Analyzing how travelers choose scenic routes using route ... · Analyzing how travelers choose scenic routes using route choice models Majid Alivand, Hartwig Hochmair, Sivaramakrishnan

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Analyzing how travelers choose scenic routes

using route choice models

Majid Alivand, Hartwig Hochmair, Sivaramakrishnan Srinivasan

Abstract Finding a scenic route between two locations is a common trip planning task, in particular for tourists and recreational travelers. For the automated computation of a scenic route in a trip planning system it is necessary to identify which attributes of a route and its surroundings are associated with attractive scenery. This study uses a route choice model, more specifically a Path Size Logit (PSL) model, to identify the relevant attributes and their relative importance. Three hypotheses are formulated and tested with three PSL models to understand the effects of different attributes on scenic route selection. The set of chosen scenic routes are based on various VGI (Volunteered Geographic Information) data that have been extracted for California as a study region. The results identify several variables of the surrounding environment as significant contributors to route scenery after controlling for road type. Keywords: Scenic route, VGI, route choice model, viewshed analysis, geo-tagged photos, path size logit

1. Introduction Online route planners have become part of our everyday lives. They allow users to find the optimal path between two locations based on a specific criterion such as travel time, travel distance, or complexity between the predefined locations in street networks (Su, et al., 2010). Recent approaches focused on the computation of optimized routes for tourists or recreational travelers (Hochmair, 2004; Hochmair & Navratil, 2008; Zhang, et al., 2008). A shortest and in general single criterion optimal path is not what a tourist typically needs when planning a trip. That is, the computed path should not only be short or fast but at the same time satisfy other conflicting optimization criteria, such as passing through landscapes (Sun and Lee, 2004). Thus, the computation of a scenic route is inherently a multi-criteria problem. While there is undoubtedly a variation in how individual travelers judge the attractiveness of a given route, this research is based on the assumption that at least some criteria are commonly viewed as contributing to route scenery. Thus this paper examines which attributes are associated with scenic routes chosen by travelers. The presented approach includes obtaining a collection of selected routes, generating alternative routes, extracting attribute values of all routes and the surrounding environment, and analyzing how the attribute values of chosen routes differ from those of alternative routes. We formulate three hypotheses that relate predictor attributes to route attractiveness, which are then verified through statistical analysis. For the latter we start with a series of non-parametric tests to identify significant differences in attribute values between two related samples, i.e. the set of scenic and alternative routes. Then the combined effect of several variables on route scenery is determined through multiple regression. For this task we use the mathematical framework of route choice models, which are a special case of discrete choice models. Route choice models answer the question of how individuals select a route from a set of alternative routes. The results of these models indicate the significant attributes with their

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coefficients which can be used for the computation of scenic routes in automated route planning systems. A route choice model in this context requires the following data:

A set of selected scenic routes between origins and destinations A set of alternative routes for the same origin-destination pairs Attribute values related to all routes A regression model to estimate the contribution of the individual attributes to route

attractiveness. The choice set for an individual traveler includes the selected scenic route and the alternative routes available to that traveler to choose from. Various Web-based data sources based on Volunteered Geographic Information (VGI) (Goodchild, 2007) provide relevant information that captures people’s travel behavior, which will be used in this study to extract a set of traveled scenic routes. As an alternative in each choice set we use the fastest route since it is plausible that a traveler knew about the fastest route, e.g. from a GPS based car navigation system (Mainali, et al., 2011), at the time when planning the route. The route attributes are subdivided into those relating to the route itself, such as route geometry or travel time, and those relating to the surroundings of the route, i.e., landscape scenery. The attribute values are computed for all routes in the choice set, and different Path Size Logit (PSL) models are used to derive the coefficients and their levels of significance for these attributes, based on the following three general hypotheses:

Landscape scenery is associated with the selection of a scenic route when controlled for travel on local roads (Model 1)

A richer set of landscape related variables is associated with the selection of a scenic route when omitting road type (Model 2)

The density of geo-tagged Panoramio photos is associated with the selection of a scenic route (Model 3)

While previous work has already used route choice models to identify the significance of pre-defined scenic areas as a deciding factor in route choice (Ben-Akiva, et al., 1984), this study goes further in depth by identifying which different facets of the route and the surrounding landscape contribute to route scenery. The remainder of this paper is structured as follows. Section 2 reviews previous work on identifying attributes related to scenic routes and the computation of scenic routes. Section 3 describes our approach of extracting scenic routes from VGI data sources, followed by the computation of route characteristics in section 4. Section 5 performs a paired samples test to identify differences in attribute values between the sets of fastest and chosen routes. Section 6 describes the used route choice models and presents the estimated model results. This is followed by conclusions in section 7 which summarize the findings and novel contributions of the conducted research. 2. Literature review Previous studies on scenic routes can be divided into those that demonstrate the significance of scenic attributes in route choice behavior in general, those that highlight the importance of specific attributes for perceiving a route as scenic, and those that introduce algorithms for computing scenic routes. Studies analyzing the individual effect of different route and environmental attributes on the perception of route scenery and route choice are sparse, which is therefore the research focus in this paper.

