Multilevel Event History Analysis of the Formation and Outcomes of Cohabiting and

Marital Partnerships

Fiona SteeleCentre for Multilevel Modelling

University of Bristol

Based on research carried out under the ESRC RMP with Constantinos Kallis, Heather Joshi and Harvey Goldstein

2

Outline of talk

• Research questions

• Selection effects

• Scope of study and definitions of partnership transitions

• Methods: multilevel simultaneous equation modelling

• Data: British Cohort Study

• Findings

3

Research Questions: Overview

• Examine women’s repartnering behaviour and how it is shaped by past partnership events

• What is the relationship between previous cohabitation/marriage and the timing of the formation and dissolution of subsequent partnerships?

4

Research Questions

What are the effects on the timing of partnership formation and dissolution of …

• previous partnership experience

– Are premarital cohabitors at higher risk of marital dissolution?

– Does prior experience of marital breakdown deter remarriage?

– Are 2nd+ partnerships at higher or lower risk of dissolution?

• pregnancy and the presence of children

5

The Role of Previous Partnership Experience on Subsequent Events: Selection

• Past partnership outcomes are likely to be endogenous w.r.t. the risk of subsequent events

• There may be time-invariant characteristics affecting the occurrence of events in the same or a related process throughout the study period

– E.g. religious belief may influence the probability of cohabiting and the risk of marital dissolution

– Not all of these variables will be observed

• Important to allow for unobserved heterogeneity when studying repeated events

6

Example of Selection Bias: Effect of Divorce on Subsequent Marital Dissolution

Suppose there are time-invariant unobservables influencing an individual’s dissolution risk in any marriage they form

→ selection of individuals with high dissolution risk into remarriage → if uncontrolled, 2nd+ marriages may appear to carry a higher risk of dissolution than 1st marriages

See Aassve et al. (2006) and Lillard et al. (1995)

7

Example of Selection Bias: Effect of Cohabitation on Subsequent Marital Dissolution

Often observe increased dissolution risk among couples who lived together before marriage

In US, Lillard et al. (1995) found that this was due to selection of women with a high risk of dissolution into cohabitation; and this selection was not captured by covariates

No British study has allowed for selection on unobservables

8

The Effect of Current Fertility Status on Partnership Events: Selection

• Indicators of current fertility status are past outcomes of the fertility process which may be endogenous w.r.t. partnership events

• Timing of fertility and partnership events may be correlated due to time-invariant unobservables affecting both childbearing and partnership decisions

– E.g. women with a high risk of marital dissolution tend also to have low odds of marital childbearing (Lillard & Waite, 1993)

– This is a residual correlation, i.e. not explained by covariates

– If uncontrolled, leads to biased estimate of effect of having children on dissolution risk

9

Study Overview

• Partnership transitions between ages 16 and 30 among women born in 1970

• Consider all partnerships and distinguish between marriage and cohabitation

• Jointly model partnership formation and outcomes to allow for endogeneity of previous partnership experience

• Treat current fertility status as exogenous (based on previous research on 1958 and 1970 cohorts)

10

S

Stay S

MDissolution

Stay M

M

Formation

Partnership Transitions(S=single, M=marriage, C=cohabitation)

Outcomes

S

M

Formation Outcomes

Dissolution

Stay C

C

M

M (same partner)

C

11

Episodes, States and Competing Risks

An episode is a continuous period spent in the same partnership

state. Denote by sij the state (S,M,C) occupied in episode i of

woman j , tij the episode duration, and δij a censoring/event

indicator.

For sij = M: δij = 0 for no event (censored), 1 for dissolution

For transitions from states C and S we have competing risks:

sij = C: δij = 0 for no event, 1 for dissolution, 2 for marriage

sij = S: δij = 0 for no event, 1 for cohabitation, 2 for marriage

12

Discrete-time Data Structure

From observed data (sij, tij, δij) create the following for each time interval t:

For sij = M: a binary response yij(t) =0 for t < tij and δij for t = tij.

For sij = C or S: two binary responses { } coded 0 for t < tij and value at t=tij determined by sij and δij

E.g. if sij = C

= 1 if dissolution and 0 if marry or censored

= 1 if marry and 0 if dissolution or censored

)(),( )2()1( tyty ijij

)()1(ijij ty

)()2(ijij ty

13

Example of Data Structure

j i s i j t i j δ i j 1 1 S 2 1 1 2 C 3 2 1 3 M 1 0

i t s i j( t ) )( ty ij )()1( ty ij )()2( ty ij

1 1 S - 0 0 1 2 S - 1 0 2 1 C - 0 0 2 2 C - 0 0 2 3 C - 0 1 3 1 M 0 - -

14

Hazard Functions

Partnership formation (transition from S):

)()( th rSij hazard of entering partnership of type r (1=C, 2=M)

in time interval t for episode i of woman j

Partnership outcomes (transition from M or C):

)(thMij hazard of marital dissolution

)()( th rCij hazard that cohabitation ends for reason r

(1=dissolution, 2=marriage to same partner)

