There is a great deal of literature regarding use of non-geographically based connectivity matrices or combinations of geographic and nongeographic structures in spatial econometrics models. We focus on convex combinations of weight matrices that result in a single weight matrix reflecting multiple types of connectivity, where coefficients from the convex combination can be used for inference regarding the relative importance of each type of connectivity. This type of model specification raises the question — which connectivity matrices should be used and which should be ignored. For example, in the case of L candidate weight matrices, there are M = 2L −L−1 possible ways to employ two or more of the L weight matrices in alternative model specifications. When L = 5, we have M = 26 possible models involving two or more weight matrices, and for L = 10, M = 1, 013. We use Metropolis-Hastings guided Monte Carlo integration during MCMC estimation of the models to produce log-marginal likelihoods and associated posterior model probabilities for the set of M possible models, which allows 1 for Bayesian model averaged estimates. We focus on MCMC estimation for a set of M models, estimates of posterior model probabilities, model averaged estimates of the parameters, scalar summary measures of the non-linear partial derivative impacts, and associated empirical measures of dispersion for the impacts.