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Ben-Akiva et al. (1984) and Wu & Fleming (2012) describe studies where route scenery was found to contribute significantly to the utility function of a route choice model and to play an important role in route selection. Furthermore, Wu & Fleming (2012) conclude, based on an Internet survey of 396 respondents, that scenic view influences to some extent route choice decisions even for daily commutes to work. The main focus of these two studies was to examine route choice behavior but not the identification of attributes involved with the selection of a scenic route. Eby & Molnar (2002) examined the demographic characteristics of tourists who drove along scenic byways, revealing that the presence of choosing a scenic byway was more important to the traveler when the trip purpose was vacation, when the trip was long distance, and when the trip was planned well in advance. It was, however, not examined whether scenic byways are perceived more scenic than alternative routes, and which attributes exactly contribute to route scenery. A few studies focus on quantifying the factors contributing to the scenic beauty of locations or routes. Bishop & Hulse (1994) assessed the scenic value of landscapes based on a viewer’s evaluation of various panorama pictures and subsequent regression analysis, identifying visible foreground river and range of visible relief as key predictor variables for scenery. Hochmair (2010) found that the density of geo-tagged photos from Panoramio was higher along scenic routes (which were first extracted from the EveryTrail1 website) than the density along corresponding fastest routes between the same origin and destination. The paper did, however not further discuss specific landscape features contributing to route scenery. Various algorithms for the computation of scenic routes are presented in the literature, including a single objective shortest path methodology on a network with modified weights (Hochmair & Navratil, 2008), or the use of Internal Path Discovering (IPD) and Bellman-Ford algorithms with VGI data sources, such as geo-tagged photos of Panoramio and Flickr (Lu, et al., 2010; Zheng, et al., 2013). Byon et al. (2010) used a multi criteria shortest path algorithm which considers scenic zones, slope and crime ratio in the cost function. Scenic views throughout the city were evaluated in paper surveys distributed to 29 travel agents in Toronto. A weighted linear combination method was then used to express the multi criteria planning problem as a single objective function that was to be minimized through the Dijkstra shortest path algorithm. Similar to Ben-Akiva et al. (1984) the scenic zones were not characterized by more refined scenic attributes. They varied only in their rated scenery based on the results obtained from the paper surveys. Hochmair & Navratil (2008) used a single objective shortest path algorithm to compute scenic routes where costs were reduced for edges running nearby scenic locations. Similar to other related studies this approach relied on the a-priori knowledge of scenic locations, such as parks, lakes, or rivers, for route computations. Zhang et al. (2008) developed a planning system that, based on a Web search engine, automatically extracts touristic spots and scenic sight recommendations upon a user’s region input. The user can then select from the recommended locations, and the system computes a route that runs nearby scenic sights that are identified through visibility analysis based on a Digital Elevation Model (DEM). Although the route planning system considers touristic and scenic spots, attributes of landscape scenery are not explicitly utilized. Further the DEM used for the visibility analysis does not account for the elevation of buildings. Zheng et al. (2013) used clustering of geo-tagged photos to identify scenic hot spots, followed by the compilation of a database of scenic roadways based on road segments that were visible from the scenic hot spots. The scenic route was then determined by solving a

1 www.everytrail.com

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single criteria shortest path problem using the Bellman-Ford algorithm. Sun et al. (in press) apply a spatial cluster method on geo-tagged Flickr images to identify prominent travel landmarks, between which the best travel routes are recommended. For the latter, the authors use a linear combination of the number of images and number of image contributors for a road, the number of points of interest (POI) in different POI categories along a road, and road length, to compute a recommendation index for a road segment. The recommendation index is then used as edge cost in the Dijkstra algorithm to determine a scenic route between two specified landmarks. In summary, only few of the reviewed studies tackle the question of which criteria are involved in the selection of scenic routes. Our research expands previous approaches by estimating route choice models that use chosen scenic routes as input and by identifying scenery related attributes affecting route choice.

3. Route set We chose California as our case study area due to its diverse landscape and the fact that many tourists travel to California each year. Various data portals provide information that allows extracting a diverse set of self-reported scenic routes. The TomTom 2013 dataset for California has been used as the street network for the different network analyses, and the speed limit provided by the TomTom dataset combined with the length of each link was used to compute travel times. 3.1. Chosen routes (scenic routes) Web 2.0 technology and specifically VGI provide a suitable data source to obtain a set of scenic routes. Photo sharing websites, such as Panoramio and Flickr, are Web 2.0 portals which host numerous geo-tagged digital photos with timestamps and additional information in textual tags. Most of this information can be accessed through designated API’s. Websites that can be used to extract scenic routes from VGI can be divided into two categories:

Photo-sharing websites that provide geo-tagged photos Travel diary websites that provide complete tracks of scenic routes traversed by users

Our data retrieval approach is based on the assumption that travelers typically share photos or their trip trajectory with the Web community when they consider a place or trip scenic (Hochmair & Navratil, 2008; Navratil, 2012). Details of the scenic route extraction approach from photo-sharing and travel diary Web sites for the California test area are described in (Alivand & Hochmair, 2013). The set of 96 scenic routes that were extracted from different VGI data sources are the basis for the analysis in this paper. 63 of the 96 routes were extracted from photo sharing websites and 33 from travel diary websites (Figure 1). These routes (only the parts that do not overlap between scenic and fastest routes) cover around 11000 km of the TomTom street network which amounts to around 2 percent of the total network length in the area. The length of the scenic routes ranges between 10 km and 800 km. Similar methods of route extraction from shared geo-tagged photos are described in Lu et al. (2010) and Zheng et al. (2012).