15

Multilevel Simultaneous Equation Model

Define 5 hazards equations, e.g. multilevel logit equations for partnership formation (r = 1, 2)

)()()()( )()()](logit[ rSj

Sij

rSSij

rSrSij uttth XβDα

)()( tSij

rS Dα function of the duration of the current single episode by time t

)(tSijX covariates, with coefficients )(rSβ

)(rSju is woman-specific random effect

5 random effects correlated across equations

16

Estimation

• Model can be framed as a multilevel binary response model, and estimated in standard software

• Stack binary responses into a single response vector and, for sij=S or C, define 2 dummy variables for responses

• Define another 3 dummy variables for state

• Allow coefficients of 5 dummies to vary randomly across women to define random effects

• Interact dummies with covariates

17

Example of Data Structure for Estimation

j i t sij(t) r )(tyij

1 1 1 S 1 0 1 1 1 S 2 0 1 1 2 S 1 1 1 1 2 S 2 0 1 2 1 C 1 0 1 2 1 C 2 0 1 2 2 C 1 0 1 2 2 C 2 0 1 2 3 C 1 0 1 2 3 C 2 1 1 3 1 M 1 0

Define a dummy for every combination of sij(t) and r

18

Data

• 1970 British birth cohort (BCS70):

– Partnership (living together for >1 month) and birth histories collected retrospectively at age 30

– Covariates from childhood and adulthood

• Analysis sample: n=5495 women; n=15032 partnership episodes (48% single, 32% cohabitation, 20% marriage)

19

Explanatory Variables(Exact specification varies by type of transition)

• Current and previous partnerships: age, previously married/cohabited, current duration in state

• Current fertility status (TV): pregnant, presence of children by age and relationship to current partner

• Education (TV): current enrolment, no. post-16 years

• Family background: region of residence at birth, social class at birth, family disruption

20

Summary of Transitions by Age 30(all % based on total sample, n=5495)

• 13% still unpartnered• 53% had married• 72% had cohabited

• 70% had only 1 partner– 46% C+M, 20% M only, 34% C only

• 17% had >1 partner

21

Years to Partnership Transitions

Transition Lower quartile

Median

Partnership formation Cohabitation (1st ) 4.8 7.8 Cohabitation (2nd+) 1.4 3.3 Marriage 11.4 - Outcomes of cohabitation Marriage 1.9 4.3 Separation 2.8 7.0 Marital separation 8.5 -

22

Selected Random Effect Correlations

Partnership formation

Outcomes of cohab.

Marital diss.

C M Diss. M Marital dissolution

0.49 0.11 -0.07 0.46 1

Women with high (low) hazard of partnership formation tend also to have high (low) hazard of marital dissolution.

i.e. fast formation associated with high risk of dissolution.

23

Effects of Previous Partnership Experience: Partnership Formation

(Estimated coefficients and standard errors)

Cohabitation Marriage M1 M2 M1 M2

Previously partnered

0.69 (0.09)

0.73 (0.11)

-0.22 (0.41)

-0.15 (0.41)

M1: Zero random effect correlations M2: Correlations freely estimated

24

Effects of Previous Partnership Experience: Outcomes of Cohabitation

(Estimated coefficients and standard errors)

Separation Marriage M1 M2 M1 M2

Previously married 0.25 (0.19)

0.39 (0.35)

-0.26 (0.17)

-0.67 (0.31)

Previously cohabited -0.27 (0.14)

-0.17 (0.14)

-0.02 (0.11)

-0.01 (0.14)

M1: Zero random effect correlations M2: Correlations freely estimated

25

Effects of Previous Partnership Experience: Marital Separation

(Estimated coefficients and standard errors)

M1 M2

Previously married 0.46 (0.33) -0.34 (0.44)

Previously cohabited with … (ref=no one)

Current partner only 0.16 (0.12) -0.33 (0.26)

Previous partner(s) only 0.47 (0.56) 0.28 (0.68)

Current + previous 0.61 (0.22) -0.05 (0.43)

M1: Zero random effect correlations M2: Correlations freely estimated

26

Summary of Effects of Previous Partnership Experience

• Among cohabitors, the never-married are more likely to marry than the previously married

• No effect of previous partnership breakdown on the stability of later partnerships

• No effect of premarital cohabitation on the risk of marital dissolution

27

Summary of Effects of Current Fertility Status

• Pregnancy hastens cohabitation and marriage among single women, and transition from cohabitation to marriage

• Marriage rate lower among cohabitors with a young child (selection?)

• Presence of an older child fathered by a previous partner inhibits marriage

• Stabilising effect of pregnancy and children by current partner on cohabitation and marriage

28

Conclusions

• Findings on effects of presence of children on partnership outcomes are similar for 1958 and 1970 cohorts

• Allowing for selection on time-invariant unobservables is important when assessing the role of previous partnership experience on subsequent transitions

• Important to distinguish between cohabitation and marriage