A Machine Learning Approach to Study the Relationship between Features of the Urban Environment and Street Value

Abstract

Understanding what aspects of the urban environment are associated with better socioeconomic/liveability outcomes is a long standing research topic. Several quantitative studies have investigated such relationships. However, most of such works analysed single correlations, thus failing to obtain a more complete picture of how the urban environment can contribute to explain the observed phenomena. More recently, multivariate models have been suggested. However, they use a limited set of metrics, propose a coarse spatial unit of analysis, and assume linearity and independence among regressors. In this paper, we propose a quantitative methodology to study the relationship between a more comprehensive set of metrics of the urban environment and the valorisation of street segments that handles non-linearity and possible interactions among variables, through the use of Machine Learning (ML). The proposed methodology was tested on the French Riviera and outputs show a moderate predictive capacity (i.e., adjusted $R^2=0.75$) and insightful explanations on the nuanced relationships between selected features of the urban environment and street values. These findings are clearly location specific; however, the methodology is replicable and can thus inspire future research of this kind in different geographic contexts.

1. Introduction

Since the advent of Geographic Information Systems (GIS), several researchers have quantitatively investigated the relationship between aspects of the urban environment and various liveability and socioeconomic outputs, in particular in the fields of urban design and urban morphology. For example, Vaughan et al. analysed the relationship between street network accessibility and socioeconomic levels in East London and found that more segregated streets were associated with more disadvantaged social classes [1]. Hillier studied whether dead-end roads were related to more or less crimes in a London neighbourhood and found that they were not associated with more criminal activity, if the surrounding streets were characterised by through passage and buildings abutting on them [2]. Urban crimes have also been studied in relation to density. While Harries did not find a significant relationship [3], other researchers found that more density was associated with less reported crimes [4]. Other researchers analysed density in relation to social aspects. While Duany et al. found that the former was associated with better social ties [5], Burchell et al. reported that lower densities not only diminished social interactions, but also favoured car use [6]. Such studies clearly provide relevant empirical results on the relationships between single urban features and different socioeconomic aspects. However, the urban environment is a much more complex entity, characterised by multiple factors that act together rather than in isolation [7,8]. More recently, a methodology to study socioeconomic indexes that accounted for multiple urban features and utilised multivariate spatial regression rather than correlation has been proposed [9]. It was tested on six UK cities and showed that more population density, unbuilt land, and dead-end roads, as well as a more regular street layout were associated with more socioeconomically deprived neighbourhoods. However, the methodology proposed only nine metrics, which is certainly an improvement over previous works, but, we argue, they are not enough to obtain a comprehensive picture of the urban realm. Furthermore, the use of linear models implies linearity and independence among regressors. These two conditions are hardly met considering that the phenomena under exam might not behave in a linear fashion. For example, if we consider socioeconomic deprivation, it might well be that areas near major infrastructures are more deprived. However, this relationship might decay faster than in a linear manner in areas located further away. Secondly, variables measuring spatial phenomena in the same study area tend to be correlated, thus violating the assumption of independence of observations. Thirdly, it was suggested to use areas as spatial units of analysis, although street segments (i.e., the line connecting two street intersections), in our view, might be a better choice, especially when analysing configurational and morphological aspects of cities.

The phenomenon investigated in this paper is place value—or at least one of its aspects—as more widely discussed by Carmona [10]. More precisely, we aimed at explaining the geography of place value of each street segment, in any large metropolitan area, as it emerges from housing transactions (i.e., street value). Without denying the interest in other facets of social valorisation of urban space (e.g., symbolic and cultural valorisation), we used housing prices as a practical thermometer to gauge a fairly comparable social value, granted by households and urban actors in different city areas. Explaining the spatial distribution of street value using metrics of the urban environment is a challenging task for which no unified theoretical approach exists. Natural movement theory [11], urban morphology approaches [8], human ecology and its subsequent reinterpretations by urban geography [12] propose different and concurrent theoretical frameworks. Together with the aforementioned methodological issues, this justifies more exploratory approaches in high-dimensional databases of metrics of the urban environment, which can today be investigated through ML.

In this paper, we thus propose an ensemble method based on ML—and thus able to handle non-linearity and interactions among regressors—to analyse the relationship between a comprehensive set of features of the urban environment and street value. More specifically, such method: (i) computes a metric of residential valorisation at the street level (i.e., street value), through the aggregation of housing transactions; (ii) provides instructions on how to characterise the urban environment of any study area in the most comprehensive way possible; (iii) applies a ML feature selection algorithm to select the best descriptors for the study area under exam; (iv) implements Gradient Boosting (GB) to model the relationships between street value and the selected variables; (v) tests residuals for spatial autocorrelation, whose presence is sign of model under-specification; and (vi) uses a recently developed algorithm to render the outcomes of the GB model human-interpretable. Such methodology was tested on the French Riviera to study the relationship between street values, obtained from around 110,000 housing transactions exchanged in the period 2008–2017, and more than 100 metrics quantifying different aspects of the urban environment, including configurational, morphological, and natural features. Outcomes of such analysis show a moderately high predictive capacity (i.e., adjusted $R^2=0.75$) and provide insightful information not only on what urban features are best related to street value in the French Riviera, but also on the subtleties of such relationships. For example, reach centrality to the coastline, a metric that should constantly be associated with street value, does not hold a positive relationship with it across the entire study area. This is found to be due to an interaction effect with distance to rail track. Being at easy reach to the coast but, at the same time, close to rail tracks depresses street values.

The use of housing transaction data echoes a well-developed line of research in econometrics, i.e., the explanation of housing price formation through hedonic modelling [13]. These models traditionally rely on a set of intrinsic (e.g., habitable surface, number of bedrooms, and presence of a garden and other elements of comfort) and extrinsic features (e.g., proximity to the closest underground station and accessibility to services and amenities) to explain house prices. They are also increasingly integrating place-based effects through multi-level approaches [14,15] and the combination of spatial (e.g., geographically weighted regression) and repeat sales models [16]. More recently, ML techniques have also been adopted, for example, to correct spatial errors in predictions of repeat sales models [17] and to improve the aggregation of spatial effects in econometric models [18]. Our aim is however different. We are not interested in the prediction of prices per se or in discovering the monetary contribution of each of the features used in the model. Our focus is understanding the subtleties of the relationship between a set of relevant features of the urban environment and the valorisation of fragments of urban space (i.e., street segments) widely recognised as fundamental spatial units for the study of urban phenomena [11,19,20].

