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Determining attributes of Indian real property valuation using principal

component analysis

Sayali Sandbhor, N.B. Chaphalkar Assistant Professor and Research Scholar, Civil Engineering Department, SIT, SIU, India Professor, Civil Engineering Department, RSCOE, Pune, India

Abstract

Introduction: Accurate property valuation depends on correct analysis of the contributing factors. Real property valuation is required to be carried out for various purposes including buying, selling, mortgage, tax calculation etc. Aim of this study is to ascertain the prominent factors affecting property value in Indian housing market. Methodology: Total nineteen variables were identified from literature as well as discussion with experts. Opinion of the experts about the level of significance of each of the variables towards value of property was taken through a well structured questionnaire survey. Data obtained from the survey was processed using Principal Component Analysis (PCA) which helped to decrease the number of variables into seven most important factors affecting value of real property in Indian housing market. Results: The seven most important factors that affect Indian real property value included living conditions of residents; characteristics of housing; regional influence; utilities; age of property; economic, political & social influence; area & legal aspect. Conclusion: The study is an effort of its kind in applying PCA for Indian housing market and can form the basis for preparing automated value prediction model. Keywords: Housing market, attributes, valuation, residential property, principal component analysis, developing country

1. Introduction

Property price is one of the most important criteria for buyers in making their property sell, purchase and related decisions [‎1]. Accuracy in value prediction can be attained if the impact of various factors affecting it is correctly mapped. Thus, it needs to be ascertained with great accuracy. The rapid growth in housing prices in many cities around the world since the late 1990s has motivated a growing number of studies to examine the variation in housing price dynamics across regions [‎2].‎ Being‎ one‎ of‎ the‎most‎ volatile‎ sectors‎ of‎ nation’s‎ economy,‎ the‎

behavior of housing prices has been attracting considerable research attention. Several studies have indicated that property price is usually affected by various intrinsic and extrinsic parameters [‎3]. Careful attention needs to be given to the dynamics of these factors for full understanding of the determinants of the property value [‎4]. Trend of housing prices can be captured if these attributes are correctly identified and studied. Indian housing market has observed fluctuations in property rates which are attributed to movements at macroeconomic level. Value of property on the other hand also depends on property characteristics. The objective of an appraisal or property valuation is to establish the market value which is the most probable price that would be paid for

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a property under competitive market conditions [5]. Probing into the reasons of value fluctuations due to property related attributes is necessary. Present study aims to identify variables affecting property value for Indian housing market and group them under few prominent factors using PCA.

2 Literature review

It is generally acknowledged that the price of real estate is highly complicated and is interrelated with a multitude of factors [6]. Various researchers have used a diverse set of factors for their analysis due to differing perceptions as to what should be emphasized most among the different factors affecting value. In the past researches, efforts have been made to identify variables affecting value of real property for specific case regions. Present study focuses on analysis of only instrinsic variables i.e. variables that are directly related to property characteristics. A summary of various intrinsic variables considered in past researches is presented. It has been noted that surrounding neighborhood [7,8,9], location and economic status of the surroundings, availability of access road [10] for the property under consideration impacts the value. Land formation on which the property has been built is also one of the variables that influence value [11]. Also, built up area [7,8,9,10,12], construction quality [7], age of building [7,10,13], condition of structure [9,11,12], internal specifications [7], view from property [12,14], availability of parking space [7,8,13], water supply, future scope of development [15], nearness to nuisance [‎16,17] , nearness to transport facilities [18] have been found to be effective features of property contributing to property value. These are a few studies that address the effect of variables on value of property for specific study areas. There is a need to find out list of important parameters that drive property value in Indian real property market. Application of some data analysis technique would certainly help in finding a comprehensive list of such parameters. With due consideration to the vastness of the subject, it is required to map exact relation of various parameters and value of properties in India. Following is an attempt to partially achieve the same.

2.1 Variables affecting property value in India

Indian property market is mainly driven by the predominant economy of the nation and in turn the rates of properties across various regions in the country which are derived from the macroeconomic drivers. Value of existing property, in turn, is dependent on property characteristics and is a certain fraction of the standard rate of any newly constructed property. Prevalent market rates, in addition to fraction of property characteristics, give the property value for an existing structure. In addition to common parameters as observed in literature, there are certain characteristics like future scope of development, shape and margin of plot, water supply, lift with generator backup which are uniquely observed for Indian property market.

