The environmental product variety and retail rents on central urban shopping areas: A multi-stage spatial data mining method

Abstract

This study examines the relationship between various measures of environmental product variety and retail rents in central urban shopping areas. Using a Geographic Information System (GIS)-based detailed survey database, this research identified 34 layers of environmental product variety in the most representative single-centred shopping areas of the six largest cities in Taiwan. This research extracted layers of product variety and other measures of product variety, such as the number of layers of product variety above each point of interest, the density, the Core/Periphery factor scores, the Shannon entropy index, the Simpson diversity index and the Herfindahl–Hirschman index of each street line buffer area. The proposed method was used to generate three-dimensional maps of the rent gradient and the extracted core and periphery layers of product variety. Thus, a tool was developed for examining the variety features from various angles. The results showed that, in general, the higher the product variety, the higher the rents. Nevertheless, the scores for the core and periphery of the environmental product variety were the dominant determinants; street line buffer areas can only have lower rents if they lacked the correct (i.e. the core layers) environmental product variety, even if they have higher measurements of other variety features.

Keywords

Retail agglomeration economies environmental externalities retail rent gradient GIS-based spatial database high-street stores retail amenities

Introduction

Preferences for product variety have long constituted a central concern in urban and spatial research (Dixit and Stiglitz, 1977; Lancaster, 1990; Van Nes, 2005). Product variety is generally treated as a significantly favourable and productive factor in urban and industrial agglomeration (Fujita and Thisse, 2002; Ogawa, 1998; Schiff, 2015), but the methods for precisely measuring variety are insufficient, whether in academia or practice, for two possible reasons. First, regarding the intangibility of spatial features, such as product variety¹ and rental value, researchers and practitioners can only imagine these ambiguous and intangible variety features of a city or spatial study region. However, the spatial distribution of variety sometimes lacks a visual context, leading to contradictions between theory and practice. These intangible locational or environmental externalities, both Marshallian-specialised and Jacobian-diversification, become crucial in determining city sizes and inducing regional innovativeness (Abdel-Rahman and Fujita, 1990; Carlino and Kerr, 2015; van der Panne, 2004). However, what if the spatial distribution of product variety could be observed? The environmental product variety could then be analysed. The patterns of retail agglomeration would then become visible and measurable. Such visibility of intangible rental distributions and environmental features could induce more extensive research.

The second reason why current methods for measuring variety are unsatisfactory derives from the conceptual ambiguity of product variety. Variety, diversity, difference and even complexity could be, to some extent, synonymous (Batty, 2005; Gans and Hill, 1997; Jost, 2006; Straathof, 2007). When variety is discussed from a spatial perspective (e.g. a city or a shopping area), the characteristics of variety become a relative concept of agglomeration and the clustering of activities. Under this circumstance, the concepts of variety include not only higher ‘abundance’, ‘difference’ or ‘number’ but also the degrees of ‘richness’, ‘concentration’ or ‘evenness’. Moreover, the characteristics of this product variety depend on whether or not the spatial pattern of agglomeration can generate higher increasing returns, and such quality can entail different concepts. For example, a higher number of retail stores of different categories indicate higher variety (in scope); a higher number of retail stores in the same category are also treated as a higher variety (in scale). A heterogeneous agglomeration and its incentive are based on the economies of scope (Fujita, 1989). Moreover, a homogeneous agglomeration pursues increasing returns from economies of scale (Fujita and Thisse, 2002). Their benefits increase the frequency of consumer searches or reduce the shopping costs of the same trip in multipurpose shopping (Fischer and Harrington, 1996).

Due to the above-discussed complexity in measuring environmental product variety, this paper proposes a multi-stage method to tackle this significant subject. The retail agglomeration in central urban places, therefore, is the most observable environment for product variety, in terms of data availability in number, type and location of retail stores. Using detailed survey data from the central shopping areas of the six largest cities in Taiwan, this paper develops a six-stage process to extract different retail-category layers, each with exact clustering locations. This spatial data mining process provides the specific environmental retail distribution of each defined measuring unit. The specific distributions of retail-category layers of measuring units later generate different diversity and variety indices. Retail rental data of measuring units, as the performance variable, are then examined to understand if a higher product variety translates into an higher rental level. Because of the exact locational extraction process of product variety, three-dimensional visualised maps were generated in the final stage, providing an observer-friendly interface for later research.

Literature review: agglomeration and diversity

For a city or town centre pursuing vitality and viability, a retail development and business environmental management strategy plays a crucial role in generating the power of attraction (Cirman and Pahor, 2009; Dolega and Lord, 2020; Ravenscroft, 2000). Shopping atmosphere and retail amenities have undoubtedly become the engines of customer drawing power for a city centre (Teller et al., 2016; Teller and Elms, 2012; Weiler et al., 2003). The clustering of various retail stores and service providers attracts consumers with multiple demands. Product variety is, thus, closely related to productivity (Behrens and Robert-Nicoud, 2015; Ciccone and Hall, 1996;; Koster et al., 2014). Retail-led urban planning and development have become essential instruments for city centre regeneration (Balsas, 2018; Guimarães, 2017). Consequently, such a cluster of various retail stores or shops also shows the personality of a city and forms its attractiveness (Scoppa and Peponis, 2015). Moreover, the role of diversity and heterogeneous agglomeration has been considered as the source of sorting of heterogeneous location choices of workers and firms as well as the selection opportunities (Behrens and Robert-Nicoud, 2015). All these externalities generated from diversity and spatial clustering stimulate the ‘natural advantage’ for innovation (Carlino and Kerr, 2015).

