Modelling house prices using multilevel structured additive regression

Abstract

This paper analyzes house price data belonging to three hierarchical levels of spatial units. House selling prices with associated individual attributes (the elementary level-1) are grouped within municipalities (level-2), which form districts (level-3), which are themselves nested in counties (level-4). Additionally to individual attributes, explanatory covariates with possibly nonlinear effects are available on two of these spatial resolutions. We apply a multilevel version of structured additive regression (STAR) models to regress house prices on individual attributes and locational neighbourhood characteristics in a four-level hierarchical model. In multilevel STAR models the regression coefficients of a particular nonlinear term may themselves obey a regression model with structured additive predictor. The framework thus allows to incorporate nonlinear covariate effects and time trends, smooth spatial effects and complex interactions at every level of the hierarchy of the multilevel model. Moreover, we are able to decompose the spatial heterogeneity effect and investigate its magnitude at different spatial resolutions allowing for improved predictive quality even in the case of unobserved spatial units. Statistical inference is fully Bayesian and based on highly efficient Markov chain Monte Carlo simulation techniques that take advantage of the hierarchical structure in the data.

Value of urban views in a bay city: Hedonic analysis with the spatial multilevel additive regression (SMAR) model

“…(i) it can capture the non-linear effects of the view variables as well as the other variables; (ii) it can consider the multilevel structure of condominiums by the introduction of the normally distributed error term, u j ; and (iii) it can consider the spatial autocorrelation by the introduction of the term s(lon j , lat j ). To the author's knowledge, only Brunauer et al (2013) have considered all of these aspects in hedonic analyses, although they did not focus on views.…”

Estimation of Housing Price Variations Using Spatio-Temporal Data

“…On the other hand, the error term includes the spatial dependence structure and the random component. In regard to the specification of the hedonic housing price model, it is very common to use a semilog model [66][67][68][69].…”

Monitoring 15 Years of Residential House Price Development in Hungary With the Help of the FHB House Price Index

“…and build the data model on top of it. Although not directly concerned with price indices, Brunauer et al (2013) offers an example of such an approach.…”