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A GIS-BASED HEDONIC PRICE MODEL FOR AGRICULTURAL
LAND
Demetris Demetriou*a,b
aSchool of Geography, University of Leeds, Leeds LS2 9JT, UK
bLand Consolidation Department, 131 Prodromou street, 1419 Nicosia, Cyprus
ABSTRACT
Land consolidation is a very effective land management planning approach that aims towards rural/agricultural
sustainable development. Land reallocation which involves land tenure restructuring is the most important, complex and
time consuming component of land consolidation. Land reallocation relies on land valuation since its fundamental
principle provides that after consolidation, each landowner shall be granted a property of an aggregate value that is
approximately the same as the value of the property owned prior to consolidation. Therefore, land value is the crucial
factor for the land reallocation process and hence for the success and acceptance of the final land consolidation plan.
Land valuation is a process of assigning values to all parcels (and its contents) and it is usually carried out by an ad-hoc
committee. However, the process faces some problems such as it is time consuming hence costly, outcomes may present
inconsistency since it is carried out manually and empirically without employing systematic analytical tools and in
particular spatial analysis tools and techniques such as statistical/mathematical. A solution to these problems can be the
employment of mass appraisal land valuation methods using automated valuation models (AVM) based on international
standards. In this context, this paper presents a spatial based linear hedonic price model which has been developed and
tested in a case study land consolidation area in Cyprus. Results showed that the AVM is capable to produce acceptable
in terms of accuracy and reliability land values and to reduce time hence cost required by around 80%.
Keywords: Land consolidation; land valuation; automated valuation models, hedonic price model, GIS
1. INTRODUCTION
Land consolidation is considered to be the most effective land management planning approach1 for eliminating land
fragmentation2 and promoting agricultural and rural sustainable development. Land consolidation which is applied in
many countries around the world including 26 out 28 EU countries, consists of two main components: land reallocation
(or land readjustment) and the construction of agricultural infrastructure such as roads and irrigation networks. Land
reallocation is the most critical, complex and time-consuming part of the land consolidation process3,4 because it
involves the land tenure restructuring both in terms of ownership exchange and land parcels boundaries modification.
Land reallocation based on parcels’ land values because each landowner should receive after land consolidation a
property with approximately the same land value as the original. If this value exceeds the original value then the
landowner should pay the extra cost to the Land Consolidation Corporation and vice-versa. Therefore, land value is a
very critical parameter that directly affects the monetary interests of landowners hence it should be reliable, accurate and
fair among all landowners. This value can be the market value or the agronomic value5. In contrast to other countries, in
Cyprus the market value is utilized because agricultural land has broader development prospects hence it is attracted by
farmers and non-farmers as well.
In practice, in Cyprus, land valuation is a mass appraisal process6 carried out by the Land Valuation Committee (LVC)
which assigns a market value for each land parcel and its contents i.e. farmstead, wells etc. by employing the sales
comparison method that based on similar sales transactions occurred in the area concerned or the neighbourhoods. The
practical experience shows that the certain process faces some problems. In particular, it is time consuming hence costly
(it may take some months on a non-regular work basis) because the process is undertaken manually by inspecting all
parcels by the five members of the LVC. Furthermore and most importantly, outcomes present inconsistencies because
the LVC empirically tries to compare land parcels attributes that define land value, with the attributes of some typical
land parcels for which LVC assigned values based on sales transactions. As a result, due to not employing systematic
analytical tools such as GIS and thanks to the human weakness in estimating and processing so much information, it has
been shown a strong regional variation7 (within the case study area) of the coefficients of land valuation factors. This
variation that reflects the importance assigned by LVC for each factor has been revealed through geographically
weighted regression (GWR)8. Therefore, the process is not standardized, fully transparent and sometimes causes
unfairness and bias to the land reallocation hence it produces objections (officially or not) by landowners who usually
compare the land value assigned in their land parcels with other similar or neighbourhood parcels. Consequently,
Demetriou7 has proposed a framework involving a new land valuation process in land consolidation areas having in its
core automated valuation models (AVMs) 9,10 aiming to overcoming these problems.
