnership transitions But children are prior outcomes of a potentially correlated process (fertility) There may be factors (some unobserved) which influence decisions about partnership transitions and childbearing If ignored, effects of interest will be biased

6. 6 Joint Modelling of Partnership Transitions and Fertility Current research builds on US study (Lillard & Waite 1993) which used a multiprocess model to allow for possibility that the processes of divorce and childbearing are jointly determined. –BUT only marital unions are considered We extend their approach to include outcomes of cohabitating partnerships

7. 7 Methodology: Overview Use multilevel multistate event history model (Steele et al. 2004) for partnership transitions –States are marriage and cohabitation – Competing risks from cohabiting state Estimate jointly with model for births within partnerships using simultaneous equation (multiprocess) model. Multilevel data structure: repeated partnerships and births (level 1) within individuals (level 2).

8. 8 Multilevel Modelling Some women have > 1 partnership and/or birth –May be unobserved characteristics which influence risk of all partnership transitions/births –Leading to correlation between durations of partnerships/birth intervals for the same woman In a multilevel model, include random effects for each type of transition. These represent unobserved time- constant variables Correlation between random effects for different transitions are of substantive interest

9. 9 Multiprocess Model of Partnership Transitions and Fertility Probability of partnership transition at time t Probability of birth at time t Children born before t X P (t) (Observed) X F (t) (Observed) u F (Unobserved) u P (Unobserved)

10. 10 Event History Model for Partnership Transitions Model duration to transition using discrete- time model For each transition, define hazard function: h(t)=Probability that a transition occurs during time interval t given no transition before t

11. 11 Model for Partnership Transitions: Marriage to Separation

12. 12 Model for Partnership Transitions: Cohabitation to Separation (r=1) or Marriage (r=2)

13. 13 Why Model Partnership Transitions Jointly? May be unobserved factors which influence more than one transition (or unobservables may be correlated across transitions) –E.g. might expect correlation between separation from marital and non-marital unions –Explore and test for this Test for differences in covariate effects across transitions

14. 14 Event History Model for Fertility Model hazard of a live birth within partnership Multilevel discrete-time event history model

15. 15 Model for Fertility Marriage Cohabitation

16. 16 Correlation Between Processes u P =(u PM,u PC(1), u PC(2) ) and u F =(u FM,u FC ) are random effects for partnership transitions and fertility Estimate pairwise correlations between elements of u P and u F both within and across processes –allows for correlation between unobservables

17. 17 Reverse Causality Can extend fertility models to allow for effects of partnership stability on fertility (Lillard & Waite 1993), e.g. But requires identifying variables, which are difficult to find

18. 18 Data 1958 British birth cohort (National Child Development Study) –Partnership (living together for >1 month) and birth histories collected retrospectively at ages 33 and 42. Linked to form history for age 16-42. –Covariates from childhood and adulthood. Analysis sample: n=4062 women with 1 partner by age 42; n=5495 partnerships and n=7121 partnership episodes

19. 19 Repeated episodes (Multilevel structure) NoneOct 99 C4 DeathMar 96Sep 79M3 MarSep 79Oct 78C2 SepAug 78Mar 74M1 TransitionEndBeginStateEpisode

20. 20 Cleaning and Linking Partnership Histories: Examples of Inconsistencies For partnerships continuing beyond age 33, different start dates reported at age 33 and 42 Missing years and/or months Start of partnership different from start of marriage, but no period of pre-marital cohabitation Overlapping partnerships

21. 21 Example: Overlapping Partnerships Age 42CDec 97May 96 Age 42MStill in progress July 78 Age 42CJuly 78Mar 78 Age 33MStill in progress Oct 78 InterviewTypeEndStart

22. 22 Measures of Prior Fertility Number of preschool and older children living with respondent. Distinguish between children from current and previous partnerships. All variables are treated as time-varying.

23. 23 Other Explanatory Variables Previously married/cohabited Age at start of partnership No. years of education (time-varying) Paternal social class Respondents social class at age 23 Family disruption before age 16 Behavioural problems at age 16

24. 24 Distribution of Total No. of Marriages and Cohabitations per Woman

25. 25 Sequencing of Partnership Transitions 1 marriage, 1 cohabitation (n=978): Cohabitation to marriage (same partner): 80% Marriage then cohabitation (2 partners): 16% Cohabitation then marriage (2 partners): 4% 2 marriages, 1 cohabitation (n=278): Marriage then (Cohabitation to marriage): 94% 3 partners: 4% (Cohabitation to marriage) then Marriage: 2% 2 cohabitations, 1 marriage (n=217): Cohabitation then (Cohabitation to marriage): 57% (Cohabitation to marriage) then Cohabitation: 28% 3 partners: 15%

26. 26 Years to Partnership Transition: Quartiles 25%50%75% Marriage Separation 13.8-- Cohab Separation 3.59.1- Cohab Marriage 1.32.910.3

27. 27

28. 28 Number of Births per Episode

29. 29 Percentage Having a Child During Episode

30. 30 No. Children Living with Woman (By Most Recent Partnership Status)

31. 31 Random Effects Covariance Matrix: Partnership Transitions (from Multiprocess Model)

32. 32 Selected Random Effect Correlations Across Processes Separation from marriage and marital birth r = -0.20* (*sig. at 5% level) Separation from cohab. and cohabiting birth r = 0.11 Cohabitation to marriage and cohabiting birth r = 0.59*

33. 33 Effects of Fertility Variables on Log- odds of Separation vs. Staying Married

34. 34 Effects of Fertility Variables on Log-odds of Separation vs. Staying Cohabiting

35. 35 Effects of Fertility Variables on Log-odds of Marrying vs. Staying Cohabiting

36. 36 Effects of Fertility Variables on Log-odds of Birth (Multiprocess model)

37. 37 Effects of Other Covariates: Summary Factors affecting separation are similar for marriage and cohabitation –E.g. strong negative effect of age, negative effect of previous marriage. For marriage, no effect of pre-marital cohabitation. Educated (6+ years post-16) and previously married cohabitants less likely to marry Factors affecting fertility are rather different for married and cohabiting women

38. 38 Conclusions Allowing for endogeneity of children born within marriage/cohabitation has little effect on substantive conclusions regarding effects of children on partnership transitions –But this will not always be the case (see Lillard) Multiprocess approach allows: –Estimation of correlation between unobservables within and across processes –Comparison of effects of covariates within and across processes

39. 39 Further Work Children from previous relationships. Distinguish between those born in marriage, cohabitation and outside partnership Modelling or weighting for drop-out from study after age 33 Compare 1958 and 1970 birth cohorts