We argue that the ensemble method proposed in this paper might help researchers in the fields of urban geography, urban morphology, and urban design who are interested in exploring the nuanced relationships existing between locally relevant features of the urban environment and street value. The methodology can also be used for comparative analysis and thus to test whether or not specific relationships hold in different geographic contexts. Finally, it contributes to an emerging need in the study of social systems (i.e., coupling predictive accuracy and interpretability of outcomes) [21].

The remainder of this paper is structured as follows. In the next section, we provide details on the methodology proposed, including the metrics of street value, metrics of the urban environment and the ensemble of ML techniques to model the relationship between them. We then follow by illustrating the empirical application of the proposed method to the French Riviera. This part includes a presentation of the data sources used to compute the metrics, the empirical outputs and their interpretations. Finally, we conclude with limitations, future work, and final remarks.

2. Methodology

In this section, we present, firstly, the spatial unit of analysis adopted; secondly, we illustrate how to compute the metric of street value by aggregating housing transactions for street segments; thirdly, we suggest what aspects of the urban environment to consider for calculating metrics; finally, we provide details on the proposed ensemble of ML techniques to model the relationship between the metrics previously calculated.

2.1. Spatial Unit of Analysis

We propose to adopt the street segment as spatial unit of analysis as it is considered the fundamental component of the urban space in much of the urban design [11,19,20] and urban morphology literature [7,8]. The reason for this lies in the fact that streets and the network they create is a simple but effective representation of the way human beings experience spatial relations in cities [19]. In the US, the research by Carpenter and Peponis [22] stressed the importance of the street segment in residential valorisation. According to the authors, census tracts and even city blocks could hide local differences, which are only discernible at the scale of the street segment. In France, seminal work by Gourdon [23] highlighted the role of the street as the main organisational unit at the basis of urban economy, including the logic of residential valorisation. The street segment, with all the characteristics linked to its location in urban space, can thus be considered an ecosystem of residential functioning.

2.2. Street Value

This step assumes that the housing transactions to be analysed are in data point format. To compute the metric of residential valorisation at the street level, it is necessary to, firstly, process the data on housing transactions to render values comparable across different years and housing types and, secondly, to compute a measure of central tendency from such processed dataset. We illustrate these two steps next.

2.2.1. Pre-Processing

Housing transactions of different years and housing typologies cannot be directly compared due to yearly inflation, housing market cycles (e.g., economic recession or upturn), and specific market behaviours affecting different housing types. For example, bigger properties tend to be sold less frequently as they are more expensive and are thus long-term investments, while smaller properties, due to their relatively lower values, tend to be exchanged more easily and tend to be short-term investments. The average price per square metre tends also to be structurally higher for small flats for technical reasons (even the smallest flat needs sanitary and cooking equipment, which proportionally weigh more on the average price per surface unit compared to a larger property). The very notion of average price per square metre can thus be challenged when applied to such diverse housing markets. To address these issues, instead of the conventional price per square metre, our method requires to separate the transactions by year and housing type and compute ventiles of prices for each subset year of transaction and housing type. We consider such statistic an appropriate normalised value, which account for different market segments and years, thus making transactions comparable among them.

2.2.2. Computation of Median of Values

Having classified each transaction in a ventile of value, the next step requires to, firstly, assign to each data point the street segment to which they belong and, secondly, aggregate the information on value at the street level through the computation of a measure of central tendency (i.e., median). Such measure provides information on the central point of the distribution of housing values, in each spatial unit. We suggest performing such computation for the ensemble of each street segment and its immediate neighbouring streets, with at least 10 transactions, for three reasons: firstly, transactions located in streets directly connected to one another tend to have similar valuations (due to the influence of the same locational factors, presence of properties at the intersection of streets segments, etc.); secondly, data on house prices tend to be quite sparse, even for several years, and thus a local interpolation would allow having more streets covered with data; and, thirdly, we want to assure the reliability of the median statistics.

2.3. Metrics of the Urban Environment

To characterise the context of each street segment in the most comprehensive way possible, we suggest computing a set of descriptors that quantifies aspects of the urban fabric, street-network configuration, functions, housing stock, and landscape. Since the domain that we want to model has no established background, such descriptors are inspired by a variety of studies spanning from urban design to sociology, from urban morphology to economics. Configurational theory [19,24] suggests that several centrality parameters have specific functional implications (e.g., through-movement, accessibility, tranquillity, etc.) that could be attractive or repulsive for the residential function, thus influencing valorisation. Ever since Bourdieu’s seminal works on lifestyles [25], multiple studies also highlighted the importance of more aesthetic aspects, such as architectural styles, neighbourhood ambience and design [26,27]. We can thus hypothesise that different urban fabrics play an important contextual role and are thus associated with different social representations and hence valorisations. Site and local landscape features are additional important contextual factors. See, for example, the study carried out by Luttik et al. [28] on the valorisation of green/blue infrastructures in three Dutch cities. Finally, the accessibility to amenities and proximity to nuisances (e.g., noisy and polluting infrastructures) are further known factors that influence values. See, for example, the works by Bartholomew and Ewing [29] and Brainard et al. [30]. Next, we present possible metrics derived from these studies, categorised in three main urban subsystems: settlement system, infrastructural system, and environmental system. Note that the aim of this section is not to provide a fixed list of metrics, but rather to offer guidance on what aspects to measure. It is then up to the researcher to choose the best list of descriptors for her study area.

2.3.1. Settlement System

Urban Fabric

The urban fabric is the set of relations between buildings, streets, parcels and open space at the scale of a small urban fragment. Modern European cities are characterised by the presence of different types of urban fabrics; for example, there exist a dense and irregular one, typical of historic centres, a more spaced out and regular one, common to urban extensions of the XIX and early XX century, and a more discontinuous one, characterised by free-standing buildings surrounded by lawns and parking lots, typical of the modernist period. Quantitative measures of the forms of urban fabrics can be found, for example, in the works by Berghauser-Pont and Haupt [31], Gil et al. [32], Araldi and Fusco [33], and Venerandi et al. [34]. For example, Araldi and Fusco proposed the Multiple Fabric Assessment method (MFA), a technique that automatically detects types of urban fabrics based on morphometric descriptors of proximity bands around street segments, by taking into account the contextual role of interconnected street segments.

