Dáil Éireann is the principal chamber of the Irish parliament. The 31st Dáil was in session from March 11th, 2011 to February 6th, 2016. Many of the members of the Dáil were active on social media, and many were Twitter users who followed other members of the Dáil. The pattern of Twitter following amongst these politicians provides insights into political alignment within the Dáil. We propose a new model, called the generalized latent space stochastic blockmodel, which extends and generalizes both the latent space model and the stochastic blockmodel to study social media connections between members of the Dáil. The probability of an edge between two nodes in a network depends on their respective class labels, as well as sender and receiver effects and latent positions in an unobserved latent space. The proposed model is capable of representing transitivity and clustering, as well as disassortative mixing. A Bayesian method with Markov chain Monte Carlo sampling is proposed for estimation of model parameters. Model selection is performed using the WAIC criterion and models of different number of classes or dimensions of latent space are compared. We use the model to study Twitter following relationships of members of the Dáil and interpret structure found in these relationships. We find that the following relationships amongst politicians is mainly driven by past and present political party membership. We also find that the modeling outputs are informative when studying voting within the Dáil.