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Figure 1. The 96 extracted scenic routes for California

3.2. Alternative routes (fastest routes) In this study we used fastest routes as the only alternatives to the chosen scenic routes, resulting in a total of 192 routes which will be used for the 96 observed choices in the route choice model. Comparison of travel times between scenic routes (based on photo time stamps) and fastest routes (based on speed limits) shows that travelers are willing to travel on average 90 percent longer on scenic routes than on fastest routes (Figure 2), measured for the non-overlapping route portions only. This percentage number becomes smaller when considering complete routes including the overlapping parts. Figure 3 maps a choice set for an individual traveler. The red (darker) route shows the scenic route that was extracted from Panoramio, along with selected photos uploaded by one user. The brown (lighter) route shows the corresponding fastest route between the same origin and destination.

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Figure 2. Difference (in percent) between travel time on the scenic route and the corresponding fastest route, measured on non-overlapping route portions

Figure 3. A selected pair of scenic and corresponding fastest route

4. Computation of attributes Attributes that potentially influence the perceived scenery of a route and thus route choice behavior can be divided into two broad categories:

Related to the route, such as travel time, distance, road type, or number of turns Related to the surroundings, such as proximity to mountains, water bodies, green areas,

or historical buildings Whereas the second group of attributes describes attributes related to scenery itself, the first group relates to attributes typically conflicting with scenery in a route choice process, such as short travel time or distance. To determine the perceived value of a scenic attribute in route choice behavior, one needs therefore to consider both groups of attributes in the route choice model.

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4.1. Route attributes Table 1 lists the considered attributes for this category together with their explanations. Table 1. Attributes related to route characteristics

Attribute Description

TravelTime Time needed to travel the route [min] Length Total length of the route [m] Curviness An indicator of the shape of the route [unitless] NumJunc Number of junctions along the route [junction per km] PrimaryRoadTime Percent of travel time along a primary road [unitless] SecondaryRoadTime Percent of travel time along a secondary road [unitless] LocalRoadTime Percent of travel time along a local road [unitless] NumRightTurns Number of right turns at intersections along the route [turn per km] NumLeftTruns Number of left turns at intersections along the route [turn per km] RoadChange Number of road type changes along the route [road change per km]

PathSize An indicator of the overlap between scenic and fastest route [unitless] Travel time (free-flow or estimated) and length are the common explanatory variables in route choice models (Bierlaire & Frejinger, 2008; Schüssler & Axhausen, 2009). Curviness (mentioned by Kansky (1963) as detour index) is an indicator of the shape of the route and computed as the Euclidean distance between origin and destination divided by the network length of the route (Navratil, 2012). A lower value of curviness indicates a curvier route. Primary, secondary and local travel time in percent express the amount of time that a traveler uses those types of roads along the route, divided by the total travel time along the route. This categorization is based on the Functional Road Class (FRC) attribute of street links in the TomTom dataset. The FRC attribute divides roads into 7 categories including interstate highways, county highways, and city streets. These were further grouped into major, secondary and local roads for further analysis, matching the typical classification levels used in other route choice studies (Bierlaire & Frejinger, 2008; Schüssler & Axhausen, 2009). The road change attribute counts the number of times the road type changes along a route based on the three categories. This attribute and the number of right and left turns were normalized through division by the length of the route. PathSize is an indicator of the overlap between the chosen route and the alternative which will be further explained in the model section. 4.2. Attributes of surrounding scenery Table 2 lists considered attributes for this category together with data source and data type.

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Table 2. Attributes relating to surrounding scenery Attribute Data Source Data Type

Amusement park TomTom land use Polygon Bridge GNIS1 Point Convention center TomTom POI Point Cultivated area USGS land cover Raster Forest USGS land cover Raster Golf course TomTom land use Polygon Mountain peak GNIS Point Panoramio photo density Panoramio Point Park/Garden TomTom land use Polygon Rock/Sand USGS land cover Raster Scenic view point TomTom POI Point Skyline Google Earth Polygon Stadium TomTom land use Polygon Tourist attraction TomTom POI Point University TomTom land use Polygon Urban area US Census Polygon Water body TomTom land use Polygon Worship TomTom POI Point

1 Geographic Names Information System These attributes were selected from previous studies in this field (Sun & Lee, 2004; Titze, et al., 2008) but also motivated by the scenery shown on examined Panoramio and Flickr photos found along chosen scenic routes. The urban area polygons come from the Urbanized Area polygon layer of the 2010 Census data. Polygons of skylines are based on skyscrapers that were digitized from Google Earth for Los Angeles, San Francisco and San Diego. Once the points and polygons for the considered attributes had been compiled, viewshed analysis was used to determine the visibility of these points and polygons from route segments, more specifically, the midpoint of each route segment. 4.2.1. Viewshed analysis Viewshed analysis uses the elevation value of each cell in a DEM to determine the visibility to or from a particular cell. To retrieve more realistic viewsheds that are not solely based on bare ground elevations it is desirable to use a Digital Surface Model (DSM) instead. Since a DSM was not readily available for California, we added building information to an available Digital Terrain Model (DTM) as described further below. Two types of resources are required to compute viewsheds in our context:

