  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.