Because such a retail structure is crucial in generating city centre agglomeration economies, previous relevant research has focused on two aspects. The first is the retail agglomeration patterns based on classical location theories, such as the hierarchical spatial distribution of retail activities from central place theory (Clark and Rushton, 1970) and the spatial competition process under Hotelling’s principle of minimum differentiation (Meagher, 2012). These classic locational theories can be applied to explain the general spatial patterns of city activities. The second aspect of relevant research has involved focusing on the sources and optimal conditions of agglomeration patterns, including economies of scale and economies of scope caused by Marshallian (specialisation) and Jacobian (diversification) externalities (Abdel-Rahman and Fujita, 1990; Caragliu et al., 2016; Carlino and Kerr, 2015; van der Panne, 2004); optimal variety conditions under monopolistic competition (Chang, 2012; Dixit and Stiglitz, 1977; Peng and Tabuchi, 2007); and the spatial distribution of increasing and constant returns of industries as suggested by Krugman’s (1991) core and periphery relationship.³ These externalities, product variety and spatial distribution concepts are considered and designed into later empirical studies, including the influential buffering range of retail stores, spatial product variety feature extraction and generating different product variety indices.

Moreover, the pattern of spatial distribution of product variety is also closely related to the characteristics of agglomeration economies. Hence, the spatial structure of retail concentration is also a significant concern to city retail amenities (Burger et al., 2014; Konishi, 2005; Murata, 2003; Potter, 1980). According to the principle of minimum differentiation suggested by Meagher (2012), retailers selling similar products tend to cluster together. However, Fujita and Thisse (2002) indicate that in addition to agglomeration (or centripetal) forces, the spatial configuration should also be influenced by dispersion (or centrifugal) forces. This paper suggests that for a shopping area, the spatial agglomeration pattern should also follow the core and periphery relationship similar to the concept indicated by Krugman (1991) in the regional study. Moreover, the core retail categories that could generate increasing returns should occupy core areas, and other supportive retailers, who generate constant returns, should be at periphery locations.

Regarding the discussed intangibility and ambiguity, it is extremely difficult to identify and measure variety or diversity because of the ambiguity of the essence of variety. In particular, in a complex environment, the dimensions of variety may generate even greater concerns when a simplified concept is preferred. For example, the number of layers of retail categories, the number of differentiated agglomeration areas and the density of shops within observed street areas are easier to apply directly compared with the Shannon entropy index, Simpson diversity index or Herfindahl–Hirschman index (Gans and Hill, 1997; Jost, 2006; Straathof, 2007). The concepts of variety, diversity, differentiation and complexity are sometimes difficult to delineate. Nevertheless, while a model extracts specific effects and those that are influential to certain performance variables, precise measurement is the top priority.

Although retailers of the same type tend to cluster together, preferences for variety still dominate the choice of location. Therefore, a prime location with higher rent should still have higher environmental product variety and, of course, retailers within these dominant groups should have sufficient rental payment ability. Consequently, the main research hypothesis of this study is for a central urban shopping area: the higher the environmental product variety, the higher the productivity and, thus, the higher the retail rent. Furthermore, this study also suggests that not all characteristics of variety exert positive effects on productivity and rents. This concept is simple to understand if product variety is treated as a part of resource allocation; thus, the distribution of resources should follow the core and periphery relationship. The core layers generating increasing returns are generally the main purpose of shoppers; the periphery layers, by contrast, generate constant returns and perform supportive functions.

Data and methods

To connect the above theoretical concept and the empirical study, a six-stage data mining process was developed. The value of this six-stage method is to extract environmental product variety under the specific location of each retail store. Using the minimum influential buffering area of each retail store ensures that the measuring is environmental, not only the existence of each retail store at a specific location. The spatial clustering of the retail stores of the same type gives us the measure of Marshallian externalities. At the same time, a defined 34 retail-category system provides diversity measures based on Jacobian externalities. Using the spatial joint function provided by ArcGIS, the detailed distribution and the combination of product variety could be extracted. This data set allows us to generate various product variety indices, including Shannon entropy, the Simpson diversity index, HHI and the core and periphery scores. These generated indices and variables are then examined further regarding whether higher the product variety has a higher rent level. Finally, these results were presented in 3D visualisations to provide policymakers with alternative viewpoints of the spatial distribution of the environmental product variety.

The data

Data were gathered from open government data sources or other standard geographical open data sources such as OpenStreetMap or Geofabrik.⁴ However, the data quality was unsatisfactory. Therefore, establishing a GIS-based spatial database from a detailed field survey became the primary task. The fundamental layer of a retail shop data set follows the concept of a point of interest (POI) used in OpenStreetMap (OpenStreetMap Wiki, 2016). This database can identify the specific location of each retail shop, the name of the business, the retail activity or activities of the shop and the floor level(s) the store. Other than the fundamental POI layer, this research used at least three of the original layers of data sets including (1) the point data of retail rents, (2) the line data of street networks from the open data source Geofabrick and (3) the basemap from the open data source OpenStreetMap. The point data layers of retail rental data were collected from several open data sources, such as the websites of leading real estate agents. Thus, with these four basic data layers in GIS, this study generated all the extensive results, in 2D and 3D, such as the distribution of agglomeration areas of each layer of retail category, indexed product variety and the rent gradient of each selected shopping area.

To understand the product variety features of the highest retail hierarchy,⁵ six shopping areas were surveyed. The selected shopping areas of this research were as follows, from north to south: (1) the Ximending shopping area of the Taipei metropolitan area, (2) the Taoyuan railway station shopping area of the Taoyuan metropolitan area, (3) the Hsinchu railway station shopping area of the Hsinchu metropolitan area, (4) the Chungyo shopping area of the Taichung metropolitan area, (5) the Tainan railway station shopping area of the Tainan metropolitan area and (6) the Shinkuchan shopping area of the Kaohsiung metropolitan area. The field research took place from late 2014 to early 2016. The image or video data taken by surveyors were then coded into ArcGIS.