AVMs are mathematically based computer software programs that are able to estimate the value of various types of
properties based on market analysis of a specified area and the characteristics of a certain group of properties stored in
appropriate databases for a given point of time9. Two well-known properties valuation methods are the sales comparison
method noted earlier and the hedonic regression approach involving that the value of a property is composed by the
value of its various attributes. Actually the two methods can be combined since usually the aim is the estimation of a
relationship among a dependent variable and one or more independent variables (attributes) based on known land values
for a set of properties. This process called calibration and it is the core of an AVM. Various methods have been used so
far among which multiple regression analysis (MRA) is the most traditional and popular method11 which is employed in
this research. In addition, several works include a spatial component i.e. GIS12,13,14,15 or they employ artificial intelligent
(AI) techniques as an alternative calibration approach instead of MRA, such as artificial neural networks (ANN)16, 17, 18,
19, expert systems20 , case based reasoning21, agent based models22 and genetic algorithms23 (GAs) which the latter two
have been arisen very recently.
In particular, GIS technology is nowadays a necessity for land valuation modeling9 because valuation process is
inherently spatial related and involves a great amount of data that can be easily stored, managed, analyzed and visualized
(e.g. value maps) through a proprietary GIS or ideally within a Computer Aided Mass Appraisal System (CAMA)24
integrated with the former. In addition, the huge GIS toolbox for spatial analysis provided in such systems and its
capability to integrate geo-information from various resources i.e. remote sensing, photogrammetry, airborne lidar
systems, mobile GIS and cetera, make them supreme instruments that open new horizons in land valuation in terms of
efficiency, effectiveness, reliability and accuracy. A raster based GIS has been used to assign a nominal asset values25 to
urban land consolidation area. Although the study is interesting it does not involve monetary values and quality
assurance is lack. It should be noted that while there is relatively rich literature about real estate valuation and namely for
residential properties, on the other hand, research related with land valuation of agricultural land and more specifically in
land consolidation areas is very rare.
In the light of the above, the aim of this paper is to present and discuss the development and evaluation of a hedonic
price AVM for a case study land consolidation area in Cyprus by utilizing linear MRA. Because sales transactions in the
area concerned were not adequate for accurate predictions7 three sample sets of land values (i.e. 10%, 15% and 20%)
provided by the LVC employed to estimate the values of the rest land parcels. Results are evaluated based on
international standards defined by the International Association of Assessing Officers (IAAO) 6,9,26 showing that AVM is
capable to produce acceptable in terms of accuracy and reliability land values and to reduce time hence cost required by
around 80%. In this context, the structure of the rest of the paper involves Section 2 which focuses on the methodology
utilised for developing and assessing the hedonic price model followed by section 3 that presents the land consolidation
case study area and the land valuation factors involved in the model. Afterwards, section 4 discusses the outputs of the
model by employing statistical analysis and ratio studies. Eventually, conclusions and recommendations for further
research are sum up in section 5.
2. THE DEVELOPMENT AND QUALITY ASSURNACE OF A HEDONIC PRICE MODEL
2.1 The development of the hedonic price model
Hedonic regression modeling is the oldest statistical calibration methodology has been utilized for estimating property
values gained the most attention since 60s early 70s27 until nowadays 28,29,30. As noted earlier, it is based on multiple
regression analysis (MRA) which is one of the most well-known statistical methods with huge range of applications
especially for prediction and forecasting. It involves the estimations of relationship among a dependent variable and one
or more independent variables. The general regression model relates Y to a function of X and β. This function can be
either linear or non-linear.