Layers containing scenery related features (Table 2) A Digital Surface Model

The viewshed analysis was run in ESRI’s ArcGIS 10. Our base dataset was a 30m USGS DEM, which shows bare ground elevations. Since manmade and artificial objects, such as buildings, sometimes block the view of the traveler toward the scenic features, one needs to add the height

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of buildings to the USGS DEM to obtain an approximate DSM. Due to lack of Lidar data for California we approximated the building heights using three methodologies:

Supervised classification of Landsat satellite imagery Extraction of high density population and employment areas from various data sources Digitizing of skyscrapers based on Google Earth

4.2.1.1. Supervised classification Supervised classification uses the spectral signatures obtained from training samples to classify image content. We used supervised classification to remove areas with streets, parking lots, empty grounds and green areas from areas classified as medium and high density “Developed Areas” (class 23 and 24) on the USGS Land Cover (2006) raster data (Figure 4 left). This step was based on Landsat TM 5 imagery which contains seven spectral bands and has a 30 meter spatial resolution. ERDAS Imagine software was used for the supervised classification. The high resolution satellite images of ArcGIS online were used to extract training areas with known land cover types. The right image in Figure 4 shows the results of the supervised classification of the medium and high intensity areas from the Landsat images. Elevation values for cells in the DSM that overlap with areas classified as buildings (Figure 4 right) were increased by five meters to model the height of single story houses.

Figure 4. USGS developed area classes (left) and refined classification of these classes (right)

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4.2.1.2. Census and employment data Population (2010 Census) and employment data (Longitudinal Employer-Household Dynamic, LEHD) at the block level were used to identify census blocks of high population and employment density. These areas contain primarily apartment complexes and high rise buildings. The intersection of these high-density blocks with the previously generated buildings layer was used to identify the location of high rise buildings, for which 20 meters were added to the USGS DEM raster.

4.2.1.3. Skyline Further, 50 meters were added to the DEM elevations where areas overlapped with skyline polygons digitized from Google Earth. Figure 5 shows the final buildings layer for the same extent as that in Figure 4. This layer is based on two USGS “Developed Areas” classes (Figure 4 left), after removal of non-building related land cover (Figure 4 right) and refinement of building heights. The visualized area does not contain skyscrapers and shows therefore only 5 and 20 meter buildings.

Figure 5. Extracted building heights

4.2.2. Viewshed analysis In the next step the absence or presence of scenic features around network links (more specifically, their mid points) was determined through viewshed analysis that was applied on the modified DEM. The routes in the route set cover 81497 network links. The process of computing viewsheds was automated through ArcObjects programming in ArcGIS. Despite this, the computations were time consuming, and therefore, a subset of 20 percent of randomly selected links (16311) was used for the computation of viewsheds instead. As a simplification the chosen

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approach assumes that the scenery, i.e. the visibility of scenic features, does not change within 1 km along a road. Thus segments longer than 1 km were split into segments of 1 km or shorter. To check the validity of this approach we compared for several selected routes the obtained route characteristics for fastest and scenic routes based on the 20 percent segment sample and compared them to characteristics obtained for the same routes, but using the complete set of route segments. Results showed that the relative magnitude of scenic values was closely retained when using the 20 percent sub sample. For further processing a binary variable was added to the link feature class for each scenic attribute under consideration. A value of zero or one, depending on whether a point or polygon feature of the corresponding scenic attribute category could be seen from a segment mid-point, was then assigned to attribute values of records of the feature class. Next, the value for an attribute value of a complete route was computed as the sum of the lengths of route links that provide visibility towards the scenic feature, divided by the total route length. This method scales the attribute values to a range between 0 and 1. 5. Median comparison To identify scenic attributes as candidates for the route choice model median values of the attributes were compared between the pool of scenic and corresponding fastest routes. Only if the amount of exposure to a scenic attribute, such as forest, differs significantly between chosen and fastest routes, this attribute could be a possible factor affecting route choice and justify its consideration in the route choice model. While oftentimes a T-test is used for comparing mean values of paired samples, the distributions of attributes values in the scenic and fastest route sets were skewed to the right, so that the non-parametric Wilcoxon signed rank test was used instead. Since this test is not a median test, observed differences can be significant even if the compared groups have equal medians. It was, however, used since it is more powerful than median tests, such as the Mood’s median test. Table 3 shows the differences between attribute medians for scenic and fastest routes. A positive value indicates a higher value for the scenic route set. Attributes with p-values < 0.05 are printed in bold face. The first 10 rows in Table 3 (left column) refer to route attributes, the remaining rows to scenery related attributes. As the second portion of the table shows, the Wilcoxon signed rank test identified eight scenic attributes for which the visibility to scenic landscape features differs significantly between fastest and scenic routes.

