Semi-supervised clustering of time-dependent categorical sequences with application to discovering education-based life patterns

A new approach to the analysis of heterogeneous categorical sequences is proposed. The first-order Markov model is employed in a finite mixture setting with initial state and transition probabilities being expressed as functions of time. The expectation–maximization algorithm approach to parameter estimation is implemented in the presence of positive equivalence constraints that determine which observations must be placed in the same class in the solution. The proposed model is applied to a dataset from the British Household Panel Survey to evaluate the association between the education background and life outcomes of study participants. The analysis of the survey data reveals many interesting relationships between the level of education and major life events.