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A hedonic model comparison for residential land value analysis
International Journal of Applied Earth Observation and Geoinformation 12S (2010) S181–S193
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International Journal of Applied Earth Observation and Geoinformation journal homepage: www.elsevier.com/locate/jag
A hedonic model comparison for residential land value analysis Yaolin Liu a,b, Bin Zheng c,d,*, Jan Turkstra e, Lina Huang a,b a
Key Laboratory of Geographic Information System, Ministry of Education, Wuhan 430079, China School of Resource and Environment Science, Wuhan University, Wuhan 430079, China c College of Public Administration, Huazhong University of Science and Technology, Wuhan 430074, China d HUST Land & Resources and Real Estate Research Center, Wuhan 430074, China e UN-Habitat, Global Urban Observatory, P.O. Box 30030, Nairobi 00100, Kenya b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 15 April 2009 Accepted 25 November 2009
Distantial attenuation is a significant characteristic of the urban environment. In this paper we explore the relative contributions of different land uses to the urban residential environment according to distances with an analysis on the most significant scope of these factors. Two types of models are developed. One employs the distance to city center, main road, public facilities and environment factors as the variables for macro environment analysis, and the another one includes all factors to analyze the influences of the micro environment. In the models of the latter type, the contributions of the neighboring land uses are magnified with a specially designed variable measurement scheme in which variables are evaluated specially for each model so that the contributions of the variables become comparable from model to model. With an application to the case study of Danyang, China, we measure the distantial functions of the urban environment (e.g. the surrounding land uses) including both the most influential scopes and the relative contributions by means of model summary and regression coefficient comparisons. Finally, case comparison on the samples is introduced to figure out the difference of the functions under micro environment. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Distance measurement Hedonic regression model Residential land value Benchmark price Neighborhood analysis
1. Introduction Distantial attenuation is a significant feature of the location. Since every urban land use activity should consider the best location to acquire the most utilities, the distance dependences to each of the environment factors are sure to be of interest to researchers. In most of these studies land value always evolved as a substitute for the location utility. Perhaps the most fundamental one among these studies is the work done by Wingo (1963) who firstly tried to systematically analyse the relationship between the distance function of location and the urban land value by modeling the value of consumption in transport. He developed his famous location equilibrium theory which declared that transportation costs can be substituted by the space costs or land values. Then there is Alonso’s profound trade-off theory (Evans, 1987; Kivell, 1993) in which Alonso (1964) pointed out that land values are generally determined
Abbreviations: CBD, central business district; HRM, hedonic regression model; RBP, residential benchmark price; MVRL, market value of residential land; RMB, Ren Min Bi (in Chinese), or Chinese Yuan, Chinese currency unit. * Corresponding author at: College of Public Administration, Huazhong University of Science and Technology, Wuhan 430074, China. Tel.: +86 15307156122. E-mail address: [email protected] (B. Zheng). 0303-2434/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jag.2009.11.009
in the urban area, more specifically speaking, the value (or the utility) of the urban land should decline with the increasing the distance to the CBD. Based on the fundamental researches of Wingo and Alonso, more considerate investigations were performed. For decades, scholars have spent a lot of endeavor in investigating various commercial places and retail supplies other than being solely focused on the CBD (Ragas, 1987; Song and Sohn, 2007) accompanied with generalized transport including the accessibility changes (Smersh and Smith, 2000) and transporting improvements (Yiu and Wong, 2005) were considered. Location of all kinds of public services such as schools (Chin and Foong, 2006), outdoor recreations (Wilman, 1988), etc. or a synthetic supply (Randall, 2005) also provides many prostheses for such discussion. As a traditional public issue, the accessibility to the environment amenities such as open space (Jim and Chen, 2006, 2007; Kong et al., 2007) or urban forest (Tyrva¨inen, 1997; Tyrva¨inen and Miettinen, 2000) arouses a lot of interest too. Compared to the pioneers, these researches are no more rigidly macroscopic and theoretic and the results work more confidently. Recently some scholars began paying their attention to the neighborhood effects (Galster et al., 2004; Hui et al., 2007; Tse, 2002). Some founded that in the classical smooth attenuated models for urban environment influence analysis, the contiguous influences are always underestimated. Although there are no systemic and specific investigations about it yet, some of the researches have
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surely proved that the influence of the distantial attenuation of the urban environment exists in both the ‘‘unique spatial fixity in the urban area’’ (i.e. macro environment) and the ‘‘neighborhood characteristics’’ (i.e. micro environment) (Jim and Chen, 2007; Wendt, 1957). Urban land is a multiattribute utility comprising of heterogeneous characteristics (Colwell and Munneke, 1997; Qadeer, 1981; Wendt, 1957), hedonic regression method (HRM) makes its numeral measuring possible. In the HRM, land value can be specified into a bundle of the locational characteristics of the plot and expressed as some kinds of the form of Uðz1 ; B z2 ; B . . . ; B zn Þ, where U means the accumulation of a bunch of utilities ui ðzi Þ, and zi is the normalized distance functions. Statistics and regression procession figures out each value of a particular locational distance, which is described as the ‘‘pure willingness to pay’’ in Bockstael and McConnel’s (2007) manuscript. HRM has significantly promoted the progress of the locational environment studies, especially when it concerns the land value. However, in most of the HRM applications literature researches rely on mono-distance functions, in despite of the difference between macro and micro environment having been mentioned a lot. When Yeates (1965) having noticed that the land value declines only being functional in the area within 1.5 miles to the CBD, for decades the inter-activities between micro and macro environment are seldom discussed qualitatively. Occasionally relative conclusions appeared as some sort of by-products, for example Wu et al. (2004) found that the distance to the nearest park, river or lake being 1000 feet can make sufficient influence on housing price, and Mahan et al. (2000) declared that 1000 feet can
be the margin of the influential distance of the wetland in contributing to the house price, etc. Most of these findings are scattered and not specific. Yes, it is easy to tell that a plot nearing to a main street is less profitable in the city fringe than in the city center, and being near to a park is more attractive than to the main street in the city fringe. Though, how to measure them? The answer is still under the seal. This paper is intended to figure out such differences. Methodologically the paper sketches a model-analysis of the cooperation of the macro environment and the micro environment. Variables contributing to them are strictly distinguished and are selectively added to different HRM models. Firstly the influences of the macro environment are specifically figured out by employing the residential benchmark price (RBP) which is designed and adopted as a kind of general mass appraisal for the physical homogenous environment. Then micro environment is involved in, with introducing the market values of the residential land (MVRL) as the result of complex interactions between the characteristics contributing to both the macro environment and micro environment. The analysis and results cover both the influential scopes and the relative contributions. Different hedonic regressions are designed to estimate the equations for the land values under different environments (Eqs. (1) and (2)). RBP ¼ f ðmacro environmentÞ
(1)
MVRL ¼ f ðmacro environment; micro environmentÞ
(2)
With the application of the geographic information systems (GIS) in handling and processing large amounts of spatial data, it is
Fig. 1. Location of Danyang city.
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possible to associate and process the land value data and locational data we needed and to undertake the analysis with multi-original data (Nzau, 2003; Turkstra, 1998). At last, explicit case comparisons are taken for deducing the results.
Table 1 Value range of RBP of Danyang. Land class
Residential
2. Study area and data description
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RBP (RMB/M2) 1
2
3
4
5
845
640
511
354
275
2.1. Study area According to the Chinese standard, Danyang city is a ‘‘small city’’ (Li, 2001) located in the Yangtze Delta Region, which is economically one of the most successful areas of China (Fig. 1). Since Danyang’s faster urbanization started around early 1980s, a lot of industries were developed to bring to the city a better marketization environment (Danyang-Economic-Planning-Committee, 2002). However, as the urban fringe has greatly extended, the former industries and surrounding low-quality housing that used to be welcomed by industrial laborers, were gradually enveloped inside the urban area and finally become an embarrassment for the new residential development (Fig. 2). Though in the developing viewpoint, all these ‘‘unsuitable’’ land uses inside the urban area will be replaced by other ‘‘clean’’ land uses in the future, but for the current, the nearby industry and lowquality housings are still one of the major factors to be considered in local real-estate development, which finally affect as the prices in local land market. 2.2. Data description 2.2.1. Data of RBP In China, RBP is used as a standard for the official land valuation. As a general mass appraisal, it is legally required to be evaluated
according to the location to the city center, transportation condition, public infrastructure condition, facilities supply, general eco-environment conditions, population density, and land quality, etc. It makes the RBP a most suitable and easiest accessible source of the physical homogenous circumstance measurement of urban area. The spatial pattern of the RBP of Danyang is mapped as follows (Fig. 3). The RBPs distribute in five concentric circles from the city center further to the fringe of the city. Obviously, in the size of city scale, the most influential factor is the distance to the CBD. Beside, the main roads crossing the major center play an important role. Location to some directions can also get more scores in the evaluation than to other directions. The following table is the values of the RBP in different homogeneous zones (Table 1). 2.2.2. Data of MVRL There are total 34 plots of residential land transactions that happened in Danyang in the year of 2002. By eliminating the only transaction via agreement, we keep the remaining 33 auctioned ones. Using the samples from the same year can help us save the endeavor to correct the data according to the temporal change, the extra artificial operation caused by which may finally reduce the accuracy even when the sample size increases concerning the total sample size are small.
Fig. 2. Industrial and residential land uses are mixed in Danyang city.
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Fig. 3. RBP’s appearance under macro environment.