With due consideration to previous research findings, variables for present study have been shortlisted. Opinions of valuation experts have been obtained from informal discussions which has helped in narrowing down the number of variables and also validate the list with due

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consideration to practical aspects of real property valuation in India. Output of the exercise is identification of 19 variables affecting property value for further analysis. Identified variables include area of property, future scope of development, nature of workmanship, state of property/ structural condition, legal aspects of property, age of building, shape and margin of plot, locality, prospect, access road width, construction specifications, parking space, water supply, lift with generator backup, amenities by builder, nearness to facilities, nearness to nuisance, local transport facilities and intercity transport facilities. Content validity ensures that the questionnaire includes an adequate and representative set of items i.e. variables that tap the concept. The more the scale items represent the domain or universe of the concept being measured, the greater the content validity [19]. Hence, to ensure that the variables map the property value to a great extent, identified 19 variables have been validated from valuation experts before preparing the questionnaire.

3. Questionnaire Survey

3.1 Questionnaire design

A questionnaire is developed to acquire the perceptions of valuation experts regarding the relative importance of the identified variables. The questionnaire requests rating for each variable on a 5-point Likert scale. Scale for the responses is defined in accordance to the significance of the variable towards value computation. A rating of 5 represents extreme significance gradually reducing to no significance represented by 1. Consistency of the questionnaire design is checked by reliability analysis.

3.2 Reliability analysis

An experiment is considered reliable if it yields consistent results of the same measure [20]. It is thus, imperative to check for internal consistency of the decided scale. Reliability of the test scale is checked‎ using‎ SPSS‎ reliability‎ analysis‎ tool.‎ Cronbach’s‎ alpha‎ reliability‎ coefficient‎normally‎ranges‎between‎0‎and‎1.‎Cronbach’s‎alpha‎coefficient‎ for the present questionnaire is observed to be 0.750 (Table 1). This is an acceptable level of reliability which is above the recommended satisfactory level [19, 21]. It is an indication of the stability with which the questionnaire measures the concept. With due consideration to the outcome of the reliability analysis, it is decided to obtain survey responses for further analysis.

Table 1. Reliability statistics

Cronbach's Alpha Cronbach's Alpha

Based on Standardized Items

No. of Items

.750 .744 19

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3.3 Details of sample and data collection

After finalizing the questionnaire, it is presented to professionals in the Indian real property valuation domain for obtaining their views. Respondents have been identified by adopting judgmental sampling method to seek out relevance of identified variables with property value. Respondents from over 13 states of India are asked to rate identified variables on a 5 point Likert scale and a total of 160 responses are received. Sample size of 160 is observed to be sufficient for the present study based on stability of results with increasing sample size and comparison with standards mentioned in literature [22]. Obtained data is further processed using principal component analysis.

4 Application of PCA

PCA is a multivariate analysis technique which is used to reduce data [23] and it seeks to construct a new set of variables, called principal components which are less numerous than the original data, but still adequately summarize the information contained in the original variables. PCA is useful for finding clusters of related variables and is ideal for reducing a large number of variables into a more easily understood framework and a smaller set of factors [‎24,‎25,26]. It also establishes underlying dimensions between measured variables and latent constructs, thereby allowing the formation and refinement of theory [27].

A few, real property related studies have examined applicability of PCA and corresponding results. PCA has been applied to categorize identified 13 property attributes into three principal components to simplify application of nonconventional methods of valuation [8]. It is also used to reduce simultaneity and multi-colinearity in the indicators used for various parts of China to compute evaluation criteria for real market [28]. Principal component regressions and Bayesian regression to real property price forecast has also been applied and found that the principal component model with only one factor is best suited in forecasting the real house prices in the U S. relative to the Bayesian regressions [29]. In a study [6], total 17 indicators of real estate price in Chinese housing market are categorized in 7 factors using PCA by eliminating the real estate pricing indices having the relativities and overlap information. A study [30] has reduced original 15 variables to 4 factors under locational attribute and apartment attribute categories by means of PCA for two adjacent cities of France. PCA and multiple regression analysis have been used to establish relationship between demographic variables and house prices at the neighborhood level in Australia [31]. The same researcher [32] has used results of his previous study using PCA for further analysis. Researchers [33] have implemented PCA to examine the nature of housing market affordability and determine how affordability, as a key policy tool, should be analyzed. Based on the methodology, observations and results of relevant work in the past, research methodology for present work has been drafted. Following study implements PCA to valuation variables for real properties in India. Statistical procedures have been performed using Statistical Package for Social Sciences (SPSS) version 21.0 with an aim to identify latent construct underlying identified variables.