Configuration of the Street Network

The configuration of the street network concerns the way streets are arranged, the extent to which they are inter-connected among one another, and their relative importance for the functioning of the overall network. Configurational analyses can be used to characterise the positional characteristics of street segments at different scales (e.g., the whole city, a given neighbourhood around a specific street). Metrics to quantify such aspects are, for example, betweenness and closeness centrality [19]. The former is based on the concept that central means to be used by many of the shortest paths linking couples of street intersections in a street network. The latter measures centrality as a function of distance and thus street segments that are connected and lie at short distance between one another will have higher values of closeness. These two are not the only centrality measures that one can use, but they are the ones that were more widely adopted and for which there exist more robust scientific findings. See, for example, the works by Porta et al. in Parma (Italy) [35], Baton Rouge (LA, US) [36], and Barcelona (Spain) [37].

Functions

With the term functions, we refer to a broad set of activities present in urban space. These can be commercial establishments, such as shops and restaurants, as well as public services, such as schools or city councils. Previous studies often included measures of distance to any of such functions (e.g., distance to closest school, restaurant, park, etc.). In our view, this is not the best approach to quantify such aspects as it does not account for the spatial configuration of the city. A count of functions in each street segment would be a poor description either. Once again, the aim would be to take into account not only the quantity of a specific function in each street, but also its overall spatial structure within the city. A better approach would thus be to compute densities of such functions in relation to their positions in the streets and, at the same time, evaluate the position of each street segment with respect to them. This could be obtained, for example, through the Network Kernel Density Estimation (NetKDE) [38], a smoothing technique specifically created to output street-based density values. Fusco et al. utilised this very same approach to compute a measure of density of retailers in Nice, France [39].

Housing Stock

Housing stock refers to the status of the properties in each street segment, for example, their build periods or whether they are occupied as main or second homes, or whether they are vacant or not. These aspects can be quantified, for example, by calculating the proportion of properties with any special status with respect to the total number of properties present in a street. A further aspect that might affect valuations and that should thus be eventually considered is the presence of social housing. This can be quantified, for example, through the NetKDE technique mentioned in the paragraph above, whose output would consist of hotspot of social housing at the street level.

2.3.2. Infrastructural System

Public Transport Hubs

Public transport hubs are the exchange nodes in the public transport network and can be, for example, bus stops, tram stops, and train stations. The same density computation technique (i.e., NetKDE) presented in the paragraph Functions can be adopted in this case to obtain density measures of public transport hubs on the street network.

Nuisances

Nuisances in cities are usually due to noise and pollution and tend to be associated with the presence/proximity to large infrastructures, such as major roads/intersections and main transport hubs (e.g., airports and main train stations). Since noise and pollution tend to spread through air, we argue that metrics of nuisances can be computed as Euclidean distances from the midpoints of each street segment to the sources of such nuisances.

2.3.3. Environmental System

Green/Blue Infrastructures and Landforms

With the term green/blue infrastructures, we refer not only to the natural features surrounding each street segment or accessible from it (e.g., water bodies and urban forests), but also to the form of its physical site (e.g., valley, ridge, and plateau). The former can be measured, for example, by simply calculating the distance from the midpoint of a street to its nearest landscape feature or by computing the distance covered by the shortest path that connects a street midpoint to the nearest landscape feature, along the street network. The shapes of the landscape (i.e., landforms) can be classified through specific algorithms that interpret changes and patterns in altitude in a Digital Elevation Model (DEM) and also include differences in land orientation (for matter of lighting, a north facing flank does not have the same potential impact on values than a south facing one). For classification techniques of landforms, see, for example, the work by Tagil and Jenness [40].

2.4. Ensemble Method

Having computed the metrics described above, our approach requires the implementation of an ensemble of ML techniques to robustly assess the relationship between our proposed metric of street value and the metrics of the urban environment. This is a four-step process consisting of: (i) a feature selection technique to retain only the metrics that are best related to street value; (ii) a GB algorithm to model the relationship between such metric and the selected metrics of the urban environment; (iii) a topological version of the Moran’s test to ensure that the model accounts for all the possible spatial variation of street values, in the area under exam; and (iv) a ML technique that renders the outcome of the GB model human-comprehensible. We provide more details for each step next. Note that the words estimator and feature are used interchangeably in the remainder of this paper.

2.4.1. Sequential Forward Selection

In the absence of a well-established theory of the residential valorisation of urban streets, the aspects of the urban environment that one can hypothetically compute are numerous. This can potentially pose several issues at the modelling stage, for example, large computational time and data redundancy which, in turn, might add noise and ultimately lead to overfitting. To overcome these issues, we thus propose utilising the Sequential Forward Selection (SFS) technique developed by Raschka [41]. This specific type of feature selection adds one feature at the time based on a regressor performance until an optimal subset of features of the desired size is reached. In the context of this paper, the target feature would be our metric of street value, while the recursively tested features would be the metrics of the urban environment. The approach is thus both theory-driven (even if only weak theoretical assumptions are used when identifying suitable metrics of the urban environment) and data-driven (through the SFS and subsequent GB protocol). Since the modelling part of the method hereby proposed is based on GB (details on its functioning are provided in the next section), we suggest using the same kind of regressor for performance evaluation at this stage. Furthermore, to obtain a statistically robust selection, it is crucial to utilise training and testing subsets. Firstly, the algorithm should be trained on a random subset of the whole dataset. Secondly, its performance should be evaluated on the portion of dataset that has not been used. To further increase the robustness of the result, k-fold cross validation should also be implemented. This consists in splitting the dataset into k folds, using each fold $k-1$ times as training set and once as testing set to be predicted. The SFS final output is a set of very significant metrics ready to be input in the GB model.

2.4.2. Modelling

To model the relationship between the metrics of the urban environment selected by the SFS technique and our measure of street value, we propose to use GB, a very versatile and robust type of non-parametric ML technique, which can be used both for classification and regression purposes [42]. The basic approach underlying GB relies on the combination of several relatively weak simple models to obtain a stronger ensemble prediction. Other ML algorithms, for example, Random Forests (RF), are based on the same concept. However, while the RF prediction is based on a simple average of the outputs of such base models, GB iteratively fits new decision tree models to output a more accurate prediction of the response variable. At each specific iteration, a new base-learner is trained based on the error of the previous iteration. The minimisation of such error is based on a functional gradient descent that optimises a loss cost function pointing in the negative gradient direction. The definition of this loss function can be arbitrary chosen. If the purpose is regression, the error function should be the classic squared-error loss. A decision tree approach (more precisely, a refined nested sequence of decision trees) offers clear advantages over linear models as it accounts for non-linear and non-monotonic relations between the target variable and the possible regressors, and for interactions among them (i.e., a threshold rule for regressor A only applies when regressor B is above or below another given threshold).

