Analysing the Course of Trust Towards Public and Financial Institutions via Hidden Markov Models

We propose a statistical method to analyse public trust which is considered as latent concept fluctuating over time. At this aim, using measured trust's levels from individual items of a long-term survey is necessary because key variables with appropriate meaning are not available elsewhere. We conceive trust as a mental unobservable feature of each person which is related to the observed time-varying and time-fixed covariates and we propose a hidden Markov model to account for the repeated measures and for longitudinal sampling weights as well as missing responses. We estimate the model parameters by a weighted log-likelihood maximized by the Expectation-Maximization algorithm. We use data collected in an East-Central European country like Poland where the level of support to the national and international institutions is one of the lowest among the European member states. We apply a suitable algorithm based on the posterior probabilities to predict the best allocation of each individual in each latent typology. We validate the proposed model by predicting out-of-sample responses and we find reasonable predictive values. Concerning the applicative example we disentangle four hidden groups of Poles: discouraged, with no opinion, with selective trust and with fully public trust. We predict an increasing number of people that are going to select the institutions to support over time