The basic details of the six surveyed shopping areas, such as the population, size of the surveyed area, number of POIs and overall density of POIs, are shown in Table 1. Using the same survey method, the density of POIs was higher in the north rather than the central or southern cities. Furthermore, the highest density shopping area of this survey was in Taipei, the largest metropolitan area.

Table 1.

Basic details of the selected shopping areas.

Metropolitan	Population (central city area, May/2016)	Selected shopping area	Size of the surveyed area (m²)	# of surveyed POIs	Density (POIs/10,000 m²)
1) Taipei	2.702 million	Ximending	521,179	1566	30.05
2) Taoyuang	0.823 million	Taoyuang rail station	954,862	1946	20.38
3) Hsinchu	0.705 million	Hsinchu rail station	594,287	1456	24.50
4) Taichung	0.960 million	Chungyo	606,511	1176	19.39
5) Tainan	1.01 million	Tainan rail station	1,723,466	2593	15.05
6) Kaohsiung	1.51 million	Shinkuchan	1,137,209	1911	16.80

The rental value of each high-street retail store is always difficult to determine in data collection. Asking prices and after-transaction prices are both collected, but after-transaction prices were mainly used in this study. The data sources were based on open transaction websites such as the actual price registration webpage of the Ministry of the Interior and the transaction records provided by private real estate agencies such as Sinyi Realtor, Yungching Realtor and 591 Realtor. The rental data were also collected and coded in ArcGIS as point data. Time and regional differences among records were considered necessary tunings for inflation and CPI adjustments, which were conducted to prevent general bias. As described, these rental points were captured using the line of street data from the open data source, Geofabrik. The street lines with rental values then became the source of performance variables and the base for plotting the rental gradient of each shopping area.

Research design: six stages of product variety data mining process

After the field survey and coding process of retail shop POIs and rental value points, the next step entailed defining and extracting the layers of product variety. As mentioned, this extraction process is the most crucial task for verifying the characteristics of product variety. This study carried out the product variety data mining process in six stages (Figure 1).

Figure 1.

Product variety data mining process of urban shopping areas.

Stage 1. Basic data preparation of the selected areas

In this research, four basic data sets were used: (a) the POIs of each retail shop location, (b) rental data points, (c) street lines from Geofabrik and (d) the basemap from OpenStreetMap. All the subsequent extension data sets and variables were generated from these four basic data sets, such as the retail agglomeration areas and the rental gradient. The required tunings of the raw data, e.g. the rent adjustments and retail activity identification, were also completed at this stage.

Stage 2. Defining and identifying product variety

To extract the layers of retail categories, the classification and definition system of product variety was essential for deriving research results. The design of the elements for indices depends on the research objectives.

This research is the first to extract the layers of retail categories for a 3D visual demonstration of spatial distributions. Therefore, a standard retail-category system was applied according to the most general differences in retail features (Table 2), involving 34 retail categories. A retail-category system is generally used in department stores or shopping centres as the way to classify products or services into different groups or departments. Once all POIs were categorised into 34 retail categories (combined from at least 120 subcategories), the layers of retail categories could be developed.

Table 2.

The 34 layers of retail categories and the defined influential buffering range.

Layers retail categories	Buffer (m)	Layers retail categories	Buffer (m)
L1. Restaurants, café and foods	15	L18. Religious	15
L2. Apparel and accessories	15	L19. Gifts, antiques and arts	15
L3. Beauty, hair and cosmetics	15	L20. Drug stores and medical cares	15
L4. Electronic appliances, computers and mobiles	15	L21. Photography, wedding services	15
L5. After-school education	15	L22. Optical	15
L6. Hospital and clinics and dental	15	L23. Books, cards and stationary	15
L7. Jewellery and watches	15	L24. Automobile and motorcycle	15
L8. Night club, KTV and special entertainments	15	L25. Lotteries and pawn shop	15
L9. Banks, insurance and securities	15	L26. CD/DVD, musical instruments and performance	15
L10. Footwear	15	L27. DIY, hardware and interior design	15
L11. Homewares, florists and living goods	15	L28. Department store and shopping malls	50
L12. General service: dry cleaners, keys and repairs	15	L29. Hobbies, design, toys and games	15
L13. Specialty services: laws, realtor	15	L30. Tobacco, wine and betel nuts	15
L14. Public services and facilities	15	L31. Supermarket and traditional markets	30
L15. Sports, gym and cycling	15	L32. Pets	15
L16. Convenience stores	15	L33. Cinemas	50
L17. Hotels and B&B	15	L34. Vegetables, fishmongers, butcher and fruits	15

Stage 3. Generating the spatial distribution of the agglomeration areas for each layer of retail category

This stage involved generating all 34 layers of retail categories separately. Each layer presented the actual spatial distribution of agglomeration areas of the single product category. The process for determining the agglomeration areas is described as follows: (a) all POIs were classified into 34 standard retail categories, (b) the layer of each retail category was selected and exported and (c) each POI was buffered according to the effect range shown in Table 2. For example, in standard category shops such as apparel shops, footwear shops, or hair salons, 15 m is the environmental influential effect range.⁶ Hence, if one or more shops of the same type is within 15 m, then the affected buffer areas overlay. Under this condition, dissolving all the overlapping buffer areas enables generating the agglomeration areas.

Stage 4. Generating street line buffer areas: capturing rents and other variety features

These street line buffer areas (SBAs) become the basic measurement units of performance data (i.e. rents). Hence, other than the retail rental values, the number of shops, shop density of each street and the calculation of product variety indices were based on these SBAs. Data mining processes such as multiple regression, factorial analysis, clustering analysis and the 3D rental gradient also were based on SBAs of each shopping area.