In the context of this paper, the metrics of the urban environment selected through SFS are the input variables, while the street values constitute the response variable. Since the latter is ordinal (i.e., medians of ventiles of prices), the GB algorithm should be adapted to predict the exact classes of values rather than a continuous set of values, which would be wrongly specified for the purpose of this analysis. As in SFS, it is crucial to utilise training and testing regimes and k-fold cross validation. Finally, it is fundamental to set the hyperparameters of the GB regressor, as this permits control on how the algorithm learns about the data and evaluates its performance. When setting such hyperparameters, the most relevant points to consider are: using more estimators may lead to better results, but could also overfit some data; estimators (which are decision trees) can be grown to any depth, however specifying a maximum depth decreases the risk of overfitting; and to obtain higher resolution predictions, a minimum number of leaves should be used, which could also lead to overfitting. To set these hyperparameters, we suggest using a trial and error approach and inspection of learning curves, a useful tool to visualise validation and training scores for a ML model, for varying numbers of training samples. The best-case scenario, for regression purposes, has it that the curves of validation and training scores should converge to an error as close as possible to 0. This corresponds to a small variance and means that the tested model generalises well the phenomenon under exam. Usually, the most common exploratory outputs in applied research are attributable to two main scenarios: the two curves converge (i.e., low variance) but the error stays relatively high or the two curves show a significant gap (i.e., high variance), with a small error on the side of the training curve. The former scenario is synonym of poor fit and generalisation, that is no matter the amount of information we feed, the model does not represent well the underlying relationship and has high systematic errors. The latter scenario has a high variance that can eventually be reduced, for example, by adding more training instances or reducing the number of features.

Having set the GB hyperparameters through a trial and error process involving the visual inspection of learning curves, the last step consists in the performance evaluation of the fitted GB model. This can be carried out through the computation of the root mean squared error and adjusted $R^2$. The former indicates the average error that the model is making in predicting the response variable. Note that such error is measured in median of ventiles, considered as cardinal values. The latter represents the amount of variance in the response variable that is predicted from the variables used in the model.

2.4.3. Testing for Spatial Autocorrelation

Spatial Autocorrelation (SA) takes place when observations that lie next to each other have similar values [43]. This is a property that is present in most spatial phenomena [44]. Presence of SA in the residuals of a linear regression violates one of the main assumptions behind the use of such statistical technique (i.e., the error terms should be uncorrelated), thus invalidating it. This assumption is not essential in ML approaches, however, since the goal of our model is to account for all possible spatial structure of valorisation in the city, high SA of model deviates cannot be tolerated. In this context, measuring SA in the residuals can actually be useful to understand to what extent the GB model is able to fully capture the spatial phenomenon under exam (in our case, the street values) and whether potential explanatory variables are missing. A standard method to measure SA is the Moran’s test [45]. This technique quantifies SA based on both the locations and the values of the observations simultaneously. Given a set of georeferenced values, the Moran’s test assesses whether their pattern is clustered, dispersed, or random. The outputs of this test are an index (i.e., Moran’s I) that varies between $-1$ and 1 and a p-value. The former provides information on the magnitude of SA and on the type of spatial relationship, clustered for positive values and dispersed for negative ones. The p-value evaluates the statistical significance of the index. The matrix of spatial relationships that informs the computation of the Moran’s I can be based, for example, on inverse (Euclidean) distance or contiguity. Since our dataset consists of street segments, we propose computing an inverse distance matrix based on topological steps rather than Euclidean distances, where each step corresponds to a street segment. This would better account for the spatial structure of the network. As mentioned above, SA can be a signal of model under-specification. Testing different topological thresholds is thus crucial to understand what kind of spatial phenomenon is missing in the model. For example, if SA were to be significant at few topological steps, that would mean that a metric quantifying a very local aspect is missing. On the contrary, the opposite situation would signify that a macro phenomenon is not accounted for in the list of explanatory variables. Clearly, it is then up to the researcher to identify what such phenomenon could be.

2.4.4. Interpretation Tool

As mentioned above, the performance of a GB model can be evaluated through root mean squared error and adjusted $R^2$. However, these values do not provide any information on the behaviours of the variables used in the model, while, from an urban geography perspective, interpreting such behaviours is of paramount importance. To contravene this, we propose the use of SHAP, a recently developed algorithm that assigns to each feature an importance value for a local prediction [46,47]. Such algorithm belongs to the class of additive feature attribution methods, a set of techniques that explain a specific prediction from a model by choosing interpretable features sampling, and then build a linear model for the local region around that prediction. However, unlike other methods, SHAP is the only one that simultaneously satisfies three properties (i.e., local accuracy, missingness, and consistency) that guarantee the quality of local approximations. The algorithm by Lundberg and Lee is able not only to provide local predictions with relative feature importance, but also—and most importantly for the scope of our work—to compute such values for the entire dataset and then summarise such information in dependence plots and a summary plot [47]. The former shows the effects that a single feature has on model outcomes and its level of interaction with another feature, which is automatically chosen by the algorithm. The latter provides an overview of the importance of all the features used in the model and also the range of their effects (positive and negative). Both dependence plots and a summary plot are crucial to understand and interpret the effects that each feature (i.e., each of the metrics of the urban environment) has on the target variable (i.e., the residential valorisation at the street level).

3. Application to the French Riviera

This section presents the results of the application of the proposed methodology to the street values, obtained from the aggregation of the housing transactions exchanged in the period 2008–2017, in the French Riviera. This section is structured as follows: firstly, we briefly introduce the study area; secondly, we illustrate the datasets from which we extracted our metrics; thirdly, we present the street values (our target variable) in the French Riviera and the metrics of the urban environment considered (our estimators); and, finally, we illustrate and interpret the outcomes of the ensemble method proposed.

