Graphical Chain Models for Panel data

1. Graphical Chain Models for Panel data Ann Berrington University of Southampton

2. Overview • Independence and conditional independence • Undirected and directed graphs • Chain graphs for panel data • Example: Reciprocal relationship between gender role attitudes and labour force status

3. Independence • Two variables are independent if knowing one provides no information about (the distribution of) the other • E.g. knowing someone’s nationality (N) provides no information about their sex (S) • Notation: • Graph:N S N S independentdependent

4. Conditional independence • Two variables are conditionally independent given a third if once the third is known, knowing one provides no information about (the distribution of) the other • E.g. the clinic (C) a person was treated in is independent of the outcome of the treatment (O), given their initial severity (I) • Notation: I • Undirected graph: OC

5. Undirected and directed graphs • Undirected graphs not suitable when the variables are ordered, say in time • E.g. is it sensible to consider whether ethnicity is independent of the parental education given age at motherhood? Parental education Ethnicity Age at motherhood

6. Directed graph • Can be used if the variables can be a priori ordered completely • Edges replaced by arrows • Missing arrow corresponds to a conditional independence between the two variables given all the earlier variables • Built-up using a sequence of appropriate regressions • E.g. linear or logistic Parental education Age at motherhood Ethnicity

7. Chain graph • Can be used if the variables can be partially ordered into blocks • Edges within blocks, arrows between blocks • Missing edge or arrow corresponds to a conditional independence between the two variables given all the variables in the current and preceding blocks Parental education Ethnicity Reading ability Means tested benefits Age at motherhood

8. Example: Using a graphical chain model with panel data • Aim • To investigate reciprocal relationship between changes in women’s labour force participation following entry into parenthood and changes in gender role attitudes • To identify size of selection and adaptation effects using longitudinal data

9. DataThe British Household Panel Survey • Sample: women who in 1991 were childless, aged between 16 and 39 • Gender role attitude score: a summary of six items, measured biennially e.g. 1991, 1993, …. • Range from 6 to 30 • Categorical variable describing whether or not became a parent and any change in labour force status between 1991 and 1993 • Did not become a parent – same or increased hours worked • Did not become a parent – reduced hours worked or left for family care • Became a parent – same or increased hours worked • Became a parent – reduced hours worked or left for family care • Control variables: age, marital status, education, household income, father’s social class, whether mother worked

10. Analytic Framework For Graphical Model Attitude 91 • Attitude 93 • Background variables: Age • Marital Status • Education• ~Income~ Mum worked • Father’s social class • • Combined change parenthood and economic activity 91-93 This is a chain graph, but we are not going to model the associations between the background variables

11. Results • Are gender role attitudes predicted by the experience of life course events? Models 1& 2 • Is gender role attitude associated with subsequent life course events: becoming a new mother and leaving the labour force? Model 3

12. Model 1: Significant (p<0.05) parameter estimates for linear regression of attitude in 1991

13. Model 2: Significant (p<0.05) parameter estimates for linear regression of attitude in 1993

14. Model 3: Multinomial logistic regression of combined entry into parenthood/change in labour force status between 1991 and 1993

15. Final graphical chain graph Attitude 91 • Attitude 93 • Background variables: Age • Marital Status • Education • Income • Mum worked • Father’s social class • • Combined change 91-93

16. Conclusions Not entry into parenthood itself but changes in labour force activity that are important Selection and adaptation effects present Gender role attitude predicts whether leave the labour force for family care 1991-93 Changes in labour force status associated with changes in gender role attitude 1991-1993

17. References for examples • Teenage motherhood and health outcomes in adulthood: Borgoni, R., Berrington, A. M. and Smith, P. W. F. (2004) Selecting and fitting graphical chain models to longitudinal data. Southampton Statistical Sciences Research Institute Methodology Working Papers, M04/05) http://eprints.soton.ac.uk/8178/ • Gender role attitudes and labour force change: • Berrington, A., Hu, Y., Smith, P. and Sturgis, P. (2006) A Graphical Chain Model for Reciprocal Relationships Between Gender Role Attitudes and Labour Force Participation. Available from authors on request.

18. Distribution of gender role attitude score in 1991

19. For married women aged 22-29, with below A level qualifications, whose fathers were in a skilled manual occupation and whose mothers did not work