Stage 5. Connecting all data sets: generating product variety indices

The major task at Stage 5 was to establish a connection between data sets and generate more variety indices from it. The process involved (a) using ArcGIS to establish the link among POIs, rents and spatial features; (b) conducting a factorial analysis to extract the core and periphery variety layers and scores; and (c) generating variety indices (e.g. Shannon, Simpson diversity and Herfindahl indices).

Figure 2 shows the combined two-dimensional (2D) visualisation of the related data sets. These visualised results presented sufficient information; hence, illustrating the details was difficult. However, the data sets (Figure 2) were clear and enabled calculating the product variety indices.

Figure 2.

The connecting process to capture the characteristics of each POI and SBA.

Factorial analysis was used for extracting the core and periphery layers of retail categories. This basic data mining process should reveal the dominant product variety textures that generate higher rents. The factor scores for each SBA were tested in the regression model to examine their effects on rents. For other variety variables, other than the captured explicit variety variables (e.g. number of stores, number of retail-category layers and size of agglomeration area), the combined data sets provided sufficient information for calculating variety indices (e.g. Shannon entropy index, Simpson diversity index and Herfindahl–Hirschman index). These extended indices provided more information on richness, evenness and concentration. The definitions of the extended variables used in this research are as follows:

Shannon entropy index (expected value of choice and diversity⁷):

$H = - \sum_{i = 1}^{n} p_{i} \ln p_{i}$ , where n is the total number of retail categories, and p_i is the proportion of individuals (shops) in the ith retail category.

Simpson diversity index (richness and evenness):

$D = \sum n (n - 1) / N (N - 1)$ , where N = the total number of shops in the SBA, and n is the number of shops in each retail category. The Simpson diversity index usually used is Simpson = 1 – D.

Herfindahl–Hirschman index (the concentration of the market):

$HHI = \sum_{i = 1}^{n} s_{i}^{2}$ , where $s_{i} = x_{i} / X$ , where X is the total shop number in the shopping area, and x_i is the total number of type i shops.

The selection of these three indices is based on the advantage of the measuring meanings. The Shannon entropy quantifies the degree of surprise, i.e. the chance that a shopper could encounter the abundance of product variety in the measuring unit. Simpson diversity index (1 – D) for evenness and HHI for concentration are two complementarity indices, which measures if the retailers of the same category are concentrated or evenly dispersed within the measuring unit.

Stage 6. Generating data mining results

After the extraction stages, the final stage involved mining for detailed results by including (a) the factorial analysis to extract the core and periphery retail categories, (b) a regression model for examining the main hypothesis and other product variety features, (c) the TwoStep cluster analysis for SBAs and (d) 3D illustrations.

Factorial analysis, or the principal component analysis method used for dimension reduction, is widely used in data mining processes. In this analysis, the core and periphery layers of retail categories could be extracted. The research hypothesis here is that the core layers could generate higher environmental product variety externalities to the POIs but not the periphery layers. Therefore, to understand the significant contributions of each layer, this analysis involved using the distribution of the frequencies of the 34 layers in all SBAs⁸ to generate potential factors.

For the regression tests, at least three general models were examined in regression

Model 1 \ln r_{ij} = f (Ncategorie s_{ij})

where r_ij is the rent of POI i in city j; thus, j is from 1 to 6. The variable ‘ Ncategories_ij ’ is the number of retail-category layers captured by each POI_ij. This model was used to examine the main hypothesis of this research; that is, for each POI, the effect from environmental variety externality should be the higher the product variety, the higher the rent. Hence, the variable ‘ Ncategories ’ should be a positive variable for POI rent and was examined according to overall POIs and separately for each city.

Model 2 \ln r_{ij} = f_{ij} (L_{1}, L_{2}, \dots, L_{34})

where r_ij is the rent of POI i in city j, and L₁, …, L₃₄ represent the existence of variety layers for each POI. This model was used to examine the effect of the existence of each type of layer on rent. The results should reveal the direction and magnitude to rents when a certain layer exists above the POI.

Model 3 \ln r_{k} = f (Core, Perihpery, NShops, Density, Shannon, Simpson, HHI)

where r_k is the rental value of SBA _k (testing in all SBAs). This model was used to examine the variety of features in each street section. The product variety features were the core and periphery scores from the factorial analysis. The core and periphery result from the principal component analysis of overall SBAs; thus, at least the core should have a significantly positive relationship with rents. The variable ‘ NShops ’ is the number of shops of each SBA, and ‘ Density ’ is the density of the POIs of each SBA; they are explicit variety variables and were expected to have a positive relationship with rents. Shannon’s entropy and the Simpson diversity index indicate the richness and evenness of product variety; hence, they also should affect rents positively. The ‘ HHI ’, in contrast, represents the concentration of retail categories within an SBA; it should presumably be a negative effect variable.

Models 1 and 2 were examined based on the environmental externalities of each POI. Model 3, in contrast, was examined according to the variety of the SBAs. Because SBAs are the basic units of shopping areas, Model 3 was used to test seven product variety indices of SBAs regarding retail rents. The descriptive statistics of the applied product variety variables are listed in Table 3.

Table 3.

Descriptive statistics of product variety measurements.