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Table 3. Observed differences between scenic and fastest routes for route characteristics and scenery related attributes

Attribute

Mdn (scenic)-Mdn (fast)

Asymp. Sig. (2-tailed)

Attribute

Mdn (scenic)-Mdn (fast)

Asymp. Sig. (2-tailed)

TravelTime 59.874 0.000** Forest 0.942 0.042* Length 29935 0.000** Golf course 0.078 0.068

Curviness -0.197 0.000** Mountain 0.189 0.024* NumJunc 0.198 0.002** Panoramio photo density 0.078 0.000** PrimaryRoadTime -0.422 0.000** Park/Garden 5.386 0.000** SecondaryRoadTime 0.251 0.006** Rock/Sand 0.359 0.450

LocalRoadTime 0.129 0.000** Scenic/Panoramic View 0.000+ 0.173

Number of Right Turns 0.033 0.000** Skyline 0.000- 0.099

Number of Left Turns 0.027 0.000** Stadium 0.000- 0.157

RoadChange 0.023 0.000** Tourist attraction 0.000- 0.660

Amusement park 0.000+ 0.642 University 0.000- 0.572

Bridge 0.000- 0.188 Urban area -13.435 0.000** Convention center 0.000- 0.015* Water body 0.799 0.000** Cultivated area -0.197 0.033* Worship -0.027 0.469

** Significant at a 1% level of confidence * Significant at a 5% level of confidence + Mdn(scenic)=Mdn(fast), but Mean(scenic)>Mean(fast) - Mdn(scenic)=Mdn(fast), but Mean(scenic)<Mean(fast) 6. Route choice model 6.1. Theoretical background An individual invokes a decision rule to select an alternative from a choice set with two or more alternatives. The transportation literature provides a wide range of route choice models that are tailored to specifics of the choice situation under consideration (Prato, 2009). Random utility choice models assume that the utility of an alternative consists of a deterministic and stochastic (random) component. Based on the purpose of our study we used a Multinomial Logit (MNL) model to find a utility function that expresses traveler route choice behavior. The MNL model is a commonly used framework where the decision maker has more than two alternatives available. Though in our case we model the traveler to have the choice between only two options, this framework was chosen since it allows adding more alternatives in the future if necessary. The MNL model is based on the assumption of Irrelevance of Independent Alternatives (IIA) (Hensher, et al., 2005) and therefore, does not consider the similarities between alternatives in a choice set. The similarity of a route with other alternatives may affect the probability of choosing the route and needs therefore to be accounted for in a choice model. The computational benefits of the simple, closed-form MNL model structure have encouraged researchers to propose MNL modifications to capture the similarities among routes and overcome the limitation of the basic MNL model (Prato, 2009). The modifications are either

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made in the deterministic or stochastic part of the utility. Methods that modify the deterministic part of the utility include C-logit, Path Size Logit (PSL) and the Path Size Correction Logit (PSCL) models (Bliemer & Bovy, 2008). Models that account for similarities in the stochastic part of the utility (error correlations) while still retaining a closed-form formula for probabilities fall into the family of Generalized Extreme Value (GEV) models. Such models include Paired Combinatorial Logit (PCL), Cross Nested Logit (CNL), and Generalized Nested Logit (GNL) models (Bliemer & Bovy, 2008). Models that account for similarities in the stochastic part of the utility without maintaining a closed-form formula for probabilities fall into the class of mixed models. They include the mixed logit model and logit kernel models with a factor-analytic approach (Bekhor, et al., 2002). The PSL model proposed by Ben-Akiva & Bierlaire (1999) accounts for the similarity among alternatives in a choice set by introducing a similarity term called the Path Size (PS) factor within the deterministic component of the utility function. The Path Size factor indicates the fractions of the path that constitute a “full” alternative (Frejinger & Bierlaire, 2007). We use the PS formulation proposed by Ramming (2002) which expresses the amount to which a route overlaps with the other routes in the choice set. It is calculated as

PSr= lnlaLr

a∈r

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Na

where PS denotes the overlap factor for route r, the index of a network link, l the length of link that is a part of route r, L the length of route r, and N the number of alternatives in the choice set which contain link . The PSL model provides a closed-form structure for choice probability which has been shown to perform well in other studies (Daamen, et al., 2005; Hochmair, 2009; Menghini, et al., 2010; Prato & Bekhor, 2007). Before analysis in NLOGIT 5 the binary correlation between the predictor variables was determined since collinearity can lead to underestimated confidence intervals and thus inflated significance levels. After this step we ran an Ordinary Least-Squares (OLS) regression for each of the various tested models together with collinearity analysis. The Variance Inflation Factor (VIF) was below 2 for each of the estimated models, which is smaller than the recommended maximum value of 10 (DeMaris, 2004), showing that collinearity did not pose a problem. Various route choice models were manually built in a step-wise approach and estimated. We included the pathsize variable as the base variable in all models since it accounts for the correlation between the alternatives in the choice set. This model denotes the reference model. Since a common route preference is minimum travel time we tried to include this parameter in our model specifications as well. However, since each choice set consists of only two alternatives and since the travel time of the scenic route is always greater than the corresponding fastest route, travel time and choice outcome are highly correlated. Therefore models that contained travel time as a predictor did not show other significant effects on route choice. This issue could be potentially resolved in the future by adding more alternatives to the choice set. Instead, for this study we included in two estimated models an attribute that combines road type and travel time, i.e. time travelled on local roads. Next, we added attributes one after another that were significant in the Wilcoxon-Signed Rank test, trying to maximize the goodness of fit value, keeping signs of coefficients as expected, and retaining only parameters significant at p<0.10. A positive coefficient in a final model means that an increase of the value of the corresponding attribute increases the probability of choosing the scenic route.

