This article presents an empirical plugging of factor analysis and generalized linear regression (logistic regression, Cox models, ...). We show that this combination can facilitate the exploration of complex data such as that on event histories (time-varying, censored) for modelling purposes. By combining a regression method with a new type of factor analysis — Thematic Components Analysis — we show how an explanatory conceptual model for the data can be included from the start of the exploratory phase. This method is then applied to an analysis of the divorce behaviour of men in Dakar, and used to give a simple illustration of each methodological point discussed.