Variables	Description	N	Minim.	Maxim.	Mean	SD
ARent=r_k	Average rent of each SBA/month pin (1 pin = 0.3025 m²)	844	135.00	24,150.50	1942.1199	2595.2469
Shannon	Shannon entropy index	844	0.0006	0.5369	0.046598	0.0609469
Simpson	Simpson diversity index	844	0E-10	0.002095	0.00001896	0.000091
NShops	Number of shops in the SBA	844	1	1054	93.95	135.264
HHI	Herfindahl–Hirschman index	844	3.396E-9	0.00211	0.0000195	0.0000915
Core	The core retail layers from factor analysis	844	–1.1185	11.9405	0.064344	1.0800
Periphery	The periphery retail layers from FA	844	–3.5241	8.0236	0.068774	1.07153
Density	The density of POIs of the SBA (=NShops/area of SBA)	844	0.0001	0.0640	0.009027	0.0100323
Valid N	Total valid number of SBAs	844

Nevertheless, a preliminary examination of these product variety indices revealed high correlations. Consequently, as described in the last section, Model 3 was disaggregated into Model 3-1 and Model 3-2 to prevent the problem of multicollinearity. The first subtest entailed testing the core and periphery factor scores generated at Stage 5. The research hypothesis suggested that the agglomeration of core layers could generate higher rents; however, this implies that the clustering of periphery layers tends to occur in locations with lower rents. A second subtest was performed to examine the influence of the independent product variety variables of Model 3 on retail rents. However, because of highly correlated issues, multiple regression cannot be used to test the separate effects. Thus, principal component regression (PCR) was used to examine the model.

Moreover, a robust regression process was used to deal with potential problems of heteroscedasticity. White’s adjustment and weighted least squares method were applied to provide consistent standard error and covariance. The final mining process at this stage entailed using the basic clustering algorithm to explore the product variety characteristics among various clustering groups of SBAs. The TwoStep cluster component of SPSS is a scalable clustering algorithm that can handle both continuous and categorical variables, revealing the specific variety characteristics of each identified cluster.

Results

The empirical results illustrated in this section mainly pertain to the core research hypotheses at Stages 5 and 6, involving four parts: (a) the factorial analysis results of core and periphery retail categories, (b) the regression models for main hypotheses, (c) the descriptive and cluster analyses for POIs and SBAs in the six cities and (d) the 3D visualisation of the spatial allocation of product variety. The demonstrations and related implications are addressed subsequently.

Factorial analysis results

The factorial analysis results in Table 4 show the representative core and periphery retail categories. The Kaiser–Meyer–Olkin (KMO) measure of sampling and Bartlett’s test of sphericity results was favourable (KMO measure was 0.887, and the significance of Bartlett’s test of sphericity was lower than 0.001) for factorial analysis. Both the eigenvalues and scree plot show that the core factor had the highest eigenvalue and the steepest slope of the scree plot. Therefore, the representative variables of the core factor were determined to be the core layers of retail categories, and the remaining variables of the selected potential factors were the periphery layers of retail categories.

Table 4.

Extracted core and periphery factor of product variety.

Core factor Representative retail categories		Loadings	Periphery factor Representative retail categories		Loadings
L2.	Apparel and accessories	0.839	L6.	Hospital, clinics and dental	0.761
L28.	Department stores	0.827	L20.	Drug stores and medical cares	0.675
L3.	Beauty, hair and cosmetics	0.809	L27.	DIY and hardware	0.673
L10.	Footwear	0.787	L13.	Specialty services	0.621
L1.	Restaurants and foods	0.768	L30.	Tobacco, wine and betel nuts	0.493
L17.	Hotels and B&B	0.727	L12.	General service	0.482
L8.	Special entertainments	0.710	L21.	Photography and wedding	0.479
L29.	Hobbies, toys and games	0.701	L34.	Fresh foods	0.464
L16.	Convenience stores	0.691	L19.	Gifts, antiques and arts	0.447
L22.	Optical	0.601	L24.	Automobile and motorcycle	0.445
L7.	Jeweller and watches	0.601	L18.	Religious	0.435
L15.	Sports	0.566	L9.	Banks and financial	0.420
L4.	Electronic and mobiles	0.541	L23.	Books, cards and stationary	0.419
L25.	Lotteries and pawn shop	0.466	L11.	Homewares and living	0.398
L33.	Cinemas	0.411	L14.	Public services and facilities	0.368
L5.	After-school education	0.340	L26.	Music and performance	0.355
			L32.	Pets	0.319
			L31.	Super and traditional markets	0.268

The initial eigenvalue of Factor 1 is 10.146; % of the variance is 29.842; the initial eigenvalue of Factor 2 is 3.079; % of the variance is 9.055; Kaiser–Meyer–Olkin measure of sampling: 0.887. Bartlett’s test of sphericity: approx. χ² 15,545.256, sig. < 0.000.

From the strength of loadings (higher than 0.8), the most representative layers of the core factors were L2 (apparel and accessories), L28 (department stores) and L3 (beauty, hair and cosmetics); the loadings of L10 (footwear) and L1 (restaurants and foods) were also higher than 0.75. The representative layers of the periphery factor (loadings higher than 0.6) are L6 (hospital, clinic and dental), L20 (drug stores and medical care), L27 (DIY and hardware) and L13 (specialty services). In subsequent regression models, the factor scores for both core and periphery factors were examined to determine the effect of each SBA on rents. A positive effect was expected for the core factor.

Regression results

(a) Tests of Model 1

As mentioned in the previous section, three basic regression models were examined. The first was the main hypothesis of this research: the higher the variety, the higher the productivity and, thus, the higher the rent. Table 5 shows that all tests on the data sets, for overall and each of the six cities, the variable ‘ Ncategories ’ had a significant (over 99% significant level) positive relationship with the average rents. This result confirmed this study’s research hypothesis.

Table 5.

Regression tests of the significance for higher layers the higher the retail rents.