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The log likelihood at equal shares (null log likelihood) is the same in all the estimated models. It describes the value of the log-likelihood function when all parameters are zero, i.e., when the alternatives are assumed to have equal probability to be chosen. It is computed as

Log Likelihood equal shares =Number of observations x ln (0.5) The rho-squared parameter describes the overall goodness of fit of the model and has a value between 0 and 1. A value of one implies a perfect model that predicts each choice correctly. Rho-squared is computed as

ρ2=1-Log Likelihood (estimated model)

Log Likelihood (equal shares)

The adjusted rho-squared parameter takes into account the number of parameters included in a model and is computed as

adjusted ρ2=1-Log Likelihood (estimated model)-Number of parameters


The step-wise model building approach results in models with an increasing number of parameters. Using a chi-squared likelihood ratio test it can be tested whether a newly added predictor variable (or a set of newly added variables) gives a model with better estimation results than the model with fewer parameters it is compared to. The model with fewer parameters is referred to as the restricted model (R), and the one with additional parameters as the unrestricted model (U). The chi-square test statistic is computed as:

2 ∗ where LL is the log-likelihood of the restricted model and LL is the log-likelihood of the unrestricted model. The chi-square test statistic is then compared to a critical test value X2(df, α), where df stands for the degree of freedom, which equals the difference in the number of model parameters to be estimated between the restricted and unrestricted model. If the test statistic is larger than the critical value, the newly added parameter(s) lead to better estimation results. 6.2. Tested models This section shows the estimation results for three multinomial logit choice models that were built in response to the research hypotheses formulated before, as well as two additional model variations (model 4 and 5). The explanatory value and significance of each model parameter are illustrated through estimation results shown for each stage in the step-wise building approach. 6.2.1. Model 1 The first hypothesis relates landscape variables and road type to route choice. Table 4 shows the different stages for the first model which contains one travel time/road type related attribute, three scenic attributes, and one overlap correction parameter. The model goodness of fit for the final model is high with an adj. ρ2=0.76. The change in adj. ρ2 between each step shows the contribution of the added parameter to the explanatory power of the model. The fact that the chi-square test statistic is larger than the critical lookup value from the chi-square distribution table for each step (last two rows in Table 4), shows that the model fit increases significantly with

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each step. The signs of all coefficients for scenic attributes are positive, meaning that the existence of these features along a route makes choosing that route as the scenic one more likely. Also, the percentage of time driven on local roads was positive, indicating that local roads are positively associated with route attractiveness. The model is relatively sparse in terms of the number of attributes included compared to the eight scenery related attributes that were found to differ significantly between shortest and fastest routes when using the non-parametric Wilcoxon signed rank test (compare Table 3). However, adding further attributes would render current attributes non-significant. This may be due to small correlations between predictor variables (which are not considered in Table 3), and due to the small sample size of observations relative to the large number of attributes. Using all eight scenery related variables in a model, it can be expected that, at a 10% of level of significance, about one parameter would show as significant (i.e. a false positive) even if there was no true association between any of these parameters with route choice. The final model includes three scenic attributes that are significant at a 10% significance level or less, indicating that the marking of attributes as significant is not a result of multiple testing and was not obtained by chance.

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Table 4. Estimation results for model 1

Variable Name Reference +LocalRoadTime +Water body +Mountain +Forest

Pathsize Coefficient 180.476*** 148.021* 96.619* 117.213** 113.456**

t-statistic 2.74 1.88 1.74 2.26 2.32

LocalRoadTime Coefficient 14.053*** 13.731** 12.798*** 13.713***

t-statistic 2.68 2.45 2.74 2.77

Water body Coefficient 0.412** 0.662** 0.622**

t-statistic 2.47 2.57 2.09

Mountain Coefficient 0.769* 0.723*

t-statistic 1.95 1.93

Forest Coefficient 0.244*

t-statistic 1.75

No. of observations 96 96 96 96 96

No. estimated param. 1 2 3 4 5

Log Likelihood (estimated model)

-38.380 -24.749 -17.286 -13.434 -10.965


-66.542 -66.542 -66.542 -66.542 -66.542

0.423 0.628 0.740 0.798 0.835

adjusted 0.408 0.598 0.695 0.738 0.760

3.840 3.840 3.840 3.840

27.261 14.927 7.704 4.937

***Coefficient is significant at 1%

** Coefficient is significant at 5%

* Coefficient is significant at 10%

ᵡ (df, 0.05)

2 ∗ LL LL

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6.2.2. Model 2 To test the second hypothesis the travel time attribute for local roads was removed, and substituted with scenery related attributes. Thus it was tested to which extent scenery related attributes alone can explain route choice. Table 5 shows the estimation results of the different steps in obtaining the best fitting model. This final model contains four scenery related parameters, replacing local travel time and forest with park/garden and urban area parameters. Also here, the model fit increases significantly with each step. The negative coefficient of the urban area parameter implies that routes running through Urbanized Areas are perceived less scenic, which is in line with our expectations. The overall goodness of fit of this model with an adj. ρ2=0.67 is lower than that of model 1, showing that road type is important for modeling scenic route choice.

