State space mixed models for binary responses with scale mixture of normal distributions links

We propose a state space mixed models for binary time series where the inverse link function is modeled to be a cumulative distribution function of the scale mixture of normal (SMN) distributions. Specific inverse links examined include the normal, Student-t, slash and the variance gamma links. We use the threshold latent approach (Albert and Chib, 1993) to represent the binary system as a linear state space model. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. We illustrate the proposed methods with real data set. Empirical results showed that the slash inverse link fit better over the usual inverse probit link.