Markovian models are often used in modelling a time development of random phenomena. When modelling real world scenarios it is reasonable to assume that the respective phenomena may not be time homogeneous. Based on the sociological and security research, it can be assumed that there is a link between a destabilisation of a society of a given geographical region and the acts of terrorism. This link is utilised in construction of a model for description of the intensity of a terrorist threat based on given determinants/indicators of societal stability. The model is based on the theory of discrete non-homogeneous Markov chains. The theory of generalised linear models (GLMs) is used in the estimation of the probabilities of the categorised level of the terrorist threat. In the contribution the use of different estimates of the categorised level of terrorist threat probabilities is studied. The estimates are determined by GLMs with different input parameters. The influence of the resulting estimate on the transition matrix of the non-homogeneous Markov chain is assessed. Additionally, a real world example utilising the data from Global Terrorism Database of University of Maryland and Organisation for Economical Cooperation and Development is presented.