3.1. The French Riviera

The French Riviera is a coastal region located in southern France that roughly stretches 60 km in east–west direction, from the city of Menton, near the French–Italian border, to Cannes and the Esterel mountains in the West, and 20 km in south–north direction, from the Mediterranean coast to the smaller cities of Grasse, Carros, and Sospel, in the pre-alpine hinterland. The extent of the study area is presented in Figure 1. Due to its beautiful landscape, mild climate, and attractive cities and towns, the French Riviera has long been a renowned tourist destination, attracting, firstly, the British aristocracy, in the XIX century, and, more recently, mass tourism and retirees. Its population exceeds 1 million inhabitants and mainly concentrates in the coastal cities of Nice, Menton, Antibes, and Cannes. The constrained topography and the pressures coming from the tourism industry make the real estate market of this region particularly tense, but, at the same time, interesting to study. Areas with high concentration of second homes and tourism-related amenities coexist at close distance and sometimes are even intermingled with less valued districts and streets. The recent establishment of universities and R&D activities (e.g., the techno-park of Sophia Antipolis) further complexifies the picture. The Principality of Monaco, due to its fiscal and regulatory specificities, is a separate (and extremely expensive) real estate market and lies outside our study area. Next, we present the datasets concerning housing transactions and aspects of the urban environment, from which the metrics of the urban environment were then extracted.

3.2. Datasets

To compute the metrics of street value and the urban environment for the selected study area, we accessed five different data sources: PERVAL, the French registry of housing transactions; BD TOPO, the French GIS dataset of geographic features, in vector format; census data and SIRENE, for the housing stock and urban functions; an openly accessible web platform and OpenStreetMap (OSM), for public transport data; and an official DEM, for information on the physical conformation of the area under exam. Next, we present each data source in more detail.

3.2.1. Perval

PERVAL [48] is the official registry of housing transactions in France. It is owned and kept updated by the Notaires de France (the French association of notaries). The transactions in such registry are subdivided according to the type of property exchanged (e.g., flats, houses, garages, offices, and plots of land). For the purpose of this study, we only focused on the transactions of flats and houses. In addition to the price taxes included and the georeferentiation (i.e., latitude and longitude), the transactions belonging to these two typologies present further information, such as number of rooms, habitable surface, energetic label, and presence of a garden. However, the coverage of such information is not even across the dataset. For example, while the number of rooms is provided for almost all transactions (i.e., 99%), the build period is given only for 76% of them. Coverage statistics for each feature are provided with PERVAL data and were computed on the information collected in 2016. To carry out the analysis, we acquired PERVAL data for the study area, for the period 2008–2017, a time span that we considered wide enough to obtain a sufficiently detailed characterisation of the housing market. This consisted of 150,116 housing transactions, 124,236 of which belonged to the typology flat, and 25,880 to the typology house. The median inflation-adjusted price for a flat, in the time span considered, was €193,650. While the median inflation-adjusted price for a single house, in the same time period, was €475,589. In

Table 1. Number of transactions and median price for flats and single houses, for each year.

Year	Flats		Single Houses
	No. Transactions	Median Price	No. Transactions	Median Price
2008	-	-	1858	€500,000
2009	-	-	1457	€450,000
2010	13,483	€189,742	1813	€450,000
2011	14,028	€195,001	1912	€483,425
2012	11,981	€190,000	1831	€466,000
2013	12,065	€190,000	1897	€455,900
2014	12,143	€185,000	1904	€455,050
2015	12,793	€184,550	2200	€445,000
2016	10,431	€188,120	1717	€445,000
2017	9914	€190,000	1703	€445,000

, we provide more details on number of transactions and median prices, for each year.

3.2.2. BD TOPO

BD TOPO [49] is an official GIS database, freely accessible for research purposes, that provides vector data on various geographic entities, such us, roads, buildings, and natural features. It is issued and kept updated by IGN (the French National Institute of Geography and Forestry). BD TOPO is constituted by several datasets, one for each type of geographic entity. For the purpose of this analysis, we focused on the one containing the street network of the area under exam. This specific dataset not only had georeferenced representations of street segments, but also information on further aspects, such as street width, category (e.g., highway, regional road, local street), and travel directions. BD TOPO data are also necessary to identify and characterise urban fabrics through the MFA protocol previously mentioned [33]. The street dataset of the French Riviera utilised in this analysis dates back to March 2016 and consists of 98,297 street segments, with a median length of 78 m and a total length of 12,872 km.

3.2.3. Census Data and Sirene

In France, the French National Institute of Statistics and Economic Studies (INSEE) produces both census data and SIRENE, a dataset of commercial establishments and services. SIRENE [50] is monthly updated by INSEE and is freely accessible on the open portal of the French government. It covers the entirety of France and provides information on many aspects of commercial establishments, for example, name and surname of the owner, geographic coordinates, opening date, and category. The latter is based on a detailed taxonomy created by INSEE, which consists of several nested categories. For the purpose of this analysis, we focused on the meso-categories Commerce de détail (retail) and Services (services). The former contained, for example, the micro-categories shoes shop, clothes shop, and coffee shop. The latter contained, for example, the micro-categories bank, estate agency, school and post office. The SIRENE data used in this work date back to March 2018 and consist of 26,041 establishments, 7993 of which were retail and 18,048 were services. Census data are available for local areas, which are relatively coarse spatial units, with at least 2000 inhabitants. There are 426 census areas in our study area and each of them typically includes 50–100 built-up street segments. We decided not to use census data concerning socioeconomic aspects (e.g., social status, revenues, and education level) as these could be considered proxies of street values. We thus limited the use of this data source to obtain only a description of the housing stock in each spatial unit under exam. To be more specific, this concerned presence of second homes, vacant homes, and social housing. Finally, we also included the building period as further descriptor of the urban environment. INSEE data on the housing stock [51] is freely accessible. The latest dataset on the housing stock dates back to 2014 and is the one used in this work. In the 426 census areas of the French Riviera, there are a total of 712,778 properties, 492,050 of which are main residences, 159,678 are second homes, and 61,050 are vacant.

3.2.4. Public Transport Data

We relied on two sources for obtaining information on public transport hubs for the area under exam: OpenMobilityData [52], a web platform that collects and makes available for download open-source public transit data from around the world, and OSM [53], probably the most renown open platform for geographic crowd-sourcing. The former provided public transit data for the network Lignes d’Azur, the transport company that serves the metropolitan region of Nice. Such data consist of georeferenced points indicating public transport hubs, such as bus stops and stations, and means of transport (e.g., bus and tram). We obtained a total of 2691 public transport hubs for the city of Nice. To fully cover the study area, we integrated this information with OSM data. This was extracted from Geofabrik [54], a website that periodically collects, organises, and makes available for download OSM data, in shapefile format, for regions and sub-regions of the world. The number of public transport hubs collected from Geofabrik, outside the city of Nice, was 1216. Thus, the total number of such hubs for the entirety of the study area was 3907. OpenMobilityData and OSM data were both accessed and downloaded in August 2018.