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4.1 Test for adequacy of sample size and applicability of PCA

Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is used to test the sufficiency of sample size. The sample is said to be adequate if the value of KMO is greater than 0.5. For present study, KMO value obtained is 0.699 ascertaining that the sample size is sufficient and PCA can be performed on available sample (Table 2) [22]. In addition to this, possibility of applying‎PCA‎can‎also‎be‎checked‎by‎Bartlett’s‎test‎of‎sphericity‎which‎is‎used‎to‎test‎the‎null‎

hypothesis that the variables are uncorrelated and the correlation matrix is an identity matrix. The variables have to be correlated for getting principal components. When the correlation matrix is an identity matrix, application of PCA would not be suitable for the given set of samples.‎ Bartlett’s‎ test‎ of‎ sphericity‎ is‎ significant‎ for‎ 19‎ variables‎ and‎ available sample size. Based on the inferences from above two tests, adequacy of sample size and reliability of the selected dimension reduction method is proved.

Table 2. KMO and Bartlett's test statistics

Kaiser-Meyer-Olkin Measure of Sampling Adequacy 0.699 Bartlett's Test of Sphericity Approx. Chi-Square 983.034

DF 171 Sig. 0.000

Table 3 exemplifies the descriptive statistics of the selected sample. It is observed from the mean values of variables that area, age and locality are the three major parameters affecting property value. Prospect, local transport and intercity transport facilities are three bottom rated variables.

Table 3. Descriptive statistics of variables

Nomenclature Variable Mean Std. Deviation

Analysis N

V1 Area of the property in sq ft 4.869 0.406 160 V2 Future scope of development 3.375 0.815 160 V3 Nature of workmanship 3.625 0.867 160 V4 State of property/ structural condition 3.719 0.863 160 V5 Legal aspect of property 3.681 0.755 160 V6 Age of building 4.550 0.622 160 V7 Shape and margin of plot 3.444 1.109 160 V8 Locality 4.331 0.707 160 V9 Prospect (View) 2.800 0.751 160 V10 Access road width 3.469 0.824 160 V11 Construction specifications 3.431 1.068 160 V12 Parking space 3.838 0.784 160 V13 Water supply 3.294 1.019 160 V14 Lift with generator backup 3.288 0.695 160 V15 Amenities by builder 3.431 0.774 160 V16 Nearness to facilities 3.281 0.778 160

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V17 Nearness to nuisance 3.163 0.917 160 V18 Local transport facilities 2.906 0.775 160 V19 Intercity transport facilities 2.369 0.732 160

Communality of a variable is the amount of variance that a variable shares with all the other variables being considered. Initial communalities in PCA are considered to be 1. Since communalities of all the variables after extraction are greater than 0.5 (Table 4), all the variables are retained for further analysis.

Table 4. Communality

Nomenclature Initial communality

Extraction Communality

V1 1.000 0.85 V2 1.000 0.722 V3 1.000 0.666 V4 1.000 0.755 V5 1.000 0.724 V6 1.000 0.825 V7 1.000 0.694 V8 1.000 0.684 V9 1.000 0.705 V10 1.000 0.596 V11 1.000 0.69 V12 1.000 0.779 V13 1.000 0.732 V14 1.000 0.729 V15 1.000 0.653 V16 1.000 0.71 V17 1.000 0.678 V18 1.000 0.634 V19 1.000 0.676

4.2 Determining the number of factors to retain

Kaiser’s eigenvalue-greater-than-one rule

The eigenvalue-greater-than-one (K1) rule is the most utilized method to ascertain number of factors to be retained after applying PCA. In this rule, only the factors that have eigenvalues greater than one are retained [34]. Eigenvalue is a measure of how a standard variable contributes to the principal components. A factor with an eigenvalue less than 1 is considered less important than an observed factor and therefore can be ignored [20]. Table 5 suggests seven factor solution as first seven factors have eigen value greater than 1 explaining almost 71% of the total variance.