Table 2 Classification of MVRL. Classification
Value range (RMB)
Mean (RMB)
Highest High Middle Low Lowest
1000–1728 600–999 450–599 300–449 0–299
1465 789 502 371 209
To make it clearer and more comparable with the RBP, The MVRL is classified into five classes according to its natural breaks (Table 2). However, after having performed a descriptive statistics, it is observed that the mean value of the data set is 522 and the median value is 403. It indicates that the land prices do not follow the normal distribution. The univariant statistics for the data shows skewed distribution (Fig. 4).
Fig. 4. Histogram of MVRLs.
However, the log-transformed MVRLs show almost a normal distribution (Fig. 5). The QQ Plot for the transformed land prices also proves that (Figs. 6 and 7).The distribution map of MVRL (Fig. 8) is developed by thiessen polygon interpolation with the 33 samples. Differing from the regular concentric distribution of the RBP, it seems that there are no distinct rules that can be applied for the MVRL distribution. For example, in the city center where are classified as the zone with the highest value in RBP, it can be observed that the market land values ranging from the highest to the lowest. At the same time, in the city fringe there exist real high MVRL though it is already apart from the traditional city center. It means that for the residential use, the land value may be more sensitive to the neighboring environment. 2.2.3. Representation of the variables The variables of the study are deduced from the Euclidean space distances from each sample to its environment factors. Here the
Fig. 5. Histogram of log transformed MVRLs.
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Fig. 6. Q–Q plots of MVRLs.
Fig. 7. Q–Q plots of log transformed MVRLs.
‘‘environment factor’’ refers to the selected land uses that are supposed to be able to contribute to the surrounding residential land values. The selection process will be discussed in the following sections. In our models, we employ the direct distance as the source of the variables. The reasons are: firstly, the ‘‘distance’’ is always indicative in the macro scale (especially for the RBP estimation), and the distance interval can be more meaningful, that makes complicated distance transformation unnecessary; secondly, the direct distance is also more appropriate under the micro consideration because in such scale the ‘‘nonlinear coefficient’’ of the road becomes less significant (Li, 2001). The separation of the macro and micro environments can mostly simplify the methodology at the expense of accuracy.
giving period (Liu, 2003). The whole process including the selection of the variables is legally standardized in the official documents (GB/T 18507-2001; GB/T 18508-2001). So the variables for macro environment will be chosen according to these documents. In the procedure of RBP valuation, physical homogeneous zones are firstly outlined out according to the considerations of following 7 aspects (GB/T 18507-2001; GB/T 18508-2001). This phase is also called the ‘‘land gradation and classification’’. The 7 aspects include:
3. Methodology 3.1. Model analysis for macro environment analysis In China, the benchmark price means the valid value of general quality and environment of the land for a peculiar usage during the
Degree of prosperity, which refers to providing of commercial services, always measured by the distance to the commercial centers (CBD and sub-center). Transportation condition, which includes the accessibility to main roads, the convenience of public traffic services and the accessibility to the means of external transportation (e.g. stations and ports). Public infrastructure level (e.g. the condition of the water supply, electricity supply, sewage condition, etc.). Facility supply, which refers to the accessibility to the facilities such as schools, hospitals, recreational locations, etc.
Fig. 8. MVRL’s appearance under both macro environment and micro environment.
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Table 3 Variables for macro environment modeling. No.
Code
Description
1 2 3 4 5 6 7 8 9 10
D_CBD D_MROAD D_RING D_P_SCH D_S_SCH D_MARKE D_RECRE D_MEDIC D_H_IND D_GREEN
Distance Distance Distance Distance Distance Distance Distance Distance Distance Distance
to to to to to to to to to to
Environment conditions including the ratio of vegetable area and basic land quality (e.g. soil composition, topography quality, natural hazard treats). Population density. Other factors. According to these, 10 factors are adopted as independent variables for the model analysis of macro environment (Table 3). To settle the problems of potential non-linear relationship between dependent and independent variables in the models, RBPs are transformed into common logarithms (Nzau, 2003). The model is in the form of the formula shown below: X ln RBP ¼ a þ bi M i (3) where RBP is the dependent variable, a is the regression constant, bi is the value rating for the independent variables, M i is the independent variables represents the distance range of each selected micro factor. Here we use the RBP of each plot as the dependent variable Y. To test whether the independent variables listed in Table 3 are suitable for explaining macro environment, four models are developed and different variables are added progressively in Table 4): Model 1: Distance to the CBD (D_CBD). Model 2: D_CBD and distance to the main road and rings (D_MROAD, D_RING). Model 3: D_CBD, D_MROAD, and distance to the public facilities (D_P_SCH, D_S_SCH, D_MARKE, D_RECRE, and D_MEDIC). Model 4: D_CBD, D_MROAD, distance to the facilities and distance to environmental elements (D_H_IND, D_GREEN). Firstly a correlation analysis is employed to test whether there is a strong explanatory interrelationship between the variables (Appendix A). Though the correlation variables of D_MEDIC and D_RING, D_H_IND and D_MARKE are relative high (reach 0.69), the result of the multicollinearity test is quite opposite to the usual land use rules (Li, 2001) neither there exists any powerful clue from literatures to support that the medical land use is spatially related to the rings or the high pollution industry is spatially related to the market place. Hence, we tend to attribute these high correlations to the small sample size and keep all variables to the following test according to the official documents GB/T 185072001; GB/T 18508-2001.
Measurement the CBD main road ring nearest primary school nearest secondary school nearest marketplace nearest recreational place nearest hospital or clinic nearest high pollution industry nearest open green area
Interval at 400 m
In the macro environment models, the distances are measured at an interval of 400 m, about 1/5 of the radius of the urban area. For most urban facilities such as primary schools, local shopping centers or marketplaces, playfields, etc., this interval can best describe the different convenience standards of the urban facilities, especially for small cities (Chapin, 1965; Li, 2001). 3.2. Model analysis for micro environment analysis Having figured out the variables for macro environment, the primary task in this phase is to find out how the distance-related micro environment contributes to the residential land value. As part of the conclusion, all variables listed in Table 3 are migrated here. Then we employ 8 models with the same measurements for the macro variables (which are proved in the former analysis) and different measurements for micro variables. More specifically speaking, the variables are kept same in the 8 models. The only difference for them is that the values of the variables for the micro environment influences are measured differently. So the parameter estimates will also vary in different models. From which we can find out to which distance a micro environment factor contributes the most when the contributions from all the other factors are assigned the same distance-related rule. Here MVRLs are also transformed into common logarithms. The form of the models is designed as below: X X ln MVRL ¼ a þ bi M i þ cj Xj (4) where MVRL is the market land value, a is the regression constant, bi is the relative contribution of the macro factors in a given distance scale, M i represents the macro locational character of the plot, c j is the relative contribution of the micro factors, X j is the independent variable, which means the distance to the neighboring factors. bi and M i are supposed to have been figured out in the previous phase. Considering that all land use activities will influence the surrounding land use and contribute to their values, we keep 10 variables that include almost all the major land uses we can find in Danyang for the micro environments according to the urban land use classification in China (Li, 2001) and Danyang’s land use map. Neighborhood low-quality residential areas and industrial land are paid special attention. Also this selection is based on the strict correlation test (Appendix B). These variables are (Table 5). Differing from the intervals set for the macro environment, the basic scale of the intervals adopted here is chosen at 50 m, which is
Table 4 Independent variables used in macro environment models. Model
D_CBD
D_MROAD
1 2 3 4
H H H H
H H H H
D_RING
D_P_SCH
D_S_SCH
D_MARKE
D_RECRE
D_MEDIC
D_H_IND
D_GREEN
H H
H H
H H
H H
H H
H
H
H
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Table 5 Variables for micro environment modeling. No.
