A multilevel approach to modelling property prices in the United Kingdom

Abstract

Multilevel models are used to analyse datasets having a hierarchical structure, where individual units are grouped into higher level clusters. These models overcome the limitations of traditional regression and generalized linear models when the assumption of independence in the residuals is violated. In multilevel models, an error term is included at each level of nesting, enabling the study of the variation in the responses at each hierarchical level. Multilevel models incorporate both fixed and random effects in the linear predictor, where the random effects represent the unexplained variability in the intercepts and slopes. When fitting multilevel models, parameters are estimated by maximizing the marginal log-likelihood. The Gauss-Hermite quadrature or adaptive quadrature is used for numerical integration. Random effects are then predicted using an empirical Bayes estimation procedure, given the data and parameters. The dataset provides the prices of properties that were sold in three UK counties, including Greater London, Oxfordshire,and Greater Manchester during December 2017 and registered with the HM Land Registry. Several multilevel models are fitted using the facilities of the GLLAMM subroutine in the Stata package, where the properties (level-1 units) are nested within a total of forty-eight districts (level-2 units), which are further clustered into the three counties (level-3 units). The property price is the response variable, while the building type (detached,semi-detached,terraced,flats/maisonettes,or others),age of building(new or old), and tenure type (freehold or leasehold) are the explanatory variables.