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Table 5. Estimation results for model 2 Variable Name Reference +Water body +Mountain +Park/Garden +Urban

Pathsize Coefficient 180.476*** 151.195** 147.512** 144.677** 133.408**

t-statistic 2.74 2.36 2.31 2.27 2.12

Water body Coefficient 0.390*** 0.445*** 0.478*** 0.652**

t-statistic 3.04 3.27 2.83 2.57

Mountain Coefficient 0.372** 0.493** 0.422*

t-statistic 2.04 2.11 1.72

Park/Garden Coefficient 0.289** 0.282**


Urban Coefficient -0.056**

t-statistic -2.12

No. of observations 96 96 96 96 96

No. estimated param. 1 2 3 4 5


-38.380 -28.677 -24.607 -20.792 -17.184


-66.542 -66.542 -66.542 -66.542 -66.542

0.423 0.569 0.630 0.688 0.742

adjusted 0.408 0.539 0.585 0.627 0.667

3.840 3.840 3.840 3.840

19.406 8.139 7.630 7.216


** Coefficient is significant at 5% * Coefficient is significant at 10%

6.2.3. Model 3 To test the third hypothesis a model was developed that controls for travel on local roads, but substitutes scenery related variables with the density of geo-tagged Panoramio photos along routes. Table 6 shows the estimation results, indicating that the image density along the scenic routes is significant and positive, as expected. Although the model fit with an adj. ρ2=0.72 is somewhat lower than that of model 1, the density of geo-tagged Panoramio photos provides a

ᵡ (df,0.05) 2 ∗

19

close substitute for scenery related attributes in model 1 for predicting route choice. While this model does not explain which aspects of the surrounding environment contribute to scenery, the obtained result proves useful for scenic route computations, especially when the computation of scenic landscape attributes is not possible in some areas, e.g. due to missing layers with scenic feature data. Further, photo density is also easier to obtain and process than computing the visibility of scenery related point and polygon features from roads, which involves data layer compilation and viewshed analysis. Table 6. Estimation results for model 3

Variable Name

Reference +LocalRoadTime +Photo Density

Pathsize Coefficient 180.476*** 148.021* 129.147**

t-statistic 2.74 1.88 2.1

LocalRoadTime Coefficient 14.053*** 18.244***


Photo Density Coefficient

3.071***

t-statistic 2.76

No. of observations 96 96 96

No. estimated param. 1 2 3


-38.380 -24.749 -15.841


-66.542 -66.542 -66.542

0.423 0.628 0.762

adjusted 0.408 0.598 0.717

3.840 3.840

27.261 17.817


** Coefficient is significant at 5%

* Coefficient is significant at 10%

ᵡ (df, 0.05)

2 ∗ LL LL

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6.2.4. Model 4 and 5 Since the goal of this paper was to extend previous research by examining the contribution of different scenic attributes in the selection of scenic routes, as opposed to just one generic scenic attribute, we estimated two more route models that contain one comprehensive variable which consists of different scenic variables. The first of these two models, which we call the landscape model, considers one attribute that combines the three scenic attributes water body, mountain and forest, which were significant in model 1. The estimation results in Table 7 (left portion) show that the combined attribute is highly significant, but that the adjusted ρ2 value is over 10% lower than that of model 1. This confirms that the use of three separate landscape attributes better captures the choice behavior for scenic routes than one combined variable. The second model, which we label scenic aggregation model, combines all 8 scenic attributes which had significantly different values between the scenic and fastest route set(Table 3) into one single attribute. This attribute was not significant and the chi-squared test shows that adding this attribute does not improve model estimation significantly (Table 7, right portion). This implies that some of the attributes have conflicting effects on the selection of a scenic route, which is why some of them were removed from model 1 and 2. Table 7. Estimation results for model 4 and 5

Landscape Scenic aggregation

Variable Name Reference +LocalRoadTime +Landscape Reference +LocalRoadTime +Scenicagg Pathsize Coefficient 180.476*** 148.021* 138.372** 180.476*** 148.021* 140.546*

t-statistic 2.74 1.88 2.06 2.74 1.88 1.9

LocalRoadTime Coefficient 14.053*** 13.303*** 14.053*** 13.7428*** t-statistic 2.68 2.67 2.68 2.63

