Exploring a multilevel approach with spatial effects to model housing price in San José, Costa Rica

Abstract

A multilevel model of the housing market for San José Metropolitan Region (Costa Rica) was developed, including spatial effects. The model is used to explore two main questions: the extent to which contextual (of the surroundings) and compositional (of the property itself) effects explain variation of housing prices and how does the relation between price and key covariates change with the introduction of multilevel effects. Hierarchical relations (lower level units nested into higher level) were modeled by specifying multilevel models with random intercepts and a conditional autoregressive term to include spatial effects from neighboring units at the higher level (districts). The random intercepts and conditional autoregressive models presented the best fit to the data. Variation at the higher level accounted for 16% of variance in the random intercepts model and 28% in the conditional autoregressive model. The sign and magnitude of regression coefficients proved remarkably stable across model specifications. Travel time to the city center, which presented a non-linear relation to price, was found to be the most important determinant. Multilevel and conditional autoregressive models constituted important improvements in modeling housing price, despite most of the variation still occurring at the lower level, by improving the overall model fit. They were capable of representing the regional structure and of reducing sampling bias in the data. However, the conditional autoregressive specification only represented a limited advance over the random intercepts formulation.

Understanding the spatial statistical properties of a real estate listings point pattern in San José, Costa Rica

“…The location of available real estate for sale is distinctly and systematically determined by geographic factors, as should be expected from such a complex setting. Future work on the point pattern analysis of real estate markets in San José could aim to find spatio-temporal patterns (and in particular, given the collected data is for 2020 and 2021, any short run variations related to the COVID-19 pandemic); in addition, previous hedonic price models of the region (Pérez-Molina 2022) would benefit from a critical reappraisal and the consideration of preferential sampling bias, along the lines of Paci et al (2020).…”

“…The determinants of the real estate listings point process were assumed to be similar to those of property prices. Previous studies (Pérez-Molina 2022) and theoretical developments (Koomen and Stillwell 2007) have explored the role of these determinants. Five basic patterns were selected: slope, as flatter areas are more desirable than steeper locations; elevation, because relatively higher elevations correspond to the less attractive periphery of the region; Euclidean distance from the CBD and from the nearest municipal center, as main and secondary urban centralities (Euclidean distance was chosen to reduce endogeneity introduced by the local network); Euclidean distance from main roads, being close to which represents especially good accessibility.…”

Liu-type pretest and shrinkage estimation for the conditional autoregressive model

“…Table (2) above summarized the results of the relative efficiencies. The table indicates that the submodel estimator β1 SM dominates all other estimators followed by the pretest estimator β1 PTL .…”

“…For example, but not limited to, Shen X. et.al [ 1 ] proposed CA model to analyze the heterogenous genetic effects among individuals which is considered as a random effect in their model. Pérez-Molina [ 2 ] modeled hierarchical relationships using multilevel models with random intercepts and a CA component to account for spatial effects. He demonstrated that such models are significantly improve housing price modeling.…”

A Survey of Methods and Input Data Types for House Price Prediction

“…A hierarchical-spatial approach is proposed in [63] by combining spatial econometrics with a two-level approach for apartment price prediction: the first level relates to the individual apartment characteristics, and the second level includes local neighborhood characteristics. Similarly, a multilevel linear regression model is implemented in [78]; however, a conditional autoregressive term is added instead of the general spatial model that forms the basis of the multilevel model used in [63].…”