Methods for Analysis of Longitudinal Dyadic Data

Data on pairs of subjects (dyads) are commonly collected in social research. In family research, for example, there is interest in the extent of agreement in family members' perceptions of relationship quality or how the strength of parent-child relationships depends on characteristics of parents and children. In organisational research, cooperation between coworkers may depend on factors relating to their relative roles and company ethos. Dyadic data provide detailed information on interpersonal processes, but they are challenging to analyse because of their highly complex structure: they are often longitudinal because of interest in dependencies between individuals over time, dyads may be clustered into larger groups (e.g. in families or organisations), and variables of interest such as perceptions and attitudes may be measured by multiple indicators. 

The project research was organised into four strands, three concerned with primarily methodological challenges and one focusing on substantive questions.

Strand 1: Latent variable modelling of multivariate dyadic data with zero inflation.

Kuha, Zhang and Steele (2022) propose a general latent variable models for analysing bidirectional exchanges of support between respondents and their parents, when helping tendencies in each direction are measured by multiple binary indicators of specific types of help. The model combines two continuous latent variables, which represent the helping tendencies, with two binary latent class variables which allow for high proportions of responses where no help of any kind is given or received. This defines a multivariate version of a zero inflation model. The main part of the models is estimated using MCMC methods, with a bespoke data augmentation algorithm (implemented in the jsem R package). They apply the models to analyse exchanges of help between adult individuals and their non-coresident parents where the associations between giving and receiving help measure reciprocity of exchanges.  

Zhang, Kuha and Steele (2022) extend the methodology in two ways: (i) separation of practical and financial help given and received to give four correlated outcomes (with  practical help represented by continuous latent variables and financial help by binary observed variables) and (ii) allowing the correlation among the four outcomes to depend on covariates.  They propose an MCMC procedure for estimating the model which maintains the positive definiteness of the implied correlation matrices, and describe theoretical results which justify this approach and facilitate efficient implementation of it.

Strand 2: Dynamic models for longitudinal dyadic data.

In Strand 1 a latent variable modelling framework was developed for cross-sectional data. In Strand 2, we considered extensions of dynamic panel models for longitudinal dyadic data. One methodological challenge is that the use of a rotating module for the collection of data on exchanges of support between parents and children leads to data where the response measurements are unequally spaced and taken less frequently than for the time-varying covariates. Steele and Grundy (2020) propose a random effects estimator for a family of dynamic panel models that can handle continuous, binary or ordinal multivariate responses. The performance of the estimator is assessed in a simulation study. A bivariate probit dynamic panel model is then applied to estimate the effects of partnership and employment transitions in the previous year and the presence and age of children in the current year on an individual's propensity to give or receive help. Annual data on respondents' partnership and employment status and dependent children and data on exchanges of help collected at 2- and 5-year intervals are used.

In a related paper, Rebecca Pillinger, Fiona Steele, George Leckie and Jennifer Jenkins (forthcoming) propose a general dynamic panel model for dyadic data from a clustered ‘round-robin’ design where each member of a family is observed interacting with each other family member.  They consider an extension of the social relations model for longitudinal data which allows us to distinguish actor, partner and dyad effects on the level of constructiveness that one individual shows to another when working together on a task.

Strand 3: Data quality.

Skinner and Steele (2020) consider the use of sample survey data to estimate dyadic characteristics of family networks, with an application to non-coresident parent-child dyads. They suppose that survey respondents report either from a parent or child perspective about a dyad, depending on their membership of the dyad. They construct separate estimators of common dyadic characteristics using data from both a parent and a child perspective and show how comparisons of these estimators can shed light on data quality issues including differential missingness and reporting error. In their application they find that a simple missingness model explains some striking patterns of discrepancies between the estimators and consider the use of poststratification and a related redefinition of count variables to adjust for these discrepancies. They also develop approaches to combining the separate estimators efficiently to estimate means and frequency distributions within subpopulations.

Strand 4: Applications.

The final strand focuses on substantive research questions on intergenerational exchanges of support.  Burchardt et al. (2021) draw on results from across the project, finding that some families exhibit a high tendency to provide mutual support between generations and that these tendencies persist over time. Financial and practical support are generally complementary rather than substitutes. Longer travel time between parents and their offspring makes the provision of practical help less likely, whilst social class, social mobility and ethnicity exhibit complex patterns of association with intergenerational exchanges. They conclude that exchanges within families are an important complement to formal welfare institutions in the UK and that social policies should be designed to work with the grain of existing patterns of exchange, enabling family members to continue to provide help to one another but ensuring that those who are less well supported by intergenerational assistance can access effective social protection. 

