Panel data is encountered in a large variety of disciplines, from social sciences to medical studies, and has been used to examine increasingly complex processes. Recent work in the analysis of panel data, particularly under Markov assumptions, has been leading towards models for data that evolve over time. We propose a method for modeling such non-homogeneous processes through the use of splines and penalized splines. We provide a brief overview of spline theory, as well as the basic notions for modeling panel data under a Markov assumption. We then discuss the proposed method and supply
examples from simulated and previously modeled data. The proposed method is particularly well suited to exploratory analysis and simplifying complex models.