Code
Description
1 2 3 4 5 6 7 8 9 10
D_H_IND D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMMO D_GREEN D_OFFIC D_TRANS
Distance Distance Distance Distance Distance Distance Distance Distance Distance Distance
to to to to to to to to to to
Measurement high-pollution industry low-pollution industry no-pollution industry single-story residential area multi-story residential area low-quality residential area commerce and services open green area office place bus/railway station
almost the smallest length to contain a multiple-family sector whose width is normally 12–16 m in China (Li, 2001). To analyse the most influential scope of different land uses, the first scale is respectively set as 50 m, 100 m, 150 m, 200 m, 250 m, 300 m, 350 m and 400 m for different models. The value of the first scale is given the smallest 1 m, so the parameter estimation of the relative contribution will be greatly magnified. The value of 0 is carefully avoided to eliminate the immeasurable problem in GIS analysis. Besides, such arrangement best represents that the spatial relationship is not ‘‘on’’ but ‘‘adjacent to’’. The distance more than 500 m is supposed to have reached the scope of macro environment and have little immediate effect. So the value is assigned the largest 3000, which is bigger than the radius of the city to represent the smallest influence. The table below shows the measurements of the distance to different land uses (Table 6). 3.3. Measures of the influence of neighboring roads Roads are always considered as one important infrastructure in the city and may cover all over the cities and people always tend to include them into the macro environment. However, in the micro scale that influence can still be easily noticed because it is also the direct and major measurement of the accessibility even in the micro scale (Kivell, 1993; Nzau, 2003; Srour et al., 2001). That is why we assure that the influence of nearness to a road is not ignorable in the micro environment. To avoid the problem of self-dependence, the contributions of the roads are only traditionally employed as a macro environment in the above regressions. However, for the consideration of a micro comparison, the contributions of the nearby roads should be specially taking into account. As a non-normalized criterion in the road design in China, after every 200 m there should be an access to the main road (Li, 2001). That means the distance less than 200 m can be regarded as a willing distance for walking, especially in Danyang where automobile is not the prevailing method for private transport. So, in this research we investigate the road within 200 m to the main road with the distance classified into four grades with an
Dynamic according to model design
interval of 50 m. The value of 1–4 is assigned as the relative contributions with the nearness increasing gradually (Table 11). Generally, when easy accessibility to more than one main road is observed, it always means more convenience the plot can possess. So the influence of such influence is regarded to be accumulative. 3.4. Case comparison for the test In this phase, the main object is to figure out the variance among the micro influences under different macro environments. With careful case selection and comparison from the 33 samples, confident and intuitional results are deduced. 3.4.1. Case selection As mentioned in previous analysis, the RBP is an average value of certain zones that are regarded to have the same macro environment. With the classification of RBP, the 33 samples are classified into five classes according to their locations (Fig. 9). The classification is shown in Fig. 10, where the RBP morphologically appears as intervallic horizontal lines and the market land prices of the samples are represented as points. In the general sense, the land prices should be similar in the same territory (e.g. 3-5-6-8-10, 4-7, and 30-31-32-25, etc.). But there are still some cases with the similar or nearby location but have distinctly different land values (e.g. 1-12, 21-22, and 26-29, etc.). The following analysis selects typical cases and analyses their neighboring environment to answer the difference. For each zone, one pair of cases is selected for the comparison. They are: I 1-12 in the zone 1, II 11-2 in the zone 2, III 21-20 in the zone3, and IV 29-26 in the zone 4. 3.4.2. Case comparison For each pair of samples, the influences from surrounding land uses and neighboring roads are accumulated respectively for the purpose of summarization. The factors outside the first interval are regarded as having no immediate influence and are assigned the value of 0. Thus we preserve the purification of micro effects. For better comparability, each pair is normalized one by one. That is: for each pair we choose the lower one to assign the value of 1.0,
Table 6 Measurements of the micro environment in different models. Distance (m)
1–50
100
150
200
250
300
350
400
450
500
>1000
Model Model Model Model Model Model Model Model
1 1 1 1 1 1 1 1
50 1 1 1 1 1 1 1
100 100 1 1 1 1 1 1
150 150 150 1 1 1 1 1
200 200 200 200 1 1 1 1
250 250 250 250 250 1 1 1
300 300 300 300 300 300 1 1
350 350 350 350 350 350 350 1
400 400 400 400 400 400 400 400
450 450 450 450 450 450 450 450
3000 3000 3000 3000 3000 3000 3000 3000
1 2 3 4 5 6 7 8
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Fig. 9. Value distribution of 33 samples.
then the other one is also assigned relatively. The formula is designed as follows: 8 < A ¼ A=jBj B ¼ B=jBj (6) : A B; B 6¼ 0
Table 7 Measurement of neighborhood influence of main road.
where A and B are supposed to belong to the same comparable pair. They can be land prices, influence of surrounding land uses or of neighboring road. Normalized differences in each pair represent the validity of the micro influence that makes the locational characteristics differ from place to place. With model solving these differences can provide more explanation.
table below (Table 7) shows the result of the summary of the models (Table 8). Among the four models, the third model is adopted as the right one for describing the influence of the macro environment, because its R2 is the highest and most close to 1 and it also has the lowest standard error of the estimate. The result means that its variables account for 85% of the total RBP variations. There are other factors affecting macro environment, such as land quality and the population density mentioned in the chapter five, they can account for 15% of the RBP variations. The neighboring residential land use which is included in the following micro environment analysis may also make some difference, because being near to different residential land use always means different population density. Besides, the third model’s F-value is 23.112, far above the critical F.05 (8, 24), which means that the model is significant at 95%. So the variables adopted in the model 3 can be adopted as the factors of the macro environment.
4. Results and analyses 4.1. Model comparison for the macro environment analysis The macro models are summarized in SPSS software. Coefficients are worked out by the normal Least-squares method. The
Distance (m)
1–50
51–100
101–150
151–200
Influence Force
4
3
2
1
4.2. Model comparison for the micro environment analysis 4.2.1. Model summary Then the summary analyses are performed for the regressions of all these 8 models in SPSS software and the results are listed in Tables 9 and 10. In Table 8 we can observe that the range of the R2 in 8 models is very small. The result means that all these variables can account for Table 8 Model summary for macro environment.
Fig. 10. Location distribution of 33 samples.
Model
R2
Adjusted R2
Std. error of the estimate
1 2 3 4
0.527 0.588 0.885 0.887
0.511 0.546 0.847 0.835
0.1083 0.1044 6.064E02 6.286E02
Y. Liu et al. / International Journal of Applied Earth Observation and Geoinformation 12S (2010) S181–S193 Table 9 Model summary for MVRL.
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Table 11 Influence of different land uses.
Model
First interval
R2
Std. error of the estimate
1 2 3 4 5 6 7 8
50 m 100 m 150 m 200 m 250 m 300 m 350 m 400 m
0.864 0.867 0.836 0.866 0.871 0.861 0.891 0.846
0.16914 0.16727 0.18613 0.16789 0.16502 0.17134 0.15186 0.17994
Table 10 Results of variance analysis. Model
F-value
Significance
1 2 3 4 5 6 7 8
4.358 4.471 3.480 4.433 4.613 4.299 5.571 3.771
0.005 0.004 0.013 0.004 0.004 0.005 0.001 0.009
at least 84% of the total land value variations and at most 89% of the sample land values. The remaining variations should be explained by other factors, which are not included in the content of this research. The result also shows that the total regressions work well in all these models, as the values of F-statistic are greater than the critical F-value and the significance value of the F statistic is also very good (the largest significant value is 0.013). 4.2.2. Regression coefficient analysis of the influence of neighboring land use The parameter estimates of the proximity to different micro environment factors by using distance intervals are shown in Fig. 11. The regression coefficient denotes how much importance an independent variable contributes to the dependent value. With the elaborate measurements’ proper magnification of the most nearby influence, variables show different behaviors in different models, which can finally tell the farthest influential scope of an
Variable
Most influential scope
Coefficient
Normalized influence force
D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMME D_GREEN D_OFFIC D_TRANS
300 m 350 m 250 m 100 m 100 m 250 m 300 m 250 m 100 m
0.396 0.411 0.644 0.157 1.452 1.124 0.692 0.934 0.160
2.5 2.6 4.1 1.0 9.2 7.2 4.4 5.9 1.0
environment factor contributing as a neighboring environment. The significance of the variables is measured by the t-value. The variation of the regression coefficient of each individual variable among models is shown in linear figures. The dash line represents positive regression coefficient value. That means: the influence of the land use is negative, in another word, the surrounding residential land value will increase with the variable (or the distance to the land use) increasing. The high coefficient value indicates that such negative relative contribution is high. The solid line means that the regression coefficient value is negative and the influence of the land use is positive. The lower the regression coefficient value is, the higher the relative contribution does the land use have on the surrounding residential land value (Fig. 11). As to the statistic for D_H_IND, the highest absolute value of the t-values is only 0.706 (at the first interval of 200 m) and less than 1, which means that in all 8 models, the measurement of the influence of neighboring high pollution cannot confidently explain the variation of the market land values. So the factor should be excluded from this research. The summary of the figure analysis shown above is listed in the following table (Table 11). In the summarization of Table 10, the primitive regression coefficients are difficult to discern and explain. But with a normalization procedure it can make the influence force more readable and comparable. The formula of this process is shown as following: Bi ¼
bi jbjmin
(5)
Table 12 Tabular analysis of case comparison. Territory I
Land price (lp) Land price (RMB) Normalized
Territory IV
Loc.12
Loc.2
Loc.11
Loc.20
Loc.21
Loc.26
Loc.29
1728 3.1
555 1.0
151 1.0
1143 7.6
399 1.0
1668 4.2
405 1.0
750 1.9
2.5 2.6 4.1 1.0 0 7.1 0 5.9 0
0 0 0 1.0 9.3 7.1 0 5.9 0
2.5 0 0 0 0 7.1 4.4 5.9 0
2.5 2.6 0 0 9.3 0 0 5.9 0
2.5 0 0 0 0.0 0 0 5.9 0
2.5 2.6 0 0 9.3 0 0 0 0
0 2.6 0 0 9.3 0 4.4 0 0
16.2 1.1
2.7 1.0
14.9 5.5
3.3 1.0
3.4 2.0
9.2 1.0
2.3 4.0
4 0
3+2 0
4 0
0 4
4 4
3 0
4 3
4 1.0
5 1.3
4 1.0
4 1.0
8 2.0
3 1.0
7 2.3
14.6 1.0
The influence of neighboring roads (ro) MROAD 4+4 RING 0 Total Normalized
Territory III
Loc.1
The influence of surrounding land uses (lu) L_IND 300 m 0 N_IND 350 m 2.6 L_RES 250 m 0 M_RES 100 m 1.0 LQRES 100 m 0 COMME 250 m 7.1 GREEN 300 m 0 OFFIC 250 m 5.9 TRANS 100 m 0 Total Normalized
Territory II
8 2.0
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where Bi is the normalized influence force. bi is the primitive one and jbjmin is the minimal absolute value. In this analysis, jbjmin is the regression coefficient estimate of the D_M_RES with the value of 0.157. A negative sign is assigned ahead of the right part of the equation make the normalized measurement coincidental to its influence, that is, bigger positive value means more beneficial effect, vice versa.