Models of overall and each cities for # of layers		Un-std. coef.		Std. coef.	t
Models of overall and each cities for # of layers		B	SE	β	t
Nlayers	0.086***	0.011	0.173	7.641	0.000	Sig.	F	Sig.
Overall	Constant	6.882	0.019		363.207	0.000	1165.70	0.000
Overall	Nlayers	0.170***	0.005	0.315	34.142	0.000	1165.70	0.000
1) Taipei	Constant	8.294	0.037		223.302	0.000	302.25	0.000
1) Taipei	Nlayers	0.137***	0.008	0.403	17.385	0.000	302.25	0.000
2) Taoyuang	Constant	6.819	0.035		194.323	0.000	104.710	0.000
2) Taoyuang	Nlayers	0.087***	0.008	0.227	10.233	0.000	104.710	0.000
3) Hsinchu	Constant	7.166	0.033		217.748	0.000	44.205	0.000
3) Hsinchu	Nlayers	0.055***	0.008	0.173	6.649	0.000	44.205	0.000
4) Taichung	Constant	7.316	0.045		161.014	0.000	25.881	0.000
4) Taichung	Nlayers	0.064***	0.013	0.147	5.087	0.000	25.881	0.000
5) Tainan	Constant	6.775	0.026		258.201	0.000	107.195	0.000
5) Tainan	Nlayers	0.081***	0.008	0.201	10.353	0.000	107.195	0.000
6) Kaohsiung	Constant	7.026	0.035		198.501	0.000	58.391	0.000

Dependent variable: ln rent.

***<1%.

(b) Tests of Model 2

Whereas Model 1 indicated that a higher number of layers above a POI generate higher rent, Model 2 enabled a detailed examination of the effect of different retail-category layers on each POI. Table 6 shows the multiple regression results of retail-category layer above the POI regarding its rental value. There was no collinearity problem (all VIF < 2) in this test. The result indicates a general concept of the influence of different types of retail-category layers, in that they are significantly positive, significantly negative or not sufficiently significant to rent. Therefore, not all layers of retail categories are favourable sources of positive environmental externalities because some of them even lower rents. To some degree, these results match the factorial analysis results in Table 4. The representative core layers (i.e. L2, L28, L3, L10 and L1) had a significantly positive relationship with the retail rents of POIs, whereas the representative periphery layers (i.e. L6, L20, L27 and L13) had a significantly negative relationship. Therefore, in subsequent regression models, the core scores were expected to have positive effects on the rents of SBAs, whereas the periphery scores were expected to have negative effects.

Table 6.

Regression results for each layer of product variety.

Model	Description	Un-std. coef.	t	Model	Description	Un-std. coef.	t
Model	Description	B	t	Model	Description	B	t
(C)	Constant	7.005	386.089
L1	1. Restaurants and foods	0.124***	8.479	L18	18. Religious	–0.003	–0.089
L2	2. Apparel and accessories	0.361***	24.291	L19	19. Gifts, antiques and arts	0.164***	3.962
L3	3. Beauty, hair and cosmetics	0.106***	7.212	L20	20. Drug stores and medical cares	–0.158***	–6.104
L4	4. Electronic and mobiles	0.014	0.704	L21	21. Photography and wedding	–0.043	–1.348
L5	5. After-school education	–0.092***	–3.474	L22	22. Optical	0.220***	7.484
L6	6. Hospital, clinics and dental	–0.100***	–5.033	L23	23. Books, cards and stationary	0.017	0.534
L7	7. Jeweller and watches	0.060***	2.741	L24	24. Automobile and motorcycle	–0.142***	–3.987
L8	8. Special entertainments	0.207***	9.701	L25	25. Lotteries and pawn shop	0.157***	4.615
L9	9. Banks and financial	0.044	1.368	L26	26. Music and performance	0.236***	6.133
L10	10. Footwear	0.297***	12.308	L27	27. DIY and hardware	–0.110***	–3.996
L11	11. Homewares and living	0.095***	3.963	L28	28. Department stores and malls	0.682***	28.391
L12	12. General service	–0.015	–0.660	L29	29. Hobbies, toys and games	0.112***	4.189
L13	13. Specialty services	–0.150***	–5.803	L30	30. Tobacco, wine and betel nuts	–0.083**	–2.080
L14	14. Public services and facilities	–0.086**	–2.101	L31	31. Super and traditional markets	–0.448***	–9.770
L15	15. Sports	0.187***	6.047	L32	32. Pets	–0.167**	–2.465
L16	16. Convenience stores	0.159***	4.950	L33	33. Cinemas	0.664***	12.521
L17	17. Hotels and B&Bs	0.650***	20.667	L34	34. Fresh foods	–0.064	–1.466
F		145.579
Sig.		0.000
R		0.566
R ²		0.320
Adj. R²		0.318

Dependent variable: ln rent.

***<1%.

The results in Table 7 for Model 3-1 support the hypothesis that the ‘ Core ’ factor scores would have a significantly positive (more than 99%) relationship with retail rents; conversely, the ‘ Periphery ’ factor score rents would have a significantly negative (more than 95%) relationship.

Table 7.

Principal component regression of product variety measures.

(a) Factor analysis of product variety measurements (total variance explained)
Comp.	Initial eigenvalues
Comp.	Total	% of variance	Cumulative %
1	4.610	65.863	65.863
2	1.110	15.853	81.716
3	0.993	14.185	95.901
4	0.250	3.578	99.480
5	0.032	0.456	99.936
6	0.004	0.064	100.000
7	5.746E-07	8.208E-06	100.000
Extraction method: principal component analysis.

For Model 3-2, Table 7a shows the potential factor extraction process (two factors extracted with the eigenvalue > 1) and the order and loadings for each product variety index. The KMO measure of sample adequacy was 0.574, and Bartlett’s test of sphericity yielded sig. < 0.001. Table 7b shows that the six product variables had strong positive loadings (higher than 0.65) in Factor 1.

