Spatial hedonic modelling adjusted for preferential sampling

Hedonic models are widely used to predict selling prices of properties. Originally, they were proposed as simple spatial regressions, i.e. a spatially referenced response regressed on spatially referenced predictors. Subsequently, spatial random effects were introduced to serve as surrogates for unmeasured or unobservable predictors and were shown to provide better out-of-sample prediction. However, what has been ignored in the literature is the fact that the locations (and times) of the sales are random and, in fact, are an observation of a random point pattern. Here, we first consider whether there is stochastic dependence between the point pattern of locations and the set of responses. If so, a second question is whether incorporating a log-intensity for the point pattern of locations in the hedonic modelling enables improvement in the prediction of selling price. We connect this problem to what is referred to as preferential sampling. Through model comparison we illuminate the role of the point pattern data in the prediction of selling price. Using two different years of property sales from Zaragoza, Spain, we employ both the full database as well as an intentionally biased subset to elaborate this story.