4.3. Case comparison analysis 4.3.1. Result of the numerical comparisons The result of the spatial analysis and tabular comparison of the four selected case pairs shows that the micro environment including surrounding land uses and nearby main roads sometimes contributes more important to the residential land prices (Table 12).
Fig. 11. Regression coefficient analysis for different land uses.
Y. Liu et al. / International Journal of Applied Earth Observation and Geoinformation 12S (2010) S181–S193 Table 13 Model comparison of validity of micro influence. Territory
Functions
I
1.0 1.1 1.0 5.5 1.0 2.0 1.0 4.0
II III IV
lu + 2.0 lu + 1.0 lu + 1.3 lu + 1.0 lu + 1.0 lu + 2.0 lu + 1.0 lu + 2.3
ro = 3.1 ro = 1.0 ro = 1.0 ro = 7.6 ro = 1.0 ro = 4.2 ro = 1.0 ro = 1.9
Variable
Result
Linear representation
lu ro lu ro lu and ro
0.9 2.0 1.4 0.3 2.1
(Fig. 12)
lu ro
0.3 1.2
Fig. 12. Variance of micro influences under different macro environment.
With an approximate visual comparison it is not difficult to find that the location with high scores in both the influence of the surrounding land uses and location to the main road have the prevailing high land value. The good matches in all case studies prove that the measurements of the influence of neighboring land uses are correct. 4.3.2. Model comparison of the comparisons Coupled with land prices (lp), accumulated influence of surrounding land uses (lu) and accumulated influence of neighboring main road (ro) for each territory in the RBP classification, models are easy to be built (Table 13). Normalized parameters in these models cannot provide accurate result but some relative comparisons. However, such alternate variance of the importance of different influences has well portrayed the scenario as to how does the same micro influences behavior differently when macro environment changes. Finally the result of Table 13 can be visualized into Fig. 12, where the variance of the micro influences under different macro environment is clearly described. 5. Discussion and conclusions It has been generally accepted that urban land is a multiattribute utility comprising diverse, heterogeneous characteristics and distance plays an important role in the realization of such utilities. Since Alonso (1964) put forward his famous ‘‘trade-off theory’’ on the relationships between the location to the CBD and the land values/utilities, all kings of the locational influences including commerce accessibility, public services supplying, open spaces, neighboring characteristics, etc. have been investigated. These researches have covered both the macro influences and micro neighborhood characteristics. However, we also find that in most of these studies, the distance functions are always treated as a monotonous one and the difference between the two scopes (macro and micro) has seldom been emphasized. In this research, both the macro influence caused by unique spatial fixity and general environment (e.g. distance to CBD, all kinds of public services, etc.) and micro influences coming from the neighborhood characteristics are investigated. In the paper the ‘‘micro influence’’ is rigidly defined as ‘‘the influence from the most effective distance’’, or ‘‘immediate adjoined influence’’. With the
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utilization of HRM statistic and spatial analysis in GIS, such influences are figured out. The RBP is adopted for the nominalization of the macro environment. Four models are designed with different variables and then R2 statistics is used to distinguish which model works best. With the model summary there are altogether 7 factors considered to be connected to the macro environment represented by RBP, they are: distance to the CBD, main road, and several public facilities. In the analysis we find that the industries show little direct connection to the RBP with an interval distance at 400 m, the reason may lie in their scattering everywhere inside the city and becoming a universal environment. In the latter MVRL models, there exist two measurement systems, one is for macro environment and the other is for micro environment. Having figured out the variables and distance measurement for macro environment, to focus on the solving of another one become possible. For this task we developed 8 models with the assignment of different first interval from 50 m to 400 m in the distance measurement. By means of the summary of t-values and regression coefficient comparison, both the most influential scope (the first intervals) and relative contributions of the neighboring land uses are calculated. The influential scopes vary from 100 m at least to 350 m at most, with only one variable of high-polluted industry excluded because of the unreasonable t-value test. By elaborately designed normalization procedure, these relative contributions are made more discernible and comparable for further analysis. The ‘‘nearness functions’’ in micro environment are supposed to be different under different macro environments. To prove that hypothesis, an elaborately designed case comparison process is performed. For each land class defined in RBP we selected one pair of the samples that is most spatially close while having distinguished land prices. So altogether there are 4 cases of the comparisons performed with counting in the contributions from the neighboring main roads. After a set of normalization process, we are able to carry out an approximate visual comparison to provide the preliminary test for the former measurements of the micro environment. Then normalized variables are applied into a series of dualistic functions. The results are described in linear figure. The visual consequence clearly demonstrates that: In the city center, nearness to the main road is of most importance, while the influence of neighboring environment is always less cared about. That means if good accessibility can be satisfied, be near to some negative neighboring influence sometimes can also be acceptable. It can answer why in the first territory of city center the accumulated influence of surrounding land uses appears negative. When the distance from the CBD is gradually increasing, the importance of immediate influence of the main road cut down fast with the importance of neighboring land uses increasing. When it is across the secondary territory, both of the influences rise again until their peaks are reached in the third territory. After that scope (territory III) it reaches the periphery of the city where the distribution of commerce becomes rare and the environment of residential neighborhood is much better, and they are no longer so sensitive as in the city center, so both of the micro influences are low and macro influence prevails again. The results of the model comparison are quite reasonably coincident with the real situation. It can demonstrate that not only the research procedure design but also the results of the measurement of the ‘‘nearness functions’’ for micro environment analysis are correct. The study will help to improve the land valuation and make the land market more efficient especially for the countries that are under marketizing process, for example China. This research is also
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expected to bring faster market correction and reducing the state’s risks in the urban land administration.
during the Eleventh Five-Year Plan Period (Project No.: 2006BAJ05A02), the National High Technology Research and Development Program (‘‘863’’ Program) of China (Project No.: 2007AA12Z225) and the China Postdoctoral Science Foundation funded project (Project No.: 20090451050). This work was carried out as part of the MSC study at ITC and improved during the period of the Ph.D. study at Wuhan University.
Acknowledgements The research introduced in this paper is supported by the Key Projects in the National Science & Technology Pillar Program
Appendix A. Macro environmental variables correlation matrix.
D_CBD D_MROAD D_RING D_P_SCH D_H_SCH D_MARKE D_RECRE D_MEDIC D_H_IND D_GREEN
D_CBD
D_MROAD
D_RING
D_P_SCH
D_H_SCH
D_MARKE
D_RECRE
D_MEDIC
D_H_IND
D_GREEN
1.00 0.05 0.56 0.42 0.06 0.31 0.44 0.39 0.29 0.31
1.00 0.03 0.13 0.06 0.01 0.05 0.14 0.25 0.17
1.00 0.52 0.16 0.41 0.31 0.69 0.38 0.03
1.00 0.01 0.40 0.05 0.55 0.43 0.02
1.00 0.55 0.03 0.09 0.36 0.53
1.00 0.18 0.66 0.69 0.19
1.00 0.27 0.21 0.09
1.00 0.47 0.27
1.00 0.17
1.00
Appendix B. Correlation matrix for variables of all variables.