3.2.5. Digital Elevation Model

Information on the landforms of the French Riviera was obtained from the official DEM of the Département Alpes-Maritimes (Department of the Maritime Alps). Such DEM is issued by Aérodata France, a company specialised in the production of cartographic data through aerial photography, and comes in raster format, at a resolution of 5 m. An estimated altitude with respect to the sea level is assigned to each of the pixels of the DEM. For the study area under exam, such value ranged between 0 and 1331 m. The DEM used in this work dates back to 2009.

3.3. Metrics

3.3.1. Street Value

After having obtained PERVAL data for the portion of French Riviera under exam, we firstly performed a filtering and then applied the pre-processing presented above, before computing classes of housing values at the street level. Firstly, we filtered out those transactions that could have biased the analysis, that is properties with special contractual agreements (e.g., retirement homes), and those that did not have sufficient spatial accuracy (e.g., those geocoded at the municipal level). Secondly, since PERVAL does not provide housing types (an information required by our methodology), we created such types by combining the broad categorisation provided by PERVAL (i.e., flat or single house) with the number of rooms. By doing so, we ended up with seven housing types:

• T1 for studios and one-room flats;
• T2 for two-room flats;
• T3 for three-room flats;
• T4 for four-room flats:
• T5 for five (or more)-room flats;
• PM (petites maisons, small houses) for houses with up to four rooms; and
• GM (grandes maisons, big houses) for houses with five or more rooms.

We then segmented the dataset according to year of transaction and housing type and computed ventiles of prices. Finally, we calculated the median of such values for spatial units comprising each street segment and its direct neighbouring streets. In Figure 2, we present a map of such medians (i.e., our street values) for the 14,319 street segments of the French Riviera, where a minimum of 10 transactions were recorded in the period 2008–2017. Values vary between 1 (the least valued streets) and 20 (the most valued ones) and constitute the target variable of our ML ensemble method.

A first visual inspection of this map revealed some patterns. For example, more valued streets tended to be located by the sea (e.g., Boulevard de la Croisette and neighbouring streets in Cannes, Promenade des Anglais and neighbouring streets in Nice). However, this pattern was not constant. For example, the streets located by the sea but in the western part of Nice (i.e., La Californie) and Cannes (i.e., La Bocca) tended to be devalorised. A further noticeable aspect was the presence of pockets of less valued streets in some urban neighbourhoods of Nice, Cannes, and Antibes and in the historic centres of Grasse, Vallauris, and Vence. These first observations were helpful to generate hypotheses on the possible reasons of these patterns and, ultimately, to define quantitative metrics to explain such patterns.

3.3.2. Urban Environment

The considerations presented in the paragraph above, together with the indications provided in the Methodology, guided us in defining and computing a total of 111 metrics of the urban environment. To be more specific, we calculated 87 metrics concerning the settlement system: 50 measured the configuration of the street network, 32 the urban fabric, 7 urban functions, and 5 the housing stock. For what concerns the infrastructural system, we computed four metrics: one of public transport hubs and three of nuisances. Finally, for what regards the environmental system, we calculated 13 metrics of green/blue infrastructures and landforms. For matter of brevity, rather than illustrating all 111 metrics in this section, we invite the reader to check the Appendix A for more information and observed values.

3.4. Application

3.4.1. Feature Selection

As mentioned in the Methodology, a large number of estimators can pose several issues at the modelling stage (e.g., large computational time and overfitting). Since we had 111 metrics, to avoid such issues, we applied the SFS technique to select an optimal number of estimators to model street value. To do so, we split the 14,319 street segments for which we had data into training (80%) and test (20%) sets and we set the GB regressor for the feature selection. Finally, we set the SFS algorithm to select an optimal number of features comprised between 10 and 30, through a five-fold cross-validation on the training set. Furthermore, the negative mean squared error was utilised as scoring system to evaluate the performance at each iteration. The SFS algorithm selected 28 features (

Table 2. The 28 features of the urban environment selected by the SFS technique, categorised by main urban subsystems, and sub-categories of subsystems.

Urban Subsystem	Sub-Category	Name
Settlement system	Urban fabric	Traditional urban fabric
		Constrained urban fabric
		Connective artificial fabric
		4-way intersection street
		Population density
	Config. street network	Straightness centrality (20 min drive)
		Reach centrality weighted by no. buildings (600 m)
		Closeness centrality (20 min drive)
		Reach centrality to squares (1200 m)
		Reach centrality to squares (600 m)
		Closeness centrality (1200 m)
		Reach centrality to squares (300 m)
	Functions	NetKDE of commerce and services
		NetKDE of social housing
		Distance to university
		Accessibility to job hotspots
	Housing stock	Percent of second homes
		Percent of empty homes
		Percent of pre-1945 buildings
		Percent of 1992–2011 buildings
		Percent of 1946–1991 buildings
Infrastructural system	Nuisances	Distance to rail track
		Distance to major road
	Public transport hubs	NetKDE of public transport hubs
Environmental system	Green/blue infrastructures and landforms	Distance to sea
		Reach centrality to coastline (2400 m)
		Reach centrality to coastline (600 m)
		Landform valley

) and achieved a best score of $-5.67$, which we deemed satisfactory given that it corresponded to an average absolute error of $2.38$ and the target feature varied between 1 and 20. The selection process with number of features selected at each step and relative performance is presented in Figure 3.

3.4.2. GB Model

To model the relationship between the 28 features selected by the SFS technique and street value, we performed the following steps. Firstly, we split the data into training (80%) and test (20%) sets. Secondly, we set the hyperparameters of the GB regressor. More specifically, we set the maximum number of features to consider at each split and the maximum depth of each tree to a third of such number, a value commonly accepted in ML modelling [55]. Finally, we set to 128 the number of decision trees used by the algorithm. All these hyperparameters were double-checked through visual inspections of the learning curves. Finally, we set the mean squared error with improvement score by Friedman to measure the quality of each split in the decision trees and a 10-fold cross-validation. The resulting model had an average mean squared error of 1.05 for the training sets and 2.43 for the test sets. The adjusted $R^2$ values were 0.95 for the former and 0.75 for the latter, indicating that the 28 features chosen by the SFS technique could explain 75% of the variance of street value. In Figure 4, we present the plot of the predicted versus real values. In Figure 5, we present a map of the predicted street values in the study area under exam.