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Scree test

Scree test is another measure to ascertain the number of factors to be retained. It involves observing the plot of the eigenvalues for a break point or hinge, also known as an elbow. The rationale for this test is that a few major factors will account for the most variance, resulting in a cliff, followed by shallow scree depicting consistently small error variance described by minor factors. Though it works well with strong factors, it suffers from ambiguity and subjectivity when there is no clear hinge in the depicted eigenvalues [34]. In Figure 1, the break point occurs at the eighth component of the scree plot.

Table 5. Total Variance Explained

Component

Initial Eigenvalues Extraction Sums of Squared Loadings

Rotation Sums of Squared Loadings

Total % of Variance

Cumulative % Total % of

Variance Cumulative

% Total % of Variance

Cumulative %

1 4.357 22.934 22.934 4.357 22.934 22.934 3.081 16.216 16.216 2 2.211 11.636 34.570 2.211 11.636 34.570 2.658 13.992 30.208 3 1.855 9.762 44.332 1.855 9.762 44.332 1.932 10.166 40.374 4 1.508 7.936 52.268 1.508 7.936 52.268 1.655 8.712 49.086 5 1.358 7.145 59.413 1.358 7.145 59.413 1.490 7.842 56.928 6 1.209 6.363 65.776 1.209 6.363 65.776 1.364 7.179 64.107 7 1.003 5.281 71.057 1.003 5.281 71.057 1.321 6.950 71.057 8 .755 3.975 75.032 9 .696 3.663 78.696 10 .618 3.253 81.948 11 .589 3.099 85.048 12 .532 2.799 87.846 13 .450 2.368 90.215 14 .406 2.138 92.353 15 .378 1.989 94.342 16 .342 1.799 96.141 17 .263 1.386 97.527 18 .251 1.319 98.847 19 .219 1.153 100.00

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Figure 1. Scree Plot

Based on observations of both the tests, seven factor solution appears to be acceptable. First seven factors are extracted and their relation with the variables is mapped with varimax rotation as follows.

Rotation of factors

Rotation is an inherent part of performing PCA. An important output from PCA is factor matrix which gives loadings or simple correlations of variables on the identified factors. Although the initial or unrotated factor matrix indicates the relationship between the factors and individual variables, it seldom results in factors that can be interpreted, because the factors are correlated with many variables [35]. The purpose of rotation is to achieve a solution where each factor has a small number of large loadings and a large number of small loadings, simplifying interpretation, since each variable tends to have high loadings with only one or with only few factors [36]. The goal of rotation is to simplify and clarify the data structure and alleviate the interpretation of solution. Among various methods of rotation, varimax is the most popular method which is an orthogonal method of factor rotation. Table 6 below gives rotated component matrix which shows the individual variable loadings on each factor.

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Table 6. Rotated Component Matrix

Variable Component 1 2 3 4 5 6 7

Area of property .003 -.184 -.142 .062 -.049 -.044 .888 Future scope of development .082 -.139 -.032 -.077 .013 .830 .011 Nature of workmanship .746 .114 .144 -.150 .106 .171 .111 State of property/ structural condition .142 .720 .325 -.256 .083 -.196 -.016 Legal aspects of property .021 .322 .418 -.021 .316 .124 .573 Age of building -.082 .073 -.072 .021 .896 -.053 .038 Shape and margin of plot .387 -.417 .357 -.106 .118 -.466 .041 Locality .629 .024 -.150 .138 .324 -.345 .150 Prospect (View) .732 .000 .136 -.052 -.351 -.091 -.126 Access road width .404 .536 -.160 .120 .289 -.038 -.145 Construction specifications -.039 .693 .392 .199 -.004 .001 .119 Parking space -.148 -.023 -.071 .859 .064 -.091 -.023 Water supply .095 .459 .138 .683 -.020 .013 .163 Lift with generator backup .485 .030 .128 .435 .454 .274 -.078 Amenities by builder .690 .375 -.121 -.058 -.102 .031 -.081 Nearness to facilities .276 .754 .056 .191 .023 .022 -.155 Nearness to nuisance -.105 .159 .786 .034 -.040 -.142 .028 Local transport facilities .508 .246 .396 .178 -.015 .346 .081 Intercity transport facilities .396 .129 .650 -.054 -.128 .132 -.209