Steele, Zhang, Grundy and Burchardt (2022) study the correlates of exchanges of financial and practical support between parents and children from the perspective of both generations.  They employ a joint modelling approach which provides information on concurrent reciprocity and whether one form of support tends to be substituted for another.  Moreover, from longitudinal data, they can distinguish correlations among outcomes at a given year (due to unmeasured time-varying characteristics) and correlations due to time-invariant characteristics such as individual stable traits and family norms.  They propose a novel approach to modelling panel data on couples where partners’ outcomes (in this case, exchanges of support with children) are likely to be highly correlated and couples may form and separate over the observation period. 

Karagiannaki, Burchardt and Zhang (forthcoming) explore the ways in which social class and social mobility are associated with differences in the patterns of support provided to and from parents and their adult offspring. They examine patterns of intergenerational exchange of practical and financial support between adult children and their non-co-resident parents, differentiating by the current social class of the respondents and their social class origins, and controlling for demographic and socio-economic characteristics as far as possible. Overall, the results indicate a net downward flow in the provision of concurrent practical support for respondents in higher socio-economic classes and a net upward flow in the provision of practical support (from respondents to their parents) for respondents in lower socio-economic classes. There is a net downward flow in the provision of financial support for respondents in intermediate social classes and net upward flow for respondents in the highest and lowest social classes. For upwardly mobile respondents, there is a net upward flow of both practical and financial support, whilst for downwardly mobile children, there is a net downward flow of practical and financial support (from parents to their children). 

Publications 

Evidence Briefing: Intergenerational Support. March 2023.     

This briefing summarises key findings about practical and financial support across generations within families in Britain, including their policy and practical relevance.  

Title:
Burchardt T, Steele F, Grundy E, Karagiannaki E, Kuha J, Moustaki I, Skinner C, Zhang N and Zhang S. Welfare within Families beyond Households: Intergenerational Exchanges of Practical and Financial Support in the UK. LSE Public Policy Review. 2021; 2(1): 4, pp. 1–11. DOI: https://doi.org/10.31389/lseppr.41

Abstract:
Families extend well beyond households. In particular, connections between parents and their adult offspring are often close and sustained, and transfers may include financial assistance, practical support, or both, provided by either generation to the other. Yet this major engine of welfare production, distribution, and redistribution has only recently become the focus of research. Who are the beneficiaries and to what extent are the patterns of exchange socially stratified? This article discusses findings from a programme of research analysing data from two nationally representative longitudinal studies, the British Household Panel Study and its successor Understanding Society, which record help given by, and received by, respondents through exchanges with their non-coresident parents and offspring in the UK. Some families exhibit a high tendency to provide mutual support between generations; these tendencies persist over time. Financial and practical support are generally complementary rather than substitutes. Longer travel time between parents and their offspring makes the provision of practical help less likely, whilst social class, social mobility, and ethnicity exhibit complex patterns of association with intergenerational exchanges. The resulting conclusion is that exchanges within families are an important complement to formal welfare institutions in the UK and that social policies should be designed to work with the grain of existing patterns of exchange, enabling family members to continue to provide help to one another, but ensuring that those who are less well supported by intergenerational assistance can access effective social protection.

Title:
Kuha, Jouni, Zhang, Siliang and Steele, Fiona. (2023) Latent variable models for multivariate dyadic data with zero inflation: Analysis of intergenerational exchanges of family support. Annals of Applied Statistics, 17(2), pp. 1521-1542. Have a look at the preprint. 

Abstract:
Understanding the help and support that is exchanged between family members of different generations is of increasing importance, with research questions in sociology and social policy focusing on both predictors of the levels of help given and received, and on reciprocity between them. We propose general latent variable models for analysing such data, when helping tendencies in each direction are measured by multiple binary indicators of specific types of help. The model combines two continuous latent variables, which represent the helping tendencies, with two binary latent class variables which allow for high proportions of responses where no help of any kind is given or received. This defines a multivariate version of a zero inflation model. The main part of the models is estimated using MCMC methods, with a bespoke data augmentation algorithm. We apply the models to analyse exchanges of help between adult individuals and their non-coresident parents, using survey data from the UK Household Longitudinal Study.t

Title:
Skinner, Chris J. and Steele, Fiona (2020) Estimation of dyadic characteristics of family networks using sample survey data. Annals of Applied Statistics, 14 (2). pp. 706-726. ISSN 1932-6157, http://eprints.lse.ac.uk/102338/

Abstract:
We consider the use of sample survey data to estimate dyadic characteristics of family networks, with an application to non-coresident parent-child dyads. We suppose that survey respondents report either from a parent or child perspective about a dyad, depending on their membership of the dyad. We construct separate estimators of com- mon dyadic characteristics using data from both a parent and a child perspective and show how comparisons of these estimators can shed light on data quality issues including differential missingness and re- porting error. In our application we find that a simple missingness model explains some striking patterns of discrepancies between the estimators and consider the use of poststratification and a related re- definition of count variables to adjust for these discrepancies. We also develop approaches to combining the separate estimators efficiently to estimate means and frequency distributions within subpopulations.