D_H_IND D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMMO D_GREEN D_OFFIC D_TRANS D_CBD D_RING D_MROAD D_P_SCH D_H_SCH D_MARKE D_RECRE D_MEDIC
D_H_ IND
D_L_ IND
D_N_ IND
D_L_ RES
D_M_ RES
D_ LQRES
D_ COMMO
D_ GREEN
D_ OFFIC
D_ TRANS
D_ CBD
D_ RING
D_ MROAD
D_P_ SCH
D_H_ SCH
D_ MARKE
D_ RECRE
D_ MEDIC
1 0.54 0.34 0.12 0.21 0.39 0.32 0.16 0.69 0.56 0.36 0.51 0.20 0.58 0.26 0.69 0.13 0.58
1 0.11 0.09 0.20 0.34 0.21 0.18 0.58 0.31 0.20 0.42 0.24 0.25 0.33 0.44 0.04 0.35
1 0.37 0.15 0.18 0.16 0.09 0.26 0.12 0.01 0.30 0.21 0.17 0.09 0.33 0.18 0.35
1 0.22 0.38 0.01 0.05 0.13 0.11 0.28 0.22 0.38 0.01 0.28 0.13 0.35 0.09
1 0.04 0.65 0.43 0.04 0.06 0.23 0.02 0.02 0.11 0.07 0.02 0.46 0.04
1 0.02 0.21 0.58 0.38 0.35 0.40 0.02 0.23 0.66 0.68 0.41 0.54
1 0.21 0.11 0.05 0.22 0.16 0.02 0.36 0.13 0.07 0.59 0.13
1 0.26 0.35 0.39 0.18 0.17 0.08 0.45 0.13 0.06 0.22
1 0.50 0.41 0.66 0.32 0.49 0.44 0.64 0.21 0.67
1 0.68 0.62 0.05 0.57 0.17 0.54 0.12 0.46
1 0.56 0.05 0.42 0.06 0.31 0.44 0.39
1 0.03 0.52 0.16 0.41 0.31 0.69
1 0.13 0.06 0.01 0.05 0.14
1 0.01 0.40 0.05 0.55
1 0.55 0.03 0.09
1 0.18 0.66
1 0.27
1
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Contents lists available at ScienceDirect
International Journal of Applied Earth Observation and Geoinformation journal homepage: www.elsevier.com/locate/jag
A hedonic model comparison for residential land value analysis Yaolin Liu a,b, Bin Zheng c,d,*, Jan Turkstra e, Lina Huang a,b a
Key Laboratory of Geographic Information System, Ministry of Education, Wuhan 430079, China School of Resource and Environment Science, Wuhan University, Wuhan 430079, China c College of Public Administration, Huazhong University of Science and Technology, Wuhan 430074, China d HUST Land & Resources and Real Estate Research Center, Wuhan 430074, China e UN-Habitat, Global Urban Observatory, P.O. Box 30030, Nairobi 00100, Kenya b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 15 April 2009 Accepted 25 November 2009
Distantial attenuation is a significant characteristic of the urban environment. In this paper we explore the relative contributions of different land uses to the urban residential environment according to distances with an analysis on the most significant scope of these factors. Two types of models are developed. One employs the distance to city center, main road, public facilities and environment factors as the variables for macro environment analysis, and the another one includes all factors to analyze the influences of the micro environment. In the models of the latter type, the contributions of the neighboring land uses are magnified with a specially designed variable measurement scheme in which variables are evaluated specially for each model so that the contributions of the variables become comparable from model to model. With an application to the case study of Danyang, China, we measure the distantial functions of the urban environment (e.g. the surrounding land uses) including both the most influential scopes and the relative contributions by means of model summary and regression coefficient comparisons. Finally, case comparison on the samples is introduced to figure out the difference of the functions under micro environment. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Distance measurement Hedonic regression model Residential land value Benchmark price Neighborhood analysis
1. Introduction Distantial attenuation is a significant feature of the location. Since every urban land use activity should consider the best location to acquire the most utilities, the distance dependences to each of the environment factors are sure to be of interest to researchers. In most of these studies land value always evolved as a substitute for the location utility. Perhaps the most fundamental one among these studies is the work done by Wingo (1963) who firstly tried to systematically analyse the relationship between the distance function of location and the urban land value by modeling the value of consumption in transport. He developed his famous location equilibrium theory which declared that transportation costs can be substituted by the space costs or land values. Then there is Alonso’s profound trade-off theory (Evans, 1987; Kivell, 1993) in which Alonso (1964) pointed out that land values are generally determined
Abbreviations: CBD, central business district; HRM, hedonic regression model; RBP, residential benchmark price; MVRL, market value of residential land; RMB, Ren Min Bi (in Chinese), or Chinese Yuan, Chinese currency unit. * Corresponding author at: College of Public Administration, Huazhong University of Science and Technology, Wuhan 430074, China. Tel.: +86 15307156122. E-mail address: [email protected] (B. Zheng). 0303-2434/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jag.2009.11.009
in the urban area, more specifically speaking, the value (or the utility) of the urban land should decline with the increasing the distance to the CBD. Based on the fundamental researches of Wingo and Alonso, more considerate investigations were performed. For decades, scholars have spent a lot of endeavor in investigating various commercial places and retail supplies other than being solely focused on the CBD (Ragas, 1987; Song and Sohn, 2007) accompanied with generalized transport including the accessibility changes (Smersh and Smith, 2000) and transporting improvements (Yiu and Wong, 2005) were considered. Location of all kinds of public services such as schools (Chin and Foong, 2006), outdoor recreations (Wilman, 1988), etc. or a synthetic supply (Randall, 2005) also provides many prostheses for such discussion. As a traditional public issue, the accessibility to the environment amenities such as open space (Jim and Chen, 2006, 2007; Kong et al., 2007) or urban forest (Tyrva¨inen, 1997; Tyrva¨inen and Miettinen, 2000) arouses a lot of interest too. Compared to the pioneers, these researches are no more rigidly macroscopic and theoretic and the results work more confidently. Recently some scholars began paying their attention to the neighborhood effects (Galster et al., 2004; Hui et al., 2007; Tse, 2002). Some founded that in the classical smooth attenuated models for urban environment influence analysis, the contiguous influences are always underestimated. Although there are no systemic and specific investigations about it yet, some of the researches have
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surely proved that the influence of the distantial attenuation of the urban environment exists in both the ‘‘unique spatial fixity in the urban area’’ (i.e. macro environment) and the ‘‘neighborhood characteristics’’ (i.e. micro environment) (Jim and Chen, 2007; Wendt, 1957). Urban land is a multiattribute utility comprising of heterogeneous characteristics (Colwell and Munneke, 1997; Qadeer, 1981; Wendt, 1957), hedonic regression method (HRM) makes its numeral measuring possible. In the HRM, land value can be specified into a bundle of the locational characteristics of the plot and expressed as some kinds of the form of Uðz1 ; B z2 ; B . . . ; B zn Þ, where U means the accumulation of a bunch of utilities ui ðzi Þ, and zi is the normalized distance functions. Statistics and regression procession figures out each value of a particular locational distance, which is described as the ‘‘pure willingness to pay’’ in Bockstael and McConnel’s (2007) manuscript. HRM has significantly promoted the progress of the locational environment studies, especially when it concerns the land value. However, in most of the HRM applications literature researches rely on mono-distance functions, in despite of the difference between macro and micro environment having been mentioned a lot. When Yeates (1965) having noticed that the land value declines only being functional in the area within 1.5 miles to the CBD, for decades the inter-activities between micro and macro environment are seldom discussed qualitatively. Occasionally relative conclusions appeared as some sort of by-products, for example Wu et al. (2004) found that the distance to the nearest park, river or lake being 1000 feet can make sufficient influence on housing price, and Mahan et al. (2000) declared that 1000 feet can
be the margin of the influential distance of the wetland in contributing to the house price, etc. Most of these findings are scattered and not specific. Yes, it is easy to tell that a plot nearing to a main street is less profitable in the city fringe than in the city center, and being near to a park is more attractive than to the main street in the city fringe. Though, how to measure them? The answer is still under the seal. This paper is intended to figure out such differences. Methodologically the paper sketches a model-analysis of the cooperation of the macro environment and the micro environment. Variables contributing to them are strictly distinguished and are selectively added to different HRM models. Firstly the influences of the macro environment are specifically figured out by employing the residential benchmark price (RBP) which is designed and adopted as a kind of general mass appraisal for the physical homogenous environment. Then micro environment is involved in, with introducing the market values of the residential land (MVRL) as the result of complex interactions between the characteristics contributing to both the macro environment and micro environment. The analysis and results cover both the influential scopes and the relative contributions. Different hedonic regressions are designed to estimate the equations for the land values under different environments (Eqs. (1) and (2)). RBP ¼ f ðmacro environmentÞ
(1)
MVRL ¼ f ðmacro environment; micro environmentÞ
(2)
With the application of the geographic information systems (GIS) in handling and processing large amounts of spatial data, it is
Fig. 1. Location of Danyang city.
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possible to associate and process the land value data and locational data we needed and to undertake the analysis with multi-original data (Nzau, 2003; Turkstra, 1998). At last, explicit case comparisons are taken for deducing the results.
Table 1 Value range of RBP of Danyang. Land class
Residential
2. Study area and data description
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RBP (RMB/M2) 1
2
3
4
5
845
640
511
354
275
2.1. Study area According to the Chinese standard, Danyang city is a ‘‘small city’’ (Li, 2001) located in the Yangtze Delta Region, which is economically one of the most successful areas of China (Fig. 1). Since Danyang’s faster urbanization started around early 1980s, a lot of industries were developed to bring to the city a better marketization environment (Danyang-Economic-Planning-Committee, 2002). However, as the urban fringe has greatly extended, the former industries and surrounding low-quality housing that used to be welcomed by industrial laborers, were gradually enveloped inside the urban area and finally become an embarrassment for the new residential development (Fig. 2). Though in the developing viewpoint, all these ‘‘unsuitable’’ land uses inside the urban area will be replaced by other ‘‘clean’’ land uses in the future, but for the current, the nearby industry and lowquality housings are still one of the major factors to be considered in local real-estate development, which finally affect as the prices in local land market. 2.2. Data description 2.2.1. Data of RBP In China, RBP is used as a standard for the official land valuation. As a general mass appraisal, it is legally required to be evaluated
according to the location to the city center, transportation condition, public infrastructure condition, facilities supply, general eco-environment conditions, population density, and land quality, etc. It makes the RBP a most suitable and easiest accessible source of the physical homogenous circumstance measurement of urban area. The spatial pattern of the RBP of Danyang is mapped as follows (Fig. 3). The RBPs distribute in five concentric circles from the city center further to the fringe of the city. Obviously, in the size of city scale, the most influential factor is the distance to the CBD. Beside, the main roads crossing the major center play an important role. Location to some directions can also get more scores in the evaluation than to other directions. The following table is the values of the RBP in different homogeneous zones (Table 1). 2.2.2. Data of MVRL There are total 34 plots of residential land transactions that happened in Danyang in the year of 2002. By eliminating the only transaction via agreement, we keep the remaining 33 auctioned ones. Using the samples from the same year can help us save the endeavor to correct the data according to the temporal change, the extra artificial operation caused by which may finally reduce the accuracy even when the sample size increases concerning the total sample size are small.
Fig. 2. Industrial and residential land uses are mixed in Danyang city.
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Fig. 3. RBP’s appearance under macro environment.