Interpretation of factors

Interpretation is facilitated by identifying the variables that have large loadings on the same factor [35]. In Table 6, factor 1 has high loadings for variables V3 (nature of workmanship), V8 (locality), V9 (prospect/ view), V14 (lift with generator backup), V15 (amenities by builder) and V18‎ (local‎ transport‎ facilities)‎ and‎ is‎ labeled‎ as‎ ‘living‎ conditions‎ of‎ residents’.‎ Factor‎ 2‎

identified‎ as‎ ‘characteristics‎ of‎ housing’,‎ has high correlations with V4 (state of property/ structural condition), V10 (access road width), V11 (construction specifications) and V16 (nearness to facilities). Factor 3 has variables V17 (nearness to nuisance) and V19 (intercity transport facilities) loading heavily and is labeled‎as‎‘regional‎influence’.‎As‎factor‎4‎comprises‎of‎necessities‎like‎V12‎(parking‎space)‎and‎V13‎(water‎supply),‎it‎is‎labeled‎as‎‘utilities’.‎Factor‎

5 called as age of property has only V6 (age of building) loading heavily. Factor 6 is represented by‎V2‎(future‎scope‎of‎development)‎and‎V7‎(shape‎and‎margin‎of‎plot)‎identified‎as‎‘economic,‎

political‎and‎social‎influence’.‎Factor‎7‎known‎as‎‘area‎and‎legal‎aspect’‎comprises‎of‎V1‎(area‎

of property) and V5 (legal aspect of property).

5. Results and Conclusion

Identifying factors affecting property value is crucial to predict the behavior of property prices in future. The motivation behind this study is to help valuation professionals in India in assessing

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property value by identifying correlation between various parameters considered in finding value of property to optimize the process and results of valuation. Hence, the present study has been undertaken to comprehensively address the factors specifically affecting the real property prices in India. The outputs can further be used to prepare a prediction model using suitable artificial intelligence technique which is already in progress. The present study is a part of the value prediction model and throws light on the Indian property valuation and corresponding factors. With reference to applications in the past, PCA has been implemented for a more inclusive exploration of property characteristics directly affecting its present day value. The analysis includes identifying few factors which represent maximum variance of the entire dataset. These factors or components are supposed to exhibit characteristics of original variables involved.

Results of PCA have revealed that seven principal factors affect the value of property in India as the selected 19 variables are regrouped under the identified factors. The factors have been interpreted based on the variables comprising them. According to the nature of group of variables contributing to a factor, the seven categories are labeled‎ as‎ ‘living‎ conditions‎ of‎residents’,‎ ‘characteristics‎ of‎ housing’,‎ ‘regional‎ influence’,‎ ‘utilities’,‎ ‘age‎ of‎ property’,‎

‘economic,‎political‎&‎social‎influence’‎and‎‘area‎&‎legal‎aspect’.‎As‎a‎variable,‎age‎of‎building‎

shows the highest correlation of 0.896 with its factor, depicting very high significance with value of real property. Also, variables such as lift with generator backup and shape & margin of plot describe correlation less than 0.5 with their factors, depicting that these two variables do not affect value of housing significantly.

Research findings when compared with studies in the past show a high rate of similarity in identified factor categories. A study [6] applied PCA and characterized variables into seven categories for Chinese real estate market. These categories included economic, political and social factors, regional factors, living conditions of urban residents, characteristics of housing, public facilities, environment of housing and internal factors of developers. Another study [30] divided all the variables under two categories namely locational attributes similar to regional influence, economic, political and social influence identified in present study and apartment attributes‎similar‎to‎living‎conditions‎of‎residents’,‎‘characteristics‎of‎housing’.

For Indian scenario, living condition of residents is seen to be most prominent factor affecting property value followed by characteristics of housing and other factors. To exercise control over property prices in a particular region, economists and policy makers should give more attention to trend related to living standards of the residents. Valuers should give due attention to the seven identified factors to arrive at approximate estimate of property value and reliability can be checked with detailed estimate of value. Limitation of the study includes limiting significance of the research outcomes considering the cultural variation across India. There may be some additional factors for different study area but present study provides foundation for any further studies in that direction.

Consideration to identified factors and comparison of approximate & detailed estimate of value will reduce the efforts entailed in property valuation eventually minimizing the time and cost involved. Also, researchers can probe further with same methodology to find relationship of housing prices and attributes prominent in selected geographical area under study. This would also add to data availability for future comparison. Future research can be carried out using the

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outcomes of present study to predict value of housing property. Use of non-conventional methods of value assessment can be probed for Indian context for which current research results would form the basis.

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