Modelling a multivariate hidden Markov process on survey data

We show how to handle the information which is acquired in a dynamic framework when there are multiple items in a survey collected on the same individuals at different time occasions. The response variables are commonly measured on an ordinal scale and the data may show a non-monotone missing pattern. The underlying phenomenon which is related to the interest of the survey may be modelled by a latent stochastic process. The latter having dependences according to a Markov structure is able to capture the heterogeneity of the response behaviour and to account for the measurement errors that naturally arise in the survey. The maximum likelihood estimation of the model parameters allows us to handle the missing data and to take advantage of the information provided by those individuals not showing complete responses. In a similar way, it is possible to consider a counterfactual framework in which the outcomes of interest are not directly observable even for the selected treatment. Such a flexible modelling approach is illustrated with two examples based on real data.