Landscape Coefficient 0.198** 0.07364 t-statistic 2.53 1.18

No. of observations 96 96 96 96 96 96 No. estimated param. 1 2 3 1 2 2


-38.380 -24.749 -20.484 -38.380 -24.749 -24.032


-66.542 -66.542 -66.542 -66.542 -66.542 -66.542

0.423 0.628 0.692 0.423 0.628 0.639

adjusted 0.408 0.598 0.647 0.408 0.598 0.609

3.840 3.840 3.840 3.840 27.261 8.531 27.261 1.434

***Coefficient is significant at 1% ** Coefficient is significant at 5% * Coefficient is significant at 10%

ᵡ (df, 0.05) 2 ∗

21

7. Prediction accuracy We assume that our estimated models work best for California, i.e. most accurately predict scenic route choices for trips observed in this region. This is because in other regions other environmental factors (e.g. glaciers, waterfalls, etc.) are present and will contribute to route scenery. One could theoretically test the prediction accuracy for other regions to check the general validity of the model results. Practically, testing the accuracy of estimated models, and possibly finding better models in other regions, would require obtaining another set of chosen scenic routes together with all their associated environmental attribute values, using viewshed analysis and other spatial operations to derive them. We consider exploring the variation of effects of scenery related attributes on scenic route choice between different regions as a topic for future work, and, instead, limit an estimation of the prediction accuracy to the California test region, knowing that it might be lower when applying these estimated models in other areas. To do so, we divided the total of 96 scenic routes for California (and their associated choices) randomly into a training set of 76 routes and a validation set of 20 routes. Thus the first 76 routes were used for model estimation (using models 1,2,3, and 4 from section 6.2), and the remaining 20 routes were used for accuracy assessment of these four models. The random split into 76 training and 20 evaluation routes was repeated a total of five times, which allowed us to conduct a total of 20 accuracy assessments. The estimated coefficients for attribute Xi in each model were then used to estimate the utility value of each route r in the validation set using

Based on the utility of each route the probability of choosing the scenic route from within the choice set was computed as:

Table 8 summarizes the results of the accuracy assessment procedure for model 1 through 4. Integer numbers show how many of the 20 decisions in each evaluation dataset were correctly predicted. Percentage numbers show the average computed probabilities for all scenic routes in the 20 choice sets associated with each model evaluation run. The results show that in all accuracy assessments the scenic route was correctly identified in at least 85% (17/20) of decisions, demonstrating high prediction accuracy. The average computed probability for scenic routes with each model run exceeded 86% in all tests. Prediction accuracy was comparable between all four models. Table 8. Estimation results for model 3

Model Evaluation set

1 2 3 4 5 1 18 (90.18%) 20 (98.00%) 17 (86.06%) 20 (95.53%) 19 (92.95%) 2 19 (87.81%) 19 (89.45%) 18 (88.80%) 19 (88.54%) 19 (88.36%) 3 19 (88.06%) 19 (87.84%) 19 (88.14%) 19 (88.38%) 19 (88.22%) 4 18 (87.62%) 20 (93.62%) 19 (90.53%) 18 (91.39%) 18 (89.99%)

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8. Conclusions and discussion The computation of scenic routes requires knowledge of which features of a route and its surrounding environment make a route being perceived scenic, which has so far been only sparsely addressed in the literature. The study presented in this paper tried to narrow this gap by analyzing how travelers choose scenic routes, using a route choice model framework. We examined three hypotheses that related attributes of routes and the surrounding environment with the selection of a scenic route. The result of the estimated regression models can be used to construct a multi-criteria utility function with different route and scenery attributes. This advances previous results that merely looked at the effect of scenery on route choice, without providing more detail on the scenic components. The results of model 1 and 2 show that an increased presence of water bodies, mountains, forests, and parks along routes increases the probability for a route to be chosen as scenic route, whereas the presence of urban areas along a route decreases that probability. A comparison with models that collapse scenic attributes into one variable (model 4 and 5) show that the splitting of scenic attributes results in a better model fit. We expect that the first two estimated models, which include scenery related variables, work best for California, and that a similar estimation approach would have to be conducted for other regions to take into account different landscape characteristics of those regions. The third model confirmed that geo-tagged shared images are also a useful predictor for scenic route choice. That estimated route choice model could be expanded with landscape variables in the future if there is a reason to believe that such data layers complement VGI photo presence (which was not tested in this study). An advantage of this model is its independence from landscape variables, making it more general than model 1 and 2 and thus easier to apply in other regions as well. The path size variable was significant in all presented models. This shows that correlations between route alternatives in the choice set cannot be neglected since this would lead to biased model results. The final specifications of model 1 and 2, which were found through a step-wise approach, contain a relatively small number of scenic attributes, and adding more predictor variables does not increase the model fit. We can think of two possible explanations for this. First, the sample size of 96 observed route choices is small compared to the number of attributes under consideration. Fortunately, the continuous growth of VGI data sources, including geo-tagged photos, will most likely increase the number of identifiable scenic routes in the near future. More specifically, we found that the number of Panoramio photos for California grew by more than 30% over the past 12 months. Second, each choice set in the presented study consists of only two routes. Adding more alternative routes might increase the significance of certain variables. For future work we are exploring algorithms to generate a larger choice set. Since scenic routes should pass by desired regions, which may even be located on dead ends along a route, the computation of alternative routes requires specific methods to generate reasonable routes besides commonly used methods, such as labeling approaches, weighted linear combination of attributes, or link elimination. Acknowledgements The authors are grateful to Google for financial support through a Google Research Award.

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Analyzing how travelers choose scenic routes using route ... · Analyzing how travelers choose scenic routes using route choice models Majid Alivand, Hartwig Hochmair, Sivaramakrishnan