+ (1)
The dependent variable is Y whilst the independent variables denoted by X. The unknown parameters, denoted as β,
which may represent a scalar or a vector and represents random errors. In the case of linear function the development
of the above function involves a general multiple regression model with p independent variables as shown in the
equation below:
(2)
where Xij is the ith observation on the jth independent variable, and where the first independent variable takes the value 1
for all i (so it is the regression intercept). is an error term for observation i.
It should be emphasised that the reliability of MRA outcomes depends on the satisfaction of four main assumptions33
related to the residuals i.e. the difference between the actual market value and the predicted value: (i) normality, (ii)
constant variance (homoscedasticity), (iii) linearity and (iv) independence, which discussed later in the application of the
model.
2.2 International standards for quality assurnace
IAAO9 has defined standards and specifications for the development process of AVMs involving a number of steps: (i)
model specification, (ii) model calibration and (iii) model testing and quality assurance26. Specification involves the
definition of the valuation method i.e. sales comparison and the selection of independent variables will be included in the
model as predictors of the market value (depended variable) and; calibration is the process of testing model structure to
estimate variable coefficients/parameters using a different dataset employed for testing the performance of the model by
utilizing ratio studies26. Actually, specification and calibration is a common iterative process until statistical model
performance indices are acceptable. Both tasks are very important so as to develop an effective and accurate model. The
third step i.e. model testing and quality assurance involves various statistical diagnostic tests of the model performance
with a property sample (called holdout sample) that has not been used before in model calibration so as to ensure that it
fulfils the acceptable accuracy and reliability standards before its use. For this purpose ratio studies are employed that
encompasses four basic measures: (i) appraisal level (mean, median, weighted mean), (ii) variability-uniformity
(coefficient of dispersion-COD), (iii) reliability (confidence interval); and (iv) vertical inequities (price-related
differential-PRD, price related bias-PRB).
In particular, appraisal level aims to measure statistically how close appraisal are to real market values (or the LVC’s
values in our case) by employing primary measures of central tendency. While ideally the desire level is 1.0 i.e. appraisal
value equals the market value, an appraisal level between 0.90 and 1.10 is considered acceptable for any type of
property26 for certain confidence intervals. The evaluation of variability-uniformity measures the dispersion of ratios. In
general, the smaller the measure the better the uniformity, but extremely low measures suggest rather a problematic
calibration for many potential reasons i.e. sales chasing or non-representative sample. IAAO26 provides standards of
COD range for all type of properties. In our case, the standards for vacant land (with a range between 5.0 to 25.0) are
assumed because it is the closer category to agricultural land that is not exclusively involved in the list. Reliability
measures that are represented by the confidence intervals reflect the degree of confidence (for a certain percentage i.e.
95%) can be placed in a calculated statistic for a sample of appraised properties. A confidence interval noted in brackets
shows the upper and lower limits of a certain measure of central tendency and a desired level for any type of property
between 0.9-1.10. The measure of dispersion i.e. COD is a “horizontal” metric regardless of the value of individual
properties. In contrast, vertical inequities provide evidence about the accuracy of appraised individual properties. An
index for measuring vertical inequality is called price-related differential (PRD) which is calculated by dividing the mean
ratio by the weighted mean ratio. This statistic should be close to 1.0. Measures significantly above 1.0 show regressivity
i.e. low-value properties are appraised at a greater percentages market value than high-value properties. In contrast,
measures considerably lower than 1.0 indicate a progressivity, that is, low-value properties are appraised at smaller
percentages of market value than high-value properties. IAAO26 notes that PRD should be between 0.98 and 1.03.
Moreover, IAAO26 emphasizes that further to PRD, it is recommended to carry out a statistical test for price related bias
(PRB) as well, because it provides a more meaningful and easily interpreted index than the former. PRBs for which 95%
confidence interval fall outside the range of -0.10 to +0.10 indicate unacceptable vertical inequities. In addition to the
above metrics included in the ratio studies standards they have been also used the root mean squared error (RMSE), the
mean absolute percentage error (MAPE). The former measures the discrepancies between the predicted values and the
actual observations whiles the latter measures scaled discrepancies. Such measures have been also used in other case
studies 23,30. Furthermore, in order to measure how the error deviates, the absolute percentage error estimated which
called forecasting error (FE)17.