The ranking orders of the representative variables, to some degree, showed the importance of these variables; ‘ Shannon ’ and ‘ NShops ’ had the highest loadings. The only representative variable (loadings higher than 0.6) in Factor 2 is ‘ Periphery ’. Because Factor 1 entails all favourable product variety indices, a positive relationship to rents was expected, and according to the results from Model 2 and Model 3-1, a negative effect of Factor 2 on retail rents was expected. The results from Model 3-2 of Table 7c demonstrate the confirmation of these relationships. The implications of the models indicated that higher product variety had a significantly positive relationship with retail rents. However, not all types of layers of retail categories could have the same positive effect; only the locations with core layers had a higher rent, and the locations with lower rents generally had lower essential product varieties.

Descriptive and TwoStep cluster results

This part of the empirical study entailed examining the data sets by using descriptive statistics and the TwoStep cluster data mining process to unveil detailed features of the product variety of shopping areas. The results of Models 1–3 indicated that higher product variety was favourable in retail agglomeration for both individual POIs and SBAs; however, the information was insufficient for realising the detailed characteristics. The dominant layers were L1 (restaurants, cafés and foods), L2 (apparel and accessories) and L3 (beauty, hair and cosmetics). The L1 number totalled more than 300 shops (and as many as 700 shops in Taipei’s Ximending shopping area). In total, 5717 of 10,648 POIs (53.7%) were from L1, L2 and L3. Almost all of the remaining 31 layers totalled fewer than 100 shops.

Another crucial variable that had to be examined in detail was the number of layers of environmental retail categories for each POI. ANOVA showed that the difference was significant. However, the detailed information showed that, for each POI, the overall mode comprised three layers; for each shopping area, the mode comprised two to four layers. Only the shopping area in Taipei had few POIs (five points) with 10 layers of retail categories; the average rent for these five points was $NT13,335 per month, which is high but not the highest rental value area. Therefore, examining the details of SBAs was necessary for obtaining additional information on the characteristics of product variety indices.

The next data mining process used in this study required using TwoStep cluster analysis. After several trial and error processes and consideration of the main research objectives, the first TwoStep clustering was applied using the average rent in a natural logarithm as the input variable for determining the clusters, because the rental value was the main performance variable. Hence, the detailed product variety indices under different levels of rents were one of the major concerns of this study. The cluster quality chart (Figure 3(a)) indicates that the overall model quality was ‘good’. The cluster size view (Figure 3(b)) shows the frequency of each cluster. Viewing a particular slice in the pie chart indicates the number of SBAs (844 in total) assigned to the cluster. A total of 1.8% of the SBAs were assigned to the first cluster, 4.7% to the second, 10.5% to the third, 60.3% to the fourth and 22.6% to the fifth. The cluster number was obtained using SPSS, and the order from left to right was ranked according to the highest to the lowest average rent of the cluster. Clearly, Cluster 1, despite having only 15 SBAs, had the highest rental value ‘ ARent ’ of all SBAs and the highest ‘ Shannon ’, ‘ NShops ’, ‘ Core ’, ‘ Density ’, ‘ Simpson ’ and ‘ HHI ’. The only lowest variable was the unfavourable ‘ Periphery ’. Although the dominant features in Cluster 1 were obvious, the product variety characteristics of the remaining clusters were more ambiguous; this means that product variety is more complicated than expected. For example, in Figure 3(c), Cluster 5 indicates a highly favourable observation for the seemingly inconsistent results. The sample size of Cluster 5 was large (191 SBAs, 22.6%), despite having high ‘ Shannon ’, ‘ NShops ’, ‘ Simpson ’ and ‘ HHI ’, but the rental value was the second-lowest. Hence, the ‘ Core ’ and ‘ Periphery ’ were apparently the most influential variables, because the most apparent features for Clusters 5 and 6 were low in ‘ Core ’ and high in ‘ Periphery ’.

Figure 3.

The SPSS TwoStep cluster analysis results of overall SBAs. Note: The variable Simpsont and HHIt here are simply to avoid the same 0 value among clusters; hence, the transformed variables are: Simpsont = Simpson × 10⁶; HHIt = HHI × 10⁶.

Figure 3(c) presents a detailed distribution of each feature of product variety, in addition to the abundance of the texture of variety and difficulty for researchers and planners. Only 15 of the 844 SBAs indicated that the higher the product variety indices are, the higher the rent. Cluster 3 with 89 SBAs (10.5%) had the third-highest rents but the second-lowest contributions in ‘ Shannon ’, ‘ NShops ’, ‘ Density ’, ‘ Simpson ’ and ‘ HHI ’. Cluster 5 was also unexpected in this research: 60.3% (509 of 844) of SBAs had the lowest average rent, and all the values of the variety variables (except for ‘ Periphery ’, which was the highest) were the lowest as well. This means that for all shopping areas, only Clusters 1 and 2 had 6.5%; i.e. 55 of 844 SBAs had extremely high rents and all the most favourable (except for ‘ Periphery ’) product variety features.

3D illustrations

The final results of the analysis of product variety in this study were the 3D visualisation of the rental gradient and the layers of retail categories. Due to new technology in spatial analysis, the integrated GIS-based spatial data sets established in this research efficiently generated the rental gradients. They provided a clear view of the spatial distribution of each layer of the retail category; the 3D demonstration presents a specific location and allocation of the layers of retail categories. As shown in Figure 4, previously unidentified invisible rents and product variety could be easily observed at a specific location. The same method was used for the illustration in Figure 4, to demonstrate the spatial distribution of different shopping areas; only the POIs and street lines were added to the bottom layers.

Figure 4.

The spatial distribution of layers of product variety and the rent gradients of six shopping areas. Note: The values of Core and Periphery are the means of SBAs in each shopping area. The P values are all <1%.

