In the context of categorical data analysis, the case of nominal and ordinal data has been investigated in depth while the case of partially ordered data has been comparatively neglected. We first propose a new specification of generalized linear models (GLMs) for categorical response variables which encompasses all the classical models such as multinomial logit, odds proportional or continuation ratio models but also led us to identify new GLMs. This unifying framework makes the different GLMs easier to compare and combine. We then define the more general class of partitioned conditional GLMs for categorical response variables. This new class enables to take into account the case of partially ordered data by combining nominal and ordinal GLMs.