We consider the analysis of dyadic network data on ties between individuals in different clusters where the presence of a directed tie is reported by each individual in a dyad and the cluster-level network is of interest. A generalisation of the Social Relations Model (SRM) is proposed which includes actor, partner and dyad effects at the individual and cluster levels. The model additionally uses “double-sampling” of ties to estimate a measurement model which adjusts for and quantifies the extent of reporter effects. The model can be viewed as a type of multilevel structural equation model, with multiple cross-classified random effects, which can be estimated using Markov chain Monte Carlo (MCMC) methods in Bayesian software. Using parameter estimates from this multilevel SRM, we then propose two alternative ways of deriving the between-cluster network that are based on predictions of the strength of between-cluster ties. Our approach is illustrated using data on social support networks in a rural community in Nicaragua where individual reports of bidirectional exchanges of support with individuals from other households are used to derive the between-household network.

Previous cross-sectional research has found correlation in the health outcomes of coresident adults. However, the study of household effects in longitudinal data is challenging due to the complex association structure arising from changes in household membership over time. We propose a 'grouped' multilevel model where the groups (called 'superhouseholds') are specified to capture changes in household structure. Correlated household random effects are used to capture correlations between households sharing an individual(s), and correlations between household pairs can depend on covariates that describe their relationship. We develop a constrained Markov chain Monte Carlo procedure for model estimation that ensures the group-specific correlation matrices (where dimensions can vary across groups) are positive definite, and implement it as an R package. The performance and robustness of our models are evaluated in a simulation study and then applied in analyses of household and area effects on self-rated physical and mental health in the UK using data from a national household panel survey.

Simulation-based methods are an alternative approach to sample size calculations, particularly for complex multilevel models where analytical calculations may be less straightforward. A criticism of simulation-based approaches is that they are computationally intensive, so in this paper we contrast different approaches of using the information within each simulation and sharing information across scenarios. We describe the “standard error” method (using the known effect estimate and simulations to estimate the standard error for a scenario) and show that it requires far fewer simulations than other methods. We also show that transforming power calculations onto different scales results in linear relationships with a particular family of functions of the sample size to be optimized, resulting in an easy route to sharing information across scenarios.

Social relations models allow the identification of cluster, actor, partner, and relationship effects when analysing clustered dyadic data on interactions between individuals or other units of analysis. We propose an extension of this model which handles longitudinal data and incorporates dynamic structure, where the response may be continuous, binary, or ordinal. This allows the disentangling of the relationship effects from temporal fluctuation and measurement error and the investigation of whether individuals respond to their partner’s behaviour at the previous observation. We motivate and illustrate the model with an application to Canadian data on pairs of individuals within families observed working together on a conflict discussion task.

We define a model for the joint distribution of multiple continuous latent variables, which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between generations and complementarity of different kinds of help. We 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. The model is applied to data from the UK Household Longitudinal Study to analyse exchanges of practical and financial support between adult individuals and their noncoresident parents.

We consider how exchanges of support between parents and adult children vary by demographic and socio-economic characteristics and examine evidence for reciprocity in transfers and substitution between practical and financial support. Using data from the UK Household Longitudinal Study 2011-19, repeated measures of help given and received are analysed jointly using multivariate random effects probit models. Exchanges are considered from both a child and parent perspective. In the latter case, we propose a novel approach to account for correlation between mother and father reports and develop an efficient MCMC algorithm suitable for large datasets with multiple outcomes.