Table 2 Classification of MVRL. Classification
Value range (RMB)
Mean (RMB)
Highest High Middle Low Lowest
1000–1728 600–999 450–599 300–449 0–299
1465 789 502 371 209
To make it clearer and more comparable with the RBP, The MVRL is classified into five classes according to its natural breaks (Table 2). However, after having performed a descriptive statistics, it is observed that the mean value of the data set is 522 and the median value is 403. It indicates that the land prices do not follow the normal distribution. The univariant statistics for the data shows skewed distribution (Fig. 4).
Fig. 4. Histogram of MVRLs.
However, the log-transformed MVRLs show almost a normal distribution (Fig. 5). The QQ Plot for the transformed land prices also proves that (Figs. 6 and 7).The distribution map of MVRL (Fig. 8) is developed by thiessen polygon interpolation with the 33 samples. Differing from the regular concentric distribution of the RBP, it seems that there are no distinct rules that can be applied for the MVRL distribution. For example, in the city center where are classified as the zone with the highest value in RBP, it can be observed that the market land values ranging from the highest to the lowest. At the same time, in the city fringe there exist real high MVRL though it is already apart from the traditional city center. It means that for the residential use, the land value may be more sensitive to the neighboring environment. 2.2.3. Representation of the variables The variables of the study are deduced from the Euclidean space distances from each sample to its environment factors. Here the
Fig. 5. Histogram of log transformed MVRLs.
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Fig. 6. Q–Q plots of MVRLs.
Fig. 7. Q–Q plots of log transformed MVRLs.
‘‘environment factor’’ refers to the selected land uses that are supposed to be able to contribute to the surrounding residential land values. The selection process will be discussed in the following sections. In our models, we employ the direct distance as the source of the variables. The reasons are: firstly, the ‘‘distance’’ is always indicative in the macro scale (especially for the RBP estimation), and the distance interval can be more meaningful, that makes complicated distance transformation unnecessary; secondly, the direct distance is also more appropriate under the micro consideration because in such scale the ‘‘nonlinear coefficient’’ of the road becomes less significant (Li, 2001). The separation of the macro and micro environments can mostly simplify the methodology at the expense of accuracy.
giving period (Liu, 2003). The whole process including the selection of the variables is legally standardized in the official documents (GB/T 18507-2001; GB/T 18508-2001). So the variables for macro environment will be chosen according to these documents. In the procedure of RBP valuation, physical homogeneous zones are firstly outlined out according to the considerations of following 7 aspects (GB/T 18507-2001; GB/T 18508-2001). This phase is also called the ‘‘land gradation and classification’’. The 7 aspects include:
3. Methodology 3.1. Model analysis for macro environment analysis In China, the benchmark price means the valid value of general quality and environment of the land for a peculiar usage during the
Degree of prosperity, which refers to providing of commercial services, always measured by the distance to the commercial centers (CBD and sub-center). Transportation condition, which includes the accessibility to main roads, the convenience of public traffic services and the accessibility to the means of external transportation (e.g. stations and ports). Public infrastructure level (e.g. the condition of the water supply, electricity supply, sewage condition, etc.). Facility supply, which refers to the accessibility to the facilities such as schools, hospitals, recreational locations, etc.
Fig. 8. MVRL’s appearance under both macro environment and micro environment.
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Table 3 Variables for macro environment modeling. No.
Code
Description
1 2 3 4 5 6 7 8 9 10
D_CBD D_MROAD D_RING D_P_SCH D_S_SCH D_MARKE D_RECRE D_MEDIC D_H_IND D_GREEN
Distance Distance Distance Distance Distance Distance Distance Distance Distance Distance
to to to to to to to to to to
Environment conditions including the ratio of vegetable area and basic land quality (e.g. soil composition, topography quality, natural hazard treats). Population density. Other factors. According to these, 10 factors are adopted as independent variables for the model analysis of macro environment (Table 3). To settle the problems of potential non-linear relationship between dependent and independent variables in the models, RBPs are transformed into common logarithms (Nzau, 2003). The model is in the form of the formula shown below: X ln RBP ¼ a þ bi M i (3) where RBP is the dependent variable, a is the regression constant, bi is the value rating for the independent variables, M i is the independent variables represents the distance range of each selected micro factor. Here we use the RBP of each plot as the dependent variable Y. To test whether the independent variables listed in Table 3 are suitable for explaining macro environment, four models are developed and different variables are added progressively in Table 4): Model 1: Distance to the CBD (D_CBD). Model 2: D_CBD and distance to the main road and rings (D_MROAD, D_RING). Model 3: D_CBD, D_MROAD, and distance to the public facilities (D_P_SCH, D_S_SCH, D_MARKE, D_RECRE, and D_MEDIC). Model 4: D_CBD, D_MROAD, distance to the facilities and distance to environmental elements (D_H_IND, D_GREEN). Firstly a correlation analysis is employed to test whether there is a strong explanatory interrelationship between the variables (Appendix A). Though the correlation variables of D_MEDIC and D_RING, D_H_IND and D_MARKE are relative high (reach 0.69), the result of the multicollinearity test is quite opposite to the usual land use rules (Li, 2001) neither there exists any powerful clue from literatures to support that the medical land use is spatially related to the rings or the high pollution industry is spatially related to the market place. Hence, we tend to attribute these high correlations to the small sample size and keep all variables to the following test according to the official documents GB/T 185072001; GB/T 18508-2001.
Measurement the CBD main road ring nearest primary school nearest secondary school nearest marketplace nearest recreational place nearest hospital or clinic nearest high pollution industry nearest open green area
Interval at 400 m
In the macro environment models, the distances are measured at an interval of 400 m, about 1/5 of the radius of the urban area. For most urban facilities such as primary schools, local shopping centers or marketplaces, playfields, etc., this interval can best describe the different convenience standards of the urban facilities, especially for small cities (Chapin, 1965; Li, 2001). 3.2. Model analysis for micro environment analysis Having figured out the variables for macro environment, the primary task in this phase is to find out how the distance-related micro environment contributes to the residential land value. As part of the conclusion, all variables listed in Table 3 are migrated here. Then we employ 8 models with the same measurements for the macro variables (which are proved in the former analysis) and different measurements for micro variables. More specifically speaking, the variables are kept same in the 8 models. The only difference for them is that the values of the variables for the micro environment influences are measured differently. So the parameter estimates will also vary in different models. From which we can find out to which distance a micro environment factor contributes the most when the contributions from all the other factors are assigned the same distance-related rule. Here MVRLs are also transformed into common logarithms. The form of the models is designed as below: X X ln MVRL ¼ a þ bi M i þ cj Xj (4) where MVRL is the market land value, a is the regression constant, bi is the relative contribution of the macro factors in a given distance scale, M i represents the macro locational character of the plot, c j is the relative contribution of the micro factors, X j is the independent variable, which means the distance to the neighboring factors. bi and M i are supposed to have been figured out in the previous phase. Considering that all land use activities will influence the surrounding land use and contribute to their values, we keep 10 variables that include almost all the major land uses we can find in Danyang for the micro environments according to the urban land use classification in China (Li, 2001) and Danyang’s land use map. Neighborhood low-quality residential areas and industrial land are paid special attention. Also this selection is based on the strict correlation test (Appendix B). These variables are (Table 5). Differing from the intervals set for the macro environment, the basic scale of the intervals adopted here is chosen at 50 m, which is
Table 4 Independent variables used in macro environment models. Model
D_CBD
D_MROAD
1 2 3 4
H H H H
H H H H
D_RING
D_P_SCH
D_S_SCH
D_MARKE
D_RECRE
D_MEDIC
D_H_IND
D_GREEN
H H
H H
H H
H H
H H
H
H
H
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Table 5 Variables for micro environment modeling. No.
