Abstract
In this paper a hedonic price function built through a semiparametric additive model is tried out for the real estate market analysis of the central area of Reggio Calabria. The semiparametric model uses Penalized Spline functions and aims to achieve an improvement in the prediction of the market prices of housing properties in the central area of Reggio Calabria. More in particular, the final objective of the research is to detect and to identify possible potential market premium in real estate exchange and rent markets for green buildings. This is the first preliminary phase for the unavoidable verification of the robustness of the real estate sample, or for the subsequent individuation of progressive real estate sub-samples.
Keywords
The authors contributed equally to the study.
1 Introduction
The evolution of real estate markets is influenced by quantitative and qualitative characteristics, as well as by differentiation and the change in the mode of appreciation of the real estate goods. These aspects suggest the development of new and advanced models for hedonic analysis of property prices, able to recognize the different forms of appreciation, based on survey and statistical analysis of market data [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].
Final and telescopic objective of the paper is to detect and to identify possible potential market premium in real estate exchange and rent markets for green buildings [23–28]. This is the first preliminary phase for the unavoidable verification of robustness of the real estate sample, for the subsequent individuation of progressive real estate sub-samples.
In international literature many studies have applied some special non-parametric or semiparametric additive regressions for the formulation of hedonic price models for the analysis of housing market. Mainly, these studies make use to Generalized Additive Models, among the most common non-parametric multivariate regression techniques, and the “backfitting algorithm” [3] that represents main method for resolution of additive models in base to available statistics data [4, 5].
An alternative approach with limited computational difficulties in estimating the individual functions that define an additive model, consists to place and match to each of these functions some specific smoothing spline function.
Currently the use of smoothing spline functions interest many scientific fields, like chemistry, natural and physical sciences, medicine, economy (limitedly to production costs only).
Semi-parametric models applied to real estate appraisals are currently subject of specialized literature and, particularly, it concerns choice and processing of property prices and real estate features [13, 14, 16,17,18,19,20,21,22,23,24].
2 Model Specification
The relationship between selling price and explanatory variables is examined with a semi-parametric additive model, characterized by the combination of a generalized additive model, which expresses the relationship between the non-linear response and the explanatory variables, and a linear mixed effects model, which expresses the spatial correlation of observed values:
More precisely, in the expression (1) the additive component, the mixed effects and the erratic component (ε), are independent. Furthermore, in order to obtain a function estimated using the procedures relating to models mixed effects, it is considered a version of low rank both for the additive component both for the mixed effects [1].
The proposed semiparametric model can then be briefly defined by the following general formula:
where:
Z contains T ≤ N truncated power basis functions of p-degree for the approximation of nonlinear structure in f functions:
And alternatively, in reduced form:
where \( {\text{u}} = \left( {{\text{u1,}} \ldots , {\text{uk}}} \right){\text{T}} \) is the vector of random effects with:
considering the coefficients (uk) of knots (κk) as random effects independent of ε term [1].
Note that the formulation (2) is a particular case of linear mixed-effects model of Gaussian type. For non-linear components of the model are used penalized spline functions qualified by the following general expression:
in which the base of the generic function (3) is represented by the following terms:
Where the generic function \( (x - \kappa_{k} )^{p}_{ + } \) has (p − 1) continuous derivatives.
For p > 0 the expression that is used to determine the fitted values is as follows:
Where:
Simplifying, the relation (4) becomes:
The smoother matrix is defined as follows:
The λ term is usually referred to as smoothing parameter.
The smoothing parameter intervenes in the determination of the degrees of freedom for nonlinear component of the model and allows also to control the trade-off between fitting model to the observed values (smoothing parameter near to zero value) and the smoothness of the same (high values of smoothing parameters).
The selection of the smoothing parameter, for a spline function of p-degree, occurs by the Restricted Maximum Likelihood condition.
3 The Real Estate Market Analysis of the Central Area of Reggio Calabria
The market price analysis of the property carried out with the use of an additive semi-parametric model provides for the adoption of statistical tools (significance test, measures of residues, etc.) able to select both the sample data and the endogenous variables [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]; these tools also allow to verify the reliability and the quality of results.
The algebraic structure of proposed model has been specified on the basis of real estate data of the sample, as well with the help of statistical and empirical- argumentative tests, by implementing the following semiparametric additive model:
The data sample refers to a defined real estate market segment of Reggio Calabria (Calabria region, Italy) and, specifically, no. 490 sales of residential property units located in an urban central area during twenty five years (Tables 1 and 2).
The sampled properties have the same build type and quality (residential units located in used multi-storey buildings), and they are included in a homogeneous central area in terms of qualification and distribution of main services.
In the absence of multicollinearity phenomena, given the low correlation between the explanatory variables, the main verification indexes of the model are shown for completeness in tables and graphs.
The amounts related to the standard error (€ 15,313.85) and absolute percentage error (11,40%) appear congruent, because the forecast values obtained using the proposed model show a trend compliant to observed data, also even residue analysis shows no abnormalities (Fig. 1).
From the statistical point of view, significant is the determination index, equal to 0,969 (corrected index equal to 0,968), as well as the F test is significant for a 95% confidence level.
The fixed effects of model’s linear component that result statistically significant coincide with all variables.
With regard to the nonlinear part of model, there are no significant abnormalities encountered in the values assumed by smoothing parameters (spar) or freedom degrees (df), (see Table 3).
In the model’s linear component, the variables’ coefficients directly express the implicit marginal prices; for the nonlinear component, marginal prices for each variable are obtained by processing and examination of estimated functions.
For brevity of discussion, for each nonlinear variable of model, the marginal prices are not shown, being a primary objective of this paper the experimentation of proposed model and to verify the reliability of the real estate sample.
In conclusion, this work leads to results which, for their consistency with buying and selling prices detected, can be considered representative of the validity of the methodology used. The tool used for analyze the real estate data is the R-project software.
4 Conclusions
The results obtained with the application of the proposed model are excellent, and they suggest that semiparametric models can be successfully used for the prediction of residential property selling prices.
In the study case the error committed in the prediction of selling prices is lower about 3.26% respect to conventional multiple regression models, showing very high use’s potential. This result may aid to detect and to identify, as further future research developments, possible potential market premium in real estate exchange and rent markets for green buildings, as well as progressive real estate sub-samples to analyze.
More generally, in line with the experimental results obtained in this paper, the semiparametric models can lead to improved estimated between 10 and 20% in the prediction of housing market prices, compared to conventional multiparametric techniques. The objectives pursued with the theoretical model proposed are many and varied, such as the study of the various segments of the local real estate markets, or even the prediction and interpretation of phenomena related to the genesis of the income housing, with particular reference to the problems of transformation of urban areas concerned from projects or plans of action and in order to optimize the user choices of goods and resources such as energy.
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Del Giudice, V., Massimo, D.E., De Paola, P., Forte, F., Musolino, M., Malerba, A. (2019). Post Carbon City and Real Estate Market: Testing the Dataset of Reggio Calabria Market Using Spline Smoothing Semiparametric Method. In: Calabrò, F., Della Spina, L., Bevilacqua, C. (eds) New Metropolitan Perspectives. ISHT 2018. Smart Innovation, Systems and Technologies, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-92099-3_25
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