3. CASE STUDY AREA
3.1 The land consolidation area
Choirokoitia is a village in the Larnaca District of Cyprus, which is located southwest of Larnaca town (Figure 1). The
village is built on a hill with an average level of 230 m and the land consolidation area is located northwest of the village
in lowland with limited hills. The land consolidation area is included in an agricultural zone while on the east is almost
coincide with the main road that connects some of the mountainous villages of the District of Larnaca with the main
motorway in Cyprus. The land consolidation area has a size of 266 hectares and involves 488 land parcels (Figure 2).
The land use is mainly citrus, olives, various fruit trees and cereals. Some land parcels are irrigated through individual
drills and several land parcels are irrigated through a network connected with a water reservoir.
Figure 1. The location of Choirokitia village on the map Figure 2. The land consoliation case study area
of Cyprus
The land valuation in the certain area was carried out periodically from October 2008 until February 2009. The highest
land value has been defined in €35000 per decare (1000 m2) and the lowest in €2000. It should be noted that the LVC
separately valued any buildings included within the land i.e. a house, a farmstead, a drill, a fence and any isolated trees
included in the land e.g. large olive and carob trees.
Choirokitia
3.2 Land valuation factors
All information regarding the case study area built within ArcGIS 10.0. In particular, information includes a cadastral
map (Figure 2) (provided at a scale of 1:5,000) showing the original situation before land consolidation which is joined
with three databases containing information regarding landowners, ownerships and land parcels. In addition, the GIS
data model involves the official land valuation map with an associated catalogue, a soil map, a zoning map and a contour
map. All this information employed to automatically extract (using some programming routines) the scores for each
parcel for fourteen land valuation factors extensively discussed by Demetriou7. These factors are grouped31 in two major
categories: internal and external in relation to the property. Each category can be split further in two sub-categories:
physical attributes and legal factors for the former and locational characteristics and economic conditions for the latter.
In particular, each category includes the followings factors regarding each parcel with variable’s name within
parentheses: physical attributes are: size (size) in squared meters, shape (shape) measured in parcel shape index called
PSI32, mean slope (slope) measures in percentage, mean elevation from sea level (elevation) in meters, aspect (aspect)
that is measured clockwise in degrees (i.e. 0 north, 90 east, 180 south and so on), existence of a stream (stream) and soil
type (soil) has been provided by the Geological Survey Department which involves two types: Skeletic-calcaric-
REGOSOLS and calcaric-lithic-LEPTOSOLS represented by the letter “A” and calcaric-CAMBISOLS and calcaric –
REGOSOLS represented by the letter “B”. Legal factors involve the existence of irrigation rights (irrigation) for a
parcel. Locational characteristics are access through a registered road (access1), access through a registered pathway
(access2), the distance from residential zones (zone), the distance from the main road that connects the neighborhood
villages with the motorway (main_road) and the existence of sea view (sea_view). Economic conditions are land-
use/productivity (land_use) for the agricultural economic potential of a parcel which is reflected by the expected net
revenue per decare for various crops that has been provided by the Agricultural Department of Cyprus. The dependent
variable i.e. the market land value is measured in Euros per decare.
4. RESULTS AND DISCUSSION
4.1 MRA results
As noted earlier, sales transactions for the consolidated area were note sufficient to predict land values, hence, three
sample sizes i.e. 10%, 15% and 20% of land parcels values assigned by the LVC used for that purpose. In contrast to
many statistical experiments that use a random sampling, in this case it is very important that the selected land parcels
should adequately represent in terms of features the whole population. Therefore, parcels were selected based on their
attributes to cover all the range found in the population. In particular, they were selected all the parcels having the min,
max and mean score of all the continuous land valuation factors and then parcels were selected randomly to cover (as
much as possible) the whole case study area. Similarly, categorical factors (i.e. those take a binary value), parcels were
selected proportionally based on the frequency of each score (i.e. 0 or 1) and randomly taking into account to keep a
location-based balance.