As we explained above, spatial autocorrelation in the residuals of a GB model can help to identify missing explanatory features. To try to fully explain the spatial phenomenon under exam (i.e., the street values), we thus used the topological version of the Moran’s test presented in the Methodology as an exploratory tool to add further estimators to the ones selected by the SFS technique. If the Moran’s I, in the residuals of a model obtained through a specific set of features, were to be significant at 10 topological steps (i.e., 10 street segments), we added an estimator that quantified a local phenomenon. Conversely, if the Moran’s I were to be significant at a distance of 20 topological steps, we added an estimator that accounted for a more global phenomenon. This, together with an inspection of the map of the residuals, was helpful, for example, to identify the metric distance to university, a local aspect that was missing from the model and was important to explain the target feature. The output of the Moran’s test for the final model was as follows. At 10 topological steps, the Moran’s I was 0.13 and statistically significant (i.e., p-value = 0.0099), meaning that there were still traces of SA in the residuals and that some local explanatory variables were still missing. However, we could not access more data that would have allowed us to compute and test further metrics (e.g., data on housing stock at finer level of spatial granularity). At 20 topological steps, SA was significant but almost absent (i.e., Moran’s I = 0.08, p-value = 0.0099). We thus did not consider it necessary to calculate further metrics to quantify aspects at a larger scale.

3.4.3. Interpretations

To understand the output of the GB model and, in particular, to interpret the behaviours of the chosen features, we utilised SHAP, a technique that provides local estimates and condenses such information, for each estimator, in highly readable forms. To explain the output of the GB model, we firstly implemented the Tree Explainer function on the fitted model; we then applied the SHAP Value function on the estimators; and, finally, we used the plot module to produce two graphs: Figure 6, which shows the average impacts in absolute terms (i.e., SHAP values) of the features on the model output magnitude (values in tabular format are provided in the Appendix A, in

Table A1. Average impacts (i.e., SHAP values) in absolute terms of the features on the model output magnitude.

Tested Feature	Mean |SHAP Value|
Percent of second homes	1.194454
Distance to sea	0.569316
NetKDE of commerce and services	0.499561
NetKDE of social housing	0.465395
Reach centrality to coastline (2400 m)	0.416618
Population density	0.364529
Distance to rail track	0.254164
Distance to university	0.253496
Accessibility to job hotspots	0.211403
Straightness centrality (20 min drive)	0.207760
Percent of empty homes	0.204507
Reach centrality weighted by No. buildings (600 m)	0.198957
Closeness centrality (20 min drive)	0.174979
Reach centrality to coastline (600 m)	0.166626
Reach centrality to squares (1200 m)	0.161731
Percent of pre-1945 buildings	0.157978
Percent of 1992–2011 buildings	0.149031
Distance to major road	0.144553
Reach centrality to squares (600 m)	0.139323
Percent of 1946–1991 buildings	0.134130
Closeness centrality (1200 m)	0.108757
Traditional urban fabric	0.080152
Constrained urban fabric	0.080079
NetKDE of public transport hubs	0.069642
Reach centrality to squares (300 m)	0.053538
4-way intersection street	0.024855
Connective artificial fabric	0.019045
Landform valley	0.017471

), and Figure 7, which summarises, through a density scatter plot, the impacts (positive and negative) that each of the features used in the model had on street values. Vertical dispersion of points corresponds to a high concentration of observations with similar SHAP values. On the other hand, a slim dispersion corresponds to a small concentration of observations with similar SHAP values.

Percentage of second homes was the strongest feature in absolute terms and tended to have positive impacts on the valuations of properties at the street level for greater values and negative ones for smaller values. The finding thus highlights a particular feature of the housing market in the French Riviera, i.e., the exogenous market of second homes influences considerably (and positively) the valorisation of those street segments which have the most second homes. On the other hand, the exclusion of the tourism-based residential function (reflected in the absence of second homes) contributes to the devalorisation of street segments. The second most important estimator was distance to the sea, which was found to have positive effects on street values for small distances and negative impacts for greater ones. This was expected since the seaside offers aesthetic pleasure as well as many different leisure activities, which, in turn, positively impact street values. The density of commerce and services, computed on the street network, at 500 m, tended to have positive impacts for low densities and negative ones for higher densities. This finding is somehow counter intuitive as having more commercial establishments and services at a short distance walk should be a factor that increases value rather than depressing it. However, clusters of commerce and services can also produce side effects, such as more congestion or noise. This perception seems to be the prevalent one in the French Riviera. Similar explanations have already been put forward in the hedonic literature, in different geographic contexts [29]. We argue that more commerce and services at a short distance could indeed be associated with a less valued housing market but, at the same time, might also produce positive externalities for the wider neighbourhood, as Gourdon affirms in his seminal work [23]. The density of social housing, computed on the street network at 800 m, had positive impacts on the valuation of streets for smaller values of such measure, while had negative effects for greater ones. The interpretation of this regressor is straightforward: greater concentrations of social housing contribute to the depreciation of the streets that surround them. We argue that this phenomenon is due to the social stigma usually assigned to such places. This finding is corroborated by previous works that found significant relationships between house prices discounts and proximity to social housing estates [56,57].

Impacts on street values for the remaining features were less polarised, meaning that great or small values of a specific estimator had both positive and negative effects on the valuations at the street level. Reach centrality at 2400 m with coastline as target tended to have positive effects on street values for greater centrality values (i.e., street that are at easy reach from the coast are more likely to have greater appreciations). Conversely, it tended to produce negative impacts on valuations at the street level for smaller values of reach. This finding was expected as the more a street is at easy reach from the coast, the higher its value should be. However, the distribution of negative and positive impacts with respect to the values of this measure was not neat as many observations with medium to high levels of reach centrality were actually associated with negative SHAP values. We hypothesise that the reason for this is related to the presence of rail tracks on many traits of the coastline of the French Riviera. To be more specific, the combination being close to the coastline, but not directly on it, and being close to a rail track depressed street values. The dependence plot (Figure 8) between the measure of reach and the one of distance to rail track seems to confirm this hypothesis since negative SHAP interaction values are associated with higher levels of reach centrality than the average (but not in the top of the distribution) and short distances to rail tracks (i.e., between 0 and 500 m). This finding highlights the importance of using techniques that can handle non-linearity and interactions among features as they allow the investigation of complex relationships.