Figure 4 presents the results from regression and the TwoStep cluster analysis results. The 3D maps provided tools that were more specific and precise for observing environmental product variety. Exploring the rental gradient of each shopping area from different angles on the map enables the reader to identify accurately individual layers or product variety hotspots.

Discussion

This study aimed to propose an effective method to extract the environmental externalities from a multi-stage spatial data mining process. With the six-stage data mining process, this study provided more thorough and detailed measurements of environmental product variety, as compared to previous studies such as Brown (1987), Clark and Rushton (1970) and Konishi (2005). As the final results show, this multi-stage process could extract the exact locational distributions of different retail-category layers, which provide the fundamental information to generate further product variety indices. From this paper, the data mining process of the environmental product variety provides some fruitful discussions. First, the empirical results illustrated that, for a shopping area in a central city, product variety is a favourable factor of consumer preferences and is also an environmental variable that increases the productivity of retail shops. However, the concept of product variety entails numerous ambiguous and invisible features for researchers and urban planners. Hence, precisely measuring the characteristics of product variety is crucial for accurately evaluating the characteristics of the environmental features and understanding their spatial distributions. This study suggests using a series of methodologies for precisely measuring the features of product variety and establishing a six-stage data mining process.

Through data mining, a series of empirical results were used to establish a profile of product variety for central urban shopping areas. The factorial analysis of the 34 layers of product variety extracted the core and periphery layers from the original data set of the distribution of the 34 retail categories of each SBA. The regression results of the individual POIs show that, although the variable of the number of layers above each POI had a significantly positive relationship with the rental value, none of the existing layers had a higher rent.

The tests of the scores for the core and periphery layers also confirmed that the core layers had a significantly positive relationship with rents, whereas the periphery layers had a significantly negative relationship. These results showed that, although higher product variety could indicate a higher rent, only the agglomeration of the ‘correct layers’, namely the core layers, had a positive influence on retail rents. Other product variety indices provided an even clearer profile for understanding the texture of the product variety. PCR showed that the scores for the favourable product variety measurement variables had a significantly positive relationship with rents. Nevertheless, although regression models generally support the conclusion that a greater variety corresponds with a higher rent, a detailed product variety profile requires using the results from descriptive statistics and TwoStep cluster analysis to demonstrate. The findings suggest that the environmental product variety, in general, exerts a positive effect on shopping areas. Characteristics of product variety, such as the number of layers above each POI, the number of shops, density, Shannon entropy index (variety in choice), Simpson diversity index (richness and evenness) and HHI (concentration), all had a significantly positive relationship with retail rents. However, the spatial distribution of the core and periphery layers of product variety is the dominant characteristic of retail clustering. The strongest hotspots undoubtedly have favourable features with higher core factor scores. Still, areas with a high periphery and low core scores, even with higher Shannon, Simpson or HHI factors, can only have low rents.

Finally, the GIS-based spatial database of product variety enables generating 3D maps of the rental gradient and the spatial distribution of the product variety of shopping areas. The 3D maps provide an opportunity to observe the features and distributions from different angles and various purposive views. For example, the 3D maps of the spatial distribution of the core and periphery layers demonstrated that only relatively few SBAs could generate higher rents, and the concentration areas of the core layer activities were closely connected to higher rental hotspots. With this powerful 3D visualising tool, researchers and planners can explore in-depth the product variety environment.

For environment and planning policymakers, we believe that this multi-stage spatial data mining process could also be implemented in other environmental diversity identification exercises, such as in understanding the abundance of tourism resources, the sufficiency of medical services and the gaps in public facility provision. The effectiveness of this mining process could be more powerful, once the identification of the influential range of POIs could be more precise and accurately determined through, for example, the Internet of Things.

(b) Factor analysis of product variety (structure matrix)
	Component variable loadings
	Factor 1	Factor 2
Shannon	0.917	0.570
NShops	0.917	0.554
Core	0.892	0.036
HHI	0.866	0.111
Simpson diversity	0.864	0.107
Shop density	0.687	0.294
Periphery	0.248	0.980
Rotation method: Oblimin with Kaiser normalisation.

(c) Regression results of product variety measurements
Variables	Model 3-1					Model 3-2
	B		Std. error	t	Sig.	B		Std. error	t	Sig.
(Constant)	7.163	***	0.018	398.419	0.000	7.194	***	0.019	386.017	0.000
Core	0.457	***	0.026	17.280	0.000
Periphery	–0.067	***	0.015	–4.450	0.007
Factor 1 score						0.562	***	0.037	15.187	0.000
Factor 2 score						–0.183	***	0.019	–9.566	0.000
F (WEIGHTED)	193.96					167.7808
Sig.	0.00					0.000
R² (weighted)	0.3310					0.299
Adj. R² (weighted)	0.3293					0.298
Durbin–Watson stat	1.347132					1.313
Sample (adjusted)	1.842					1.842
Included observations	787 after adjustments					788 after adjustments

Weight type: inverse standard deviation (no scaling). White heteroskedasticity-consistent standard errors and covariance. Dependent variable: ln avrent.

***<1%

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Ministry of Science and Technology, Taiwan, ROC (MOST: 104-2119-M-305-001).

ORCID iD

Tzuhui Angie Tseng

Notes

Tony Shun-Te Yuo is the Director of the International Programme of Urban Governance, National Taipei University, and an Associate Professor at the Department of Real Estate and Built Environment. His research is mainly related to retail real estate and agglomeration economies. Recently his work focuses on spatial data mining and open data applications.

Tzuhui Angie Tseng is the associate professor at National Tsing Hua University, Department of Environmental and Cultural Resources in Taiwan. Her research interests include environmental behavior and landscape planning, particularly in health and welfare, culture, and education-related areas.

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