The use of discrete spatial-statistical methods for poverty analyses is important, especially in light of the fact that living standards surveys are generally dominated by categorical observations made at several locations. The proximity of these observations imposes geographical structure on the data. This study presents ordinal geo-statistical models for household poverty analyses that recognize the ordinal nature of poverty severity. For all models, Bayesian inference via Markov Chain Monte Carlo (MCMC) was used. Precision of the models, understood in terms of ease of implementation and accuracy of estimation, is compared. The objective was to quantify spatial associations, given some household features, and produce a map of poverty-severity for Ghana. The Clipped Gaussian Spatial Ordinal Probit (CG-SOP) Model was identified as best for describing spatial poverty. Positive correlation with respect to the distribution of extreme poverty was observed. We see evidence of this in the map of predictions. Significant variables include household size, education, and residency of household head. This approach to poverty analysis is relevant for policy design and the implementation of cost-effective programmes to reduce (category and site)-specific poverty, and monitoring changes in both category and geographical trends thereof. Analysis was based on the Ghana living standards survey (GLSS) 2012 data.