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Published in:
19-09-2017 | Erratum
Erratum to: Housing price prediction: parametric versus semi-parametric spatial hedonic models
Published in: Journal of Geographical Systems | Issue 1/2018
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Excerpt
In the original publication, in Table 1, there is a misprint in equations under models SDEM and SEM. The specification for the spatially correlated error term, u, must be \( {\mathbf{u}} = \lambda {\mathbf{Wu}} + {\varvec{\upvarepsilon}} \). The correct versions of these equations are given below. The original version of the article has been updated (Table 1).
Table 1
Competing hedonic house price models: parametric and semi-parametric model specifications
|
Model
|
Specification
|
Spatial lag
|
Spatial drift
|
Nonparametric functions of covariates
|
||
|---|---|---|---|---|---|---|
|
Response
|
Covariates
|
Error
|
||||
|
Parametric models
|
||||||
|
(i) Conventional a-spatial hedonic model
|
||||||
|
HM
|
\( {\mathbf{y}} = \alpha {\mathbf{i}}_{n} + {\mathbf{X{\varvec{\upbeta}}}} + {\varvec{\upvarepsilon}} \)
|
|||||
|
(iia) SAR models
|
||||||
|
SLM
|
\( {\mathbf{y}} = \rho {\mathbf{Wy}} + \alpha {\mathbf{i}}_{n} + {\mathbf{X{\varvec{\upbeta}}}} + {\varvec{\upvarepsilon}} \)
|
x
|
||||
|
SDM
|
\( {\mathbf{y}} = \rho {\mathbf{Wy}} + \alpha {\mathbf{i}}_{n} + {\mathbf{X{\varvec{\upbeta}}}} + {\mathbf{WX{\varvec{\uptheta}}}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
|||
|
SDEM
|
\( {\mathbf{y}} = \alpha {\mathbf{i}}_{n} + {\mathbf{X{\varvec{\upbeta}}}} + {\mathbf{WX{\varvec{\uptheta}}}} + {\mathbf{u}},\quad {\mathbf{u}} = \lambda {\mathbf{Wu}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
|||
|
(iib) SEM model
|
||||||
|
SEM
|
\( {\mathbf{y}} = \alpha {\mathbf{i}}_{n} + {\mathbf{X{\varvec{\upbeta}}}} + {\mathbf{u}},\quad {\mathbf{u}} = \lambda {\mathbf{Wu}} + {\varvec{\upvarepsilon}} \)
|
x
|
||||
|
Semi-parametric models
|
||||||
|
(iii) PSSD-HM and PSSD-SAR models
|
||||||
|
PSSD-HM
|
\( {\mathbf{y}} = f\left( {s_{1} ,s_{2} } \right) + {\mathbf{X{\varvec{\upbeta}}}} + {\varvec{\upvarepsilon}} \)
|
x
|
||||
|
PSSD-SLM
|
\( {\mathbf{y}} = f(s_{1} ,s_{2} ) + \rho {\mathbf{Wy}} + {\mathbf{X{\varvec{\upbeta}}}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
|||
|
PSSD-SDM
|
\( {\mathbf{y}} = f(s_{1} ,s_{2} ) + \rho {\mathbf{Wy}} + {\mathbf{X{\varvec{\upbeta}}}} + {\mathbf{WX{\varvec{\uptheta}}}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
x
|
||
|
(iv) GAM model
|
||||||
|
GAM
|
\( {\mathbf{y}} = \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + \alpha {\mathbf{i}}_{n} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\varvec{\upvarepsilon}} \)
|
x
|
||||
|
(v) GAM-SAR models
|
||||||
|
GAM-SLM
|
\( {\mathbf{y}} = \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + \alpha {\mathbf{i}}_{n} + \rho {\mathbf{Wy}} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
|||
|
GAM-SDM
|
\( {\mathbf{y}} = \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + \sum\limits_{r = 1}^{l} {f_{2,r} \left( {{\mathbf{W}}x_{r}^{ + } } \right)} + \alpha {\mathbf{i}}_{n} + \rho {\mathbf{Wy}} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\mathbf{WX}}^{*} {\varvec{\uptheta}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
x
|
||
|
(vi) PSSD-GAM model
|
||||||
|
PSSD-GAM
|
\( {\mathbf{y}} = f(s_{1} ,s_{2} ) + \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
|||
|
(vii) PSSD-GAM-SAR models
|
||||||
|
PSSD-GAM-SLM
|
\( {\mathbf{y}} = f(s_{1} ,s_{2} ) + \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + \rho {\mathbf{Wy}} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
x
|
||
|
PSSD-GAM-SDM
|
\( {\mathbf{y}} = f(s_{1} ,s_{2} ) + \sum\limits_{r = 1}^{l} {f_{1,r} \left( {x_{r}^{ + } } \right)} + \sum\limits_{r = 1}^{l} {f_{2,r} \left( {{\mathbf{W}}x_{r}^{ + } } \right)} + \rho {\mathbf{Wy}} + {\mathbf{X}}^{*} {\varvec{\upbeta}} + {\mathbf{WX}}^{*} {\varvec{\uptheta}} + {\varvec{\upvarepsilon}} \)
|
x
|
x
|
x
|
x
|
|