The multiple regression analysis model ran with the three basic methods for selecting variables i.e. forward selection,
backward elimination and stepwise variable selection. The second method gave slightly better results from the other two.
Therefore, the basic model summary statistics and the number of variables included in the final model for each sample
are presented in the following Table 1.
Table 1: Summary statistics for the linear model
Sample
R2
Adjusted
R2
Variables
remained
Durbin-
Watson
1
0.820
0.799
Size, stream, slope, access1, zone
2.50
2
0.788
0.769
Access2, size, slope, acces1, irrigation, zone
1.98
3
0.814
0.799
Access2, size, access1,irrigation, aspect, slope, zone
2.14
The square of the correlation coefficient R2, that indicates the proportion of the observed variability of the dependent
variables which is explained by the independent variables, is quite high for all samples with the highest for sample-1
(which is close to that of sample-3). This indicates that even a small sample which includes only 10% (i.e. 49 land
parcels) of the total population may fit a model very well as shown graphically for sample 1 in the Q-Q plot of the
standardized residuals in Figure 3a where the points fall close to a straight line.
Figure 3. a) The normal Q-Q plot of the standardized residuals; b) The distribution of residuals; c) The scatterplot of
studentised residuals against the standardized predicted value, all for sample 1
Similarly, the adjusted R2 (adjusted for the number of parameters in the equation and the number of data observations)
which is always smaller than R2 reflects how well the model would fit another sample from the same population is
equally the highest for samples 1 and 3. The estimated regression equations for each sample revealed that the signs of all
coefficients are reasonable, namely size, stream, slope, zone and aspect having negative signs whilst access1, access2,
and irrigation having positive signs. A critical issue among the independent variables included in each final model is the
potential correlation and the multicollinearity i.e. the linear relationship. The former statistic is measured by Pearson
correlation coefficient and the latter by the tolerance. The Pearson’s correlation matrix showed that for all samples all
potential combination of variables have a correlation less or equal to 0.5 which is a very acceptable result. Similarly,
tolerance that may take values between 0 to 1 (0 means there is a linear relations and 1 means there is not a linear
relationship) is in most cases equal or more than 0.7 except in two cases where irrigation and zone variables have a
tolerance around 0.5-0.6. However, this fact does not suggest a problem since the value is quite far from 0.
The four MRA assumptions examined in the LVC model are all fulfilled indicating reliability of results. In particular,
normality is confirmed for all three samples by utilizing Shapiro-Wilk test with an output value for sample-1 0.979 (1
means that sample data are perfectly normal) with a level 0.132 which is more than 0.05 and a standard deviation of
standardized residual 0.963. Similarly, sample-2 model results in a value 0.983, with a level 0.436 and a standard
deviation of standardized residual 0.957; and Sample -3 model results a value of 0.980, with a level 0.584 and a standard
deviation of standardized residual 0.946. Normality assumption is evident from the distribution chart which is close to
normal as shown for sample 1 in Figure 3b. Homoscedasticity is also confirmed since the scatterplot of studentised
residuals against the standardized predicted value do not present any pattern as shown for instance in Figure 3c for
sample 1.
Regarding linearity assumption, F-test showed that there is a linear relationship between the dependent and the
independent variables because the null hypothesis (i.e. there is no linear relationship between the dependent and the
independent variables) has been rejected since the F ratio is small (based on the magnitude of the regression coefficients)
for all samples with a high significance level. However, visual inspection showed that slightly non-linear function (e.g.
exponential) could fit for the variables size, slope and zone. Independence of observations also confirmed by Durbin-
Watson test for the three samples since all values are between1.50-2.5 while values close to 2 involves no correlation. In
addition, spatial autocorrelation tests (p-value and z-score) within ArcGIS showed that the p-value is not statistically
significant hence we cannot reject the null hypothesis, meaning that it is quite possible for 90% confidence level that the
spatial distribution of residuals’ values is the result of a random spatial process.