Code
Description
1 2 3 4 5 6 7 8 9 10
D_H_IND D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMMO D_GREEN D_OFFIC D_TRANS
Distance Distance Distance Distance Distance Distance Distance Distance Distance Distance
to to to to to to to to to to
Measurement high-pollution industry low-pollution industry no-pollution industry single-story residential area multi-story residential area low-quality residential area commerce and services open green area office place bus/railway station
almost the smallest length to contain a multiple-family sector whose width is normally 12–16 m in China (Li, 2001). To analyse the most influential scope of different land uses, the first scale is respectively set as 50 m, 100 m, 150 m, 200 m, 250 m, 300 m, 350 m and 400 m for different models. The value of the first scale is given the smallest 1 m, so the parameter estimation of the relative contribution will be greatly magnified. The value of 0 is carefully avoided to eliminate the immeasurable problem in GIS analysis. Besides, such arrangement best represents that the spatial relationship is not ‘‘on’’ but ‘‘adjacent to’’. The distance more than 500 m is supposed to have reached the scope of macro environment and have little immediate effect. So the value is assigned the largest 3000, which is bigger than the radius of the city to represent the smallest influence. The table below shows the measurements of the distance to different land uses (Table 6). 3.3. Measures of the influence of neighboring roads Roads are always considered as one important infrastructure in the city and may cover all over the cities and people always tend to include them into the macro environment. However, in the micro scale that influence can still be easily noticed because it is also the direct and major measurement of the accessibility even in the micro scale (Kivell, 1993; Nzau, 2003; Srour et al., 2001). That is why we assure that the influence of nearness to a road is not ignorable in the micro environment. To avoid the problem of self-dependence, the contributions of the roads are only traditionally employed as a macro environment in the above regressions. However, for the consideration of a micro comparison, the contributions of the nearby roads should be specially taking into account. As a non-normalized criterion in the road design in China, after every 200 m there should be an access to the main road (Li, 2001). That means the distance less than 200 m can be regarded as a willing distance for walking, especially in Danyang where automobile is not the prevailing method for private transport. So, in this research we investigate the road within 200 m to the main road with the distance classified into four grades with an
Dynamic according to model design
interval of 50 m. The value of 1–4 is assigned as the relative contributions with the nearness increasing gradually (Table 11). Generally, when easy accessibility to more than one main road is observed, it always means more convenience the plot can possess. So the influence of such influence is regarded to be accumulative. 3.4. Case comparison for the test In this phase, the main object is to figure out the variance among the micro influences under different macro environments. With careful case selection and comparison from the 33 samples, confident and intuitional results are deduced. 3.4.1. Case selection As mentioned in previous analysis, the RBP is an average value of certain zones that are regarded to have the same macro environment. With the classification of RBP, the 33 samples are classified into five classes according to their locations (Fig. 9). The classification is shown in Fig. 10, where the RBP morphologically appears as intervallic horizontal lines and the market land prices of the samples are represented as points. In the general sense, the land prices should be similar in the same territory (e.g. 3-5-6-8-10, 4-7, and 30-31-32-25, etc.). But there are still some cases with the similar or nearby location but have distinctly different land values (e.g. 1-12, 21-22, and 26-29, etc.). The following analysis selects typical cases and analyses their neighboring environment to answer the difference. For each zone, one pair of cases is selected for the comparison. They are: I 1-12 in the zone 1, II 11-2 in the zone 2, III 21-20 in the zone3, and IV 29-26 in the zone 4. 3.4.2. Case comparison For each pair of samples, the influences from surrounding land uses and neighboring roads are accumulated respectively for the purpose of summarization. The factors outside the first interval are regarded as having no immediate influence and are assigned the value of 0. Thus we preserve the purification of micro effects. For better comparability, each pair is normalized one by one. That is: for each pair we choose the lower one to assign the value of 1.0,
Table 6 Measurements of the micro environment in different models. Distance (m)
1–50
100
150
200
250
300
350
400
450
500
>1000
Model Model Model Model Model Model Model Model
1 1 1 1 1 1 1 1
50 1 1 1 1 1 1 1
100 100 1 1 1 1 1 1
150 150 150 1 1 1 1 1
200 200 200 200 1 1 1 1
250 250 250 250 250 1 1 1
300 300 300 300 300 300 1 1
350 350 350 350 350 350 350 1
400 400 400 400 400 400 400 400
450 450 450 450 450 450 450 450
3000 3000 3000 3000 3000 3000 3000 3000
1 2 3 4 5 6 7 8
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Fig. 9. Value distribution of 33 samples.
then the other one is also assigned relatively. The formula is designed as follows: 8 < A ¼ A=jBj B ¼ B=jBj (6) : A B; B 6¼ 0
Table 7 Measurement of neighborhood influence of main road.
where A and B are supposed to belong to the same comparable pair. They can be land prices, influence of surrounding land uses or of neighboring road. Normalized differences in each pair represent the validity of the micro influence that makes the locational characteristics differ from place to place. With model solving these differences can provide more explanation.
table below (Table 7) shows the result of the summary of the models (Table 8). Among the four models, the third model is adopted as the right one for describing the influence of the macro environment, because its R2 is the highest and most close to 1 and it also has the lowest standard error of the estimate. The result means that its variables account for 85% of the total RBP variations. There are other factors affecting macro environment, such as land quality and the population density mentioned in the chapter five, they can account for 15% of the RBP variations. The neighboring residential land use which is included in the following micro environment analysis may also make some difference, because being near to different residential land use always means different population density. Besides, the third model’s F-value is 23.112, far above the critical F.05 (8, 24), which means that the model is significant at 95%. So the variables adopted in the model 3 can be adopted as the factors of the macro environment.
4. Results and analyses 4.1. Model comparison for the macro environment analysis The macro models are summarized in SPSS software. Coefficients are worked out by the normal Least-squares method. The
Distance (m)
1–50
51–100
101–150
151–200
Influence Force
4
3
2
1
4.2. Model comparison for the micro environment analysis 4.2.1. Model summary Then the summary analyses are performed for the regressions of all these 8 models in SPSS software and the results are listed in Tables 9 and 10. In Table 8 we can observe that the range of the R2 in 8 models is very small. The result means that all these variables can account for Table 8 Model summary for macro environment.
Fig. 10. Location distribution of 33 samples.
Model
R2
Adjusted R2
Std. error of the estimate
1 2 3 4
0.527 0.588 0.885 0.887
0.511 0.546 0.847 0.835
0.1083 0.1044 6.064E02 6.286E02
Y. Liu et al. / International Journal of Applied Earth Observation and Geoinformation 12S (2010) S181–S193 Table 9 Model summary for MVRL.
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Table 11 Influence of different land uses.
Model
First interval
R2
Std. error of the estimate
1 2 3 4 5 6 7 8
50 m 100 m 150 m 200 m 250 m 300 m 350 m 400 m
0.864 0.867 0.836 0.866 0.871 0.861 0.891 0.846
0.16914 0.16727 0.18613 0.16789 0.16502 0.17134 0.15186 0.17994
Table 10 Results of variance analysis. Model
F-value
Significance
1 2 3 4 5 6 7 8
4.358 4.471 3.480 4.433 4.613 4.299 5.571 3.771
0.005 0.004 0.013 0.004 0.004 0.005 0.001 0.009
at least 84% of the total land value variations and at most 89% of the sample land values. The remaining variations should be explained by other factors, which are not included in the content of this research. The result also shows that the total regressions work well in all these models, as the values of F-statistic are greater than the critical F-value and the significance value of the F statistic is also very good (the largest significant value is 0.013). 4.2.2. Regression coefficient analysis of the influence of neighboring land use The parameter estimates of the proximity to different micro environment factors by using distance intervals are shown in Fig. 11. The regression coefficient denotes how much importance an independent variable contributes to the dependent value. With the elaborate measurements’ proper magnification of the most nearby influence, variables show different behaviors in different models, which can finally tell the farthest influential scope of an
Variable
Most influential scope
Coefficient
Normalized influence force
D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMME D_GREEN D_OFFIC D_TRANS
300 m 350 m 250 m 100 m 100 m 250 m 300 m 250 m 100 m
0.396 0.411 0.644 0.157 1.452 1.124 0.692 0.934 0.160
2.5 2.6 4.1 1.0 9.2 7.2 4.4 5.9 1.0
environment factor contributing as a neighboring environment. The significance of the variables is measured by the t-value. The variation of the regression coefficient of each individual variable among models is shown in linear figures. The dash line represents positive regression coefficient value. That means: the influence of the land use is negative, in another word, the surrounding residential land value will increase with the variable (or the distance to the land use) increasing. The high coefficient value indicates that such negative relative contribution is high. The solid line means that the regression coefficient value is negative and the influence of the land use is positive. The lower the regression coefficient value is, the higher the relative contribution does the land use have on the surrounding residential land value (Fig. 11). As to the statistic for D_H_IND, the highest absolute value of the t-values is only 0.706 (at the first interval of 200 m) and less than 1, which means that in all 8 models, the measurement of the influence of neighboring high pollution cannot confidently explain the variation of the market land values. So the factor should be excluded from this research. The summary of the figure analysis shown above is listed in the following table (Table 11). In the summarization of Table 10, the primitive regression coefficients are difficult to discern and explain. But with a normalization procedure it can make the influence force more readable and comparable. The formula of this process is shown as following: Bi ¼
bi jbjmin
(5)
Table 12 Tabular analysis of case comparison. Territory I
Land price (lp) Land price (RMB) Normalized
Territory IV
Loc.12
Loc.2
Loc.11
Loc.20
Loc.21
Loc.26
Loc.29
1728 3.1
555 1.0
151 1.0
1143 7.6
399 1.0
1668 4.2
405 1.0
750 1.9
2.5 2.6 4.1 1.0 0 7.1 0 5.9 0
0 0 0 1.0 9.3 7.1 0 5.9 0
2.5 0 0 0 0 7.1 4.4 5.9 0
2.5 2.6 0 0 9.3 0 0 5.9 0
2.5 0 0 0 0.0 0 0 5.9 0
2.5 2.6 0 0 9.3 0 0 0 0
0 2.6 0 0 9.3 0 4.4 0 0
16.2 1.1
2.7 1.0
14.9 5.5
3.3 1.0
3.4 2.0
9.2 1.0
2.3 4.0
4 0
3+2 0
4 0
0 4
4 4
3 0
4 3
4 1.0
5 1.3
4 1.0
4 1.0
8 2.0
3 1.0
7 2.3
14.6 1.0
The influence of neighboring roads (ro) MROAD 4+4 RING 0 Total Normalized
Territory III
Loc.1
The influence of surrounding land uses (lu) L_IND 300 m 0 N_IND 350 m 2.6 L_RES 250 m 0 M_RES 100 m 1.0 LQRES 100 m 0 COMME 250 m 7.1 GREEN 300 m 0 OFFIC 250 m 5.9 TRANS 100 m 0 Total Normalized
Territory II
8 2.0
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where Bi is the normalized influence force. bi is the primitive one and jbjmin is the minimal absolute value. In this analysis, jbjmin is the regression coefficient estimate of the D_M_RES with the value of 0.157. A negative sign is assigned ahead of the right part of the equation make the normalized measurement coincidental to its influence, that is, bigger positive value means more beneficial effect, vice versa.
