This is an introduction on discrete-time Hidden Markov models (HMM)
for longitudinal data analysis in population and life course studies. In the Markovian
perspective, life trajectories are considered as the result of a stochastic process
in which the probability of occurrence of a particular state or event depends on the
sequence of states observed so far. Markovian models are used to analyze the transition
process between successive states. Starting from the traditional formulation
of a first-order discrete-time Markov chain where each state is liked to the next
one, we present the hidden Markov models where the current response is driven
by a latent variable that follows a Markov process. The paper presents also a simple
way of handling categorical covariates to capture the effect of external factors
on the transition probabilities and existing software are briefly overviewed. Empirical
illustrations using data on self reported health demonstrate the relevance of the
different extensions for life course analysis.