(a)
(c)
(b)
4.2 Ratio analysis results
All the quality assurance measures noted in section 2.2 estimated. In particular, results show that all the appraisal level
statistics, that is the three main measures of central tendency the mean, median and weighted mean of ratios are within
the acceptable by IAAO26 range, namely, between 0.9 and 1.10 revealing an initial positive sign. A stronger relevant
indication is the use of confidence intervals to determine whether it can be reasonably concluded that the noted appraisal
levels differ from the established performance standards in a particular instance. Therefore, it has been confirmed that
with 95% confidence interval estimates for the mean and the median relevant standard has been met since all measures
fall within the noted range suggesting reliability evidence. Furthermore, the coefficient of dispersion-COD is within the
noted standard range for vacant land (i.e. between 5.0-25.0), ranging from 11.66 the minimum (for sample 3) to 13.83
the maximum (for sample 1), which are quite far from the highest acceptable value i.e. 25. COD is improved as the
sample increases while samples 3 and 2 present similar COD. Similarly, the price-related differential-PRD is almost the
same for all samples and it is marginally within the acceptable range 0.98-1.03 but that for sample 1. This potentially
shows a slight regressive tend i.e. low-value properties are appraised at a greater percentages market value than high-
value properties. Similarly, the estimated price related bias-PRB ranges from -0.087 to -0.036 for the three samples
which is within the acceptable limits i.e. -0.10 to 0.10, showing a trend towards the lower limit. Therefore, PRB shows
that for 95% confidence interval, assessment levels do not change by more than 10% when values are halved or doubled.
Furthermore, it was found that RMSE and MAPE decreases as the sample increases. However, the decrease is very slight
between sample-2 and sample-3 suggesting that no significant performance improvement can be achieved if the sample
increased more than a limit. Similarly, the best percentage of FE for 10% resulted from sample 2 and 3 with around 57%
of land parcels values estimated with accuracy better than 10% and around 32% of land parcels values estimated with
accuracy better than 20% compared with the true values. Therefore, it seems that a sample of 15% is adequate to
accurately predict with a discrepancy between 0%-20% from true values for the 90% of parcels. In alignment with this
finding, the AVM could carry out the site work of the LVC by employing around 80% less resources because the LVC
could carry out only 5 site valuation visits for assigning land values to the selected 15% sample of parcels (i.e. 73
parcels) instead of 25 days to assess all the 488 land parcels of the consolidated area. These figures show a proportional
reduction of both time and costs. Further to these savings, the most beneficial parameters provided by the AVM is the
quality of valuation in terms of comprehensiveness (a great number of variables are taken into account) consistency
(precise comparison of variables scores), reliability (predictions based on international standards) and transparency (the
analytical explanation of a land value is possible) of outcomes with an equity impact to the landowners involved.
5. CONCLUSIONS
The current mass land valuation process employed in land consolidation schemes is not efficient and reliable thus
authorities involved need to introduce AVMs based on international standards. Clearly, the AVM presented in this paper
is considerably more efficient than the traditional empirical process in terms of time, costs, accuracy, reliability,
consistency and transparency. Ongoing research focused on employing different calibration methods for developing
AVMs based on a non-linear function and artificial neural networks, in order to investigate and compare the performance
for all the three models.
ACKNOWLEDGEMENTS
The data used for this research have been kindly provided by various Departments of the Public Sector in Cyprus.
Therefore, I would like to thank very much the Departments of: Land Consolidation, Land and Surveys, Geological
Survey and Agriculture and the people assisted me to get and discuss further details regarding these data.
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