4.3. Case comparison analysis 4.3.1. Result of the numerical comparisons The result of the spatial analysis and tabular comparison of the four selected case pairs shows that the micro environment including surrounding land uses and nearby main roads sometimes contributes more important to the residential land prices (Table 12).
Fig. 11. Regression coefficient analysis for different land uses.
Y. Liu et al. / International Journal of Applied Earth Observation and Geoinformation 12S (2010) S181–S193 Table 13 Model comparison of validity of micro influence. Territory
Functions
I
1.0 1.1 1.0 5.5 1.0 2.0 1.0 4.0
II III IV
lu + 2.0 lu + 1.0 lu + 1.3 lu + 1.0 lu + 1.0 lu + 2.0 lu + 1.0 lu + 2.3
ro = 3.1 ro = 1.0 ro = 1.0 ro = 7.6 ro = 1.0 ro = 4.2 ro = 1.0 ro = 1.9
Variable
Result
Linear representation
lu ro lu ro lu and ro
0.9 2.0 1.4 0.3 2.1
(Fig. 12)
lu ro
0.3 1.2
Fig. 12. Variance of micro influences under different macro environment.
With an approximate visual comparison it is not difficult to find that the location with high scores in both the influence of the surrounding land uses and location to the main road have the prevailing high land value. The good matches in all case studies prove that the measurements of the influence of neighboring land uses are correct. 4.3.2. Model comparison of the comparisons Coupled with land prices (lp), accumulated influence of surrounding land uses (lu) and accumulated influence of neighboring main road (ro) for each territory in the RBP classification, models are easy to be built (Table 13). Normalized parameters in these models cannot provide accurate result but some relative comparisons. However, such alternate variance of the importance of different influences has well portrayed the scenario as to how does the same micro influences behavior differently when macro environment changes. Finally the result of Table 13 can be visualized into Fig. 12, where the variance of the micro influences under different macro environment is clearly described. 5. Discussion and conclusions It has been generally accepted that urban land is a multiattribute utility comprising diverse, heterogeneous characteristics and distance plays an important role in the realization of such utilities. Since Alonso (1964) put forward his famous ‘‘trade-off theory’’ on the relationships between the location to the CBD and the land values/utilities, all kings of the locational influences including commerce accessibility, public services supplying, open spaces, neighboring characteristics, etc. have been investigated. These researches have covered both the macro influences and micro neighborhood characteristics. However, we also find that in most of these studies, the distance functions are always treated as a monotonous one and the difference between the two scopes (macro and micro) has seldom been emphasized. In this research, both the macro influence caused by unique spatial fixity and general environment (e.g. distance to CBD, all kinds of public services, etc.) and micro influences coming from the neighborhood characteristics are investigated. In the paper the ‘‘micro influence’’ is rigidly defined as ‘‘the influence from the most effective distance’’, or ‘‘immediate adjoined influence’’. With the
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utilization of HRM statistic and spatial analysis in GIS, such influences are figured out. The RBP is adopted for the nominalization of the macro environment. Four models are designed with different variables and then R2 statistics is used to distinguish which model works best. With the model summary there are altogether 7 factors considered to be connected to the macro environment represented by RBP, they are: distance to the CBD, main road, and several public facilities. In the analysis we find that the industries show little direct connection to the RBP with an interval distance at 400 m, the reason may lie in their scattering everywhere inside the city and becoming a universal environment. In the latter MVRL models, there exist two measurement systems, one is for macro environment and the other is for micro environment. Having figured out the variables and distance measurement for macro environment, to focus on the solving of another one become possible. For this task we developed 8 models with the assignment of different first interval from 50 m to 400 m in the distance measurement. By means of the summary of t-values and regression coefficient comparison, both the most influential scope (the first intervals) and relative contributions of the neighboring land uses are calculated. The influential scopes vary from 100 m at least to 350 m at most, with only one variable of high-polluted industry excluded because of the unreasonable t-value test. By elaborately designed normalization procedure, these relative contributions are made more discernible and comparable for further analysis. The ‘‘nearness functions’’ in micro environment are supposed to be different under different macro environments. To prove that hypothesis, an elaborately designed case comparison process is performed. For each land class defined in RBP we selected one pair of the samples that is most spatially close while having distinguished land prices. So altogether there are 4 cases of the comparisons performed with counting in the contributions from the neighboring main roads. After a set of normalization process, we are able to carry out an approximate visual comparison to provide the preliminary test for the former measurements of the micro environment. Then normalized variables are applied into a series of dualistic functions. The results are described in linear figure. The visual consequence clearly demonstrates that: In the city center, nearness to the main road is of most importance, while the influence of neighboring environment is always less cared about. That means if good accessibility can be satisfied, be near to some negative neighboring influence sometimes can also be acceptable. It can answer why in the first territory of city center the accumulated influence of surrounding land uses appears negative. When the distance from the CBD is gradually increasing, the importance of immediate influence of the main road cut down fast with the importance of neighboring land uses increasing. When it is across the secondary territory, both of the influences rise again until their peaks are reached in the third territory. After that scope (territory III) it reaches the periphery of the city where the distribution of commerce becomes rare and the environment of residential neighborhood is much better, and they are no longer so sensitive as in the city center, so both of the micro influences are low and macro influence prevails again. The results of the model comparison are quite reasonably coincident with the real situation. It can demonstrate that not only the research procedure design but also the results of the measurement of the ‘‘nearness functions’’ for micro environment analysis are correct. The study will help to improve the land valuation and make the land market more efficient especially for the countries that are under marketizing process, for example China. This research is also
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expected to bring faster market correction and reducing the state’s risks in the urban land administration.
during the Eleventh Five-Year Plan Period (Project No.: 2006BAJ05A02), the National High Technology Research and Development Program (‘‘863’’ Program) of China (Project No.: 2007AA12Z225) and the China Postdoctoral Science Foundation funded project (Project No.: 20090451050). This work was carried out as part of the MSC study at ITC and improved during the period of the Ph.D. study at Wuhan University.
Acknowledgements The research introduced in this paper is supported by the Key Projects in the National Science & Technology Pillar Program
Appendix A. Macro environmental variables correlation matrix.
D_CBD D_MROAD D_RING D_P_SCH D_H_SCH D_MARKE D_RECRE D_MEDIC D_H_IND D_GREEN
D_CBD
D_MROAD
D_RING
D_P_SCH
D_H_SCH
D_MARKE
D_RECRE
D_MEDIC
D_H_IND
D_GREEN
1.00 0.05 0.56 0.42 0.06 0.31 0.44 0.39 0.29 0.31
1.00 0.03 0.13 0.06 0.01 0.05 0.14 0.25 0.17
1.00 0.52 0.16 0.41 0.31 0.69 0.38 0.03
1.00 0.01 0.40 0.05 0.55 0.43 0.02
1.00 0.55 0.03 0.09 0.36 0.53
1.00 0.18 0.66 0.69 0.19
1.00 0.27 0.21 0.09
1.00 0.47 0.27
1.00 0.17
1.00
Appendix B. Correlation matrix for variables of all variables.
D_H_IND D_L_IND D_N_IND D_L_RES D_M_RES D_LQRES D_COMMO D_GREEN D_OFFIC D_TRANS D_CBD D_RING D_MROAD D_P_SCH D_H_SCH D_MARKE D_RECRE D_MEDIC
D_H_ IND
D_L_ IND
D_N_ IND
D_L_ RES
D_M_ RES
D_ LQRES
D_ COMMO
D_ GREEN
D_ OFFIC
D_ TRANS
D_ CBD
D_ RING
D_ MROAD
D_P_ SCH
D_H_ SCH
D_ MARKE
D_ RECRE
D_ MEDIC
1 0.54 0.34 0.12 0.21 0.39 0.32 0.16 0.69 0.56 0.36 0.51 0.20 0.58 0.26 0.69 0.13 0.58
1 0.11 0.09 0.20 0.34 0.21 0.18 0.58 0.31 0.20 0.42 0.24 0.25 0.33 0.44 0.04 0.35
1 0.37 0.15 0.18 0.16 0.09 0.26 0.12 0.01 0.30 0.21 0.17 0.09 0.33 0.18 0.35
1 0.22 0.38 0.01 0.05 0.13 0.11 0.28 0.22 0.38 0.01 0.28 0.13 0.35 0.09
1 0.04 0.65 0.43 0.04 0.06 0.23 0.02 0.02 0.11 0.07 0.02 0.46 0.04
1 0.02 0.21 0.58 0.38 0.35 0.40 0.02 0.23 0.66 0.68 0.41 0.54
1 0.21 0.11 0.05 0.22 0.16 0.02 0.36 0.13 0.07 0.59 0.13
1 0.26 0.35 0.39 0.18 0.17 0.08 0.45 0.13 0.06 0.22
1 0.50 0.41 0.66 0.32 0.49 0.44 0.64 0.21 0.67
1 0.68 0.62 0.05 0.57 0.17 0.54 0.12 0.46
1 0.56 0.05 0.42 0.06 0.31 0.44 0.39
1 0.03 0.52 0.16 0.41 0.31 0.69
1 0.13 0.06 0.01 0.05 0.14
1 0.01 0.40 0.05 0.55
1 0.55 0.03 0.09
1 0.18 0.66
1 0.27
1
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