Further relevant findings concerned the estimators distance to university, accessibility to job hotspots, and straightness centrality at 20 min drive. For most observations, being close to a university had a positive but weak effect on valuations at the street level (i.e., SHAP values between 0 and 1). For fewer observations, being far from a university had a strong negative impact, instead (i.e., SHAP values between −1 and −3). We suggest that streets around universities might work both as local job hotspots (with positive impact on street values) and as local markets for investors in student housing (driving up the overall values). On the other hand, the relatively dispersed pattern of universities in the French Riviera means that areas that are relatively far from them are particularly disadvantaged with respect to the others. For what regards accessibility to job hotspots (see the Supplementary Materials for details on how this metric was computed), SHAP values vary between −1 and 1, suggesting that higher levels of accessibility to job hotspots had positive effects on street values, while lower levels had negative ones. This finding is aligned with a previous study that found a relationship between residential valorisation and job accessibility (see, for example, the work by Osland and Thorsen [58]).

Finally, straightness centrality at 20 min drive, a measure of street network performance at 20 min drive radius, was associated with positive impacts on values at the street level for smaller values, while it was related to negative effects for greater values. This suggests that streets that are highly performing and thus function as pure connective elements (e.g., major routes near airports, important infrastructural nodes) tend to be devalued. We hypothesise that this might be due to the unpleasantness of the urban environment surrounding such streets, but also to air, noise pollution, and possible congestion.

Further estimators were used in the model; however, they had weaker impacts on street values. For example, reach centrality weighted by the number of buildings in each street segment and computed at 600 m radius showed that areas with a more sparse street network tended to be more valued than areas with a denser street layout. Reach centrality at 600 m with coastline as target specified at a more local scale the relationship found at 2400 m, highlighting the positive effects on values of the capes of the French Riviera (i.e., Cap d’Ail, Cap Ferrat, and Cap d’Antibes). Greater percentages of buildings built between 1946 and 1991 seemed to affect negatively street values, as compared to buildings built before the war or after 1992. For what concerns the metrics of urban fabric computed through the MFA method [33], only probability of MFA class 2 (i.e., streets with high probability of representing the traditional urban fabric) positively affected street values.

4. Limitations

Although PERVAL is an official dataset managed and kept updated by the French association of notaries, the geolocalisation of some observations might still be imprecise. Furthermore, Casanova et al. remarked that some housing transactions are missing in PERVAL and that particular attention should be given to the treatment of transactions concerning several items [59]. These issues might have thus introduced inaccuracies in the computation of our metric of street value.

By focusing on spatial units comprising of each street and immediate neighbouring streets with more than 10 transactions, we lost part of the information present in the original housing transaction dataset. Although we have done so to make our findings more statistically robust, such data might have helped to provide a more complete picture of the relationship between our metrics of the urban environment and values at the street level. In this respect, our findings are to be considered limited to the best known sub-spaces of the study area (in terms of recorded transactions).

Some limitations also come from the use of the ensemble ML method. The hyperparameters of the GB model were set through a trial and error process based on a visual evaluation of learning curves. Although this proved to be a valid technique in the specific case of the application presented in this paper, it is also time consuming and, to a certain extent, imprecise. For example, to better tune the maximum number of features that the GB model uses at each split, one could implement a cross validated grid search, an automatic algorithm that iteratively tests different numbers of features and outputs an optimal number for any given model, in a cross validated regime.

As pointed out in the Application Section, local SA is not completely absent from the residuals of the best model we could achieve. While this does not invalidate the results obtained, it informs us that potential explanatory variables are still missing.

5. Future Work

To tackle the amount of spatial information left unexplained, we plan to access further data (e.g., geolocalised social network data and spatial information on specific urban amenities/nuisances at a finer level of spatial granularity) to compute and test further local metrics that can reduce or completely eliminate SA at the local level and also increment the amount of explained variance in our model.

The methodology presented in this paper proposes analysing the relationship between features of the urban environment and a metric of street value based on the computation of ventiles of housing prices, which were previously harmonised to account for their heterogeneity. However, more street-based metrics can potentially be extracted from housing transaction data and tested against the metrics of the urban environment. For example, future work might consider a measure of dispersion of values, which could provide relevant information on whether specific streets are able to offer a range of housing values, and thus eventually be more prone to social mix.

Finally, uncertainty-based approaches such as Bayesian probabilities and possibility theory could be used to integrate the observations that were excluded in this analysis due to the requirements of the proposed methodology. Streets with few transactions could provide uncertain information on their median valorisation, but still contribute to gain a better understanding of how factors of the urban environment can contribute to the valorisation of streets in urban space.

6. Conclusions

Previous quantitative studies in the fields of urban design and urban morphology have investigated the relationship between aspects of the urban environment and socioeconomic as well as liveability aspects. However, such studies focused on single relationships (e.g., street network accessibility and socioeconomic levels) and thus did not consider the complex nature of the urban realm. A more recent quantitative methodology did propose a multivariate analysis of the relationship between multiple aspects of the urban environment and socioeconomic indexes. However, it was limited as: (i) it described the urban environment through a small number of descriptors; (ii) it proposed the use of areal units of analysis, rather than more fine grained ones, better associated with configurational and morphological aspects of cities; and (iii) it assumed linearity and independence among variables, while it might well be that urban phenomena do not behave in a linear manner and do have interactions.

In this paper, we propose a quantitative methodology to study the relationship between features of the urban environment and street value that overcomes previous limitations by: (i) providing detailed indications on the many aspects that could be included in the model (as the application showed, these can reach the hundreds); (ii) using the street segment as spatial unit of analysis; and (iii) implementing an ensemble of ML techniques (i.e., SFS, GB, topological Moran’s test, and SHAP) that handles non-linearity and interactions among variables, addresses issues of spatial autocorrelation in model residuals, and outputs interpretable results.

Such methodology was tested to analyse the relationship between 111 features of the urban environment and street values, obtained from the aggregation of around 110,000 housing transactions exchanged in the French Riviera, in the period 2008–2017. The model could explain up to 75% of the variance of the target variable and provided insightful information on the nuanced relationships existing among the selected features and street values. For example, reach centrality to the coast, which should theoretically hold a constant and positive relationship with street values, did not behave constantly across the study area due to an interaction effect with distance to rail track that ultimately depressed street values.

The proposed methodology is replicable and can thus be of help to urban designers and geographers who want to investigate the complex relationships existing between features of the urban environment and street values in different geographic contexts. It can also be used for comparative analysis and thus to understand whether specific relationships between urban features and street values hold or not across different study areas. Finally, the ability of our methodology to deliver both predictive capacity and interpretability addresses recent concerns related to the use of novel technique of data analysis in the social sciences.