Title:
Steele, Fiona and Grundy, Emily (2020) Random effects dynamic panel models for unequally-spaced multivariate categorical repeated measures: an application to child-parent exchanges of support. Journal of the Royal Statistical Society. Series C: Applied Statistics, 70(1), pp. 3-23.Take a look at the article.  

Abstract:
Exchanges of practical or financial help between people living in different households are a major component of intergenerational exchanges within families and an increasingly important source of support for individuals in need. Using longitudinal data, bivariate dynamic panel models can be applied to study the effects of changes in individual circumstances on help given to and received from non-coresident parents and the reciprocity of exchanges. However, the use of a rotating module for collection of data on exchanges leads to data where the response measurements are unequally spaced and taken less frequently than for the time-varying covariates. Existing approaches to this problem focus on fixed effects linear models for univariate continuous responses. We propose a random effects estimator for a family of dynamic panel models that can handle continuous, binary or ordinal multivariate responses. The performance of the estimator is assessed in a simulation study. A bivariate probit dynamic panel model is then applied to estimate the effects of partnership and employment transitions in the previous year and the presence and age of children in the current year on an individual’s propensity to give or receive help. Annual data on respondents’ partnership and employment status and dependent children and data on exchanges of help collected at 2- and 5-year intervals are used. 

Presentations

Tania Burchardt "Reciprocity and the Welfare State", Panel Discussion of the new issue of the LSE Public Policy Review, Beveridge 2.0: Reciprocity Across the Life-Cycle, LSE online public event, 28 September 2021. Take a look at the webinar podcast and video. 

Tania Burchardt “Intergenerational exchanges of practical and financial support within families across households”, Beveridge 2.0 Reciprocity Across the Life-cycle, STICERD, LSE, 23 February 2021. https://sticerd.lse.ac.uk/_new/research/beveridge/reciprocity-symposium.asp

Irini Moustaki “Modelling intergenerational exchanges using models for multivariate longitudinal data with latent variables in the presence of zero excess”, City University of New York (CUNY) Graduate Center, 1 April 2019.

Irini Moustaki “Modelling intergenerational exchanges using models for multivariate longitudinal data with latent variables in the presence of zero excess”, Center for Practice and Research at the Intersection of Information, Society and Methodology (PRIISM), NYU Steinhardt, 17 April 2019.

Jouni Kuha “Latent variables models for intergenerational exchanges of family support”, International Meeting of the Psychometric Society, Santiago (Chile), 15-19 July 2109.

Irini Moustaki “multivariate longitudinal data with zero inflation: a study of intergenerational exchanges”, International Meeting of the Psychometric Society, Santiago (Chile), 15-19 July 2019.

Fiona Steele “Dynamic models for longitudinal multivariate data with responses measured at unequal intervals”, Statistical Analysis of Multi-Outcome Data, University of Manchester, 6-7 June 2019 (keynote).

Fiona Steele “Random effects dynamic panel models for unequally-spaced outcomes”, Understanding Society Scientific Conference, University of Essex, 3 July 2019.

Fiona Steele “Random effects dynamic panel models for unequally-spaced outcomes”, International Workshop on Statistical Modeling, Guimarães, Portugal, 8-12 July 2019.

Fiona Steele “Random effects dynamic panel models for unequally-spaced outcomes”, 12^th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, University of London, 14-16 December 2019 (invited presentation).

Kuha, Jouni, Zhang, Siliang and Steele, Fiona. Latent variable models for multivariate dyadic data with zero inflation: Analysis of intergenerational exchanges of family support. To appear in Annals of Applied Statistics. Download the jsem R package with example. 

Steele, Fiona and Grundy, Emily (2020) Random effects dynamic panel models for unequally-spaced multivariate categorical repeated measures: an application to child-parent exchanges of support. Journal of the Royal Statistical Society. Series C: Applied Statistics, 70(1), pp. 3-23. R and JAGs code. 

More software will be added as further papers from the research are published.