domain: shs sdv

text:
Dr Camille Perchoux
email: camille.perchoux@liser.lu

Ruben Brondeel

Rania Wasfi

Olivier Klein

Geoffrey Caruso

Julie Vallée

Sylvain Klein

Benoit Thierry

Martin Dijst

Basile Chaix

Thierry Benoit

Yan Kestens

Philippe Gerber

Walking, trip purpose, and exposure to multiple environments: A case study of older adults in Luxembourg

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

travel behaviors, the current study additionally stresses the importance of the trip purpose to emphasize "why" and "for what" people walk.

Keywords: utilitarian walking, multi-place exposure, trip purpose, older adults, distance traveled 1. Introduction "There are many ways to walk" [START_REF] Gatrell | Mobilities and health[END_REF], depending on speed, intensity, or distance; each being potentially explained by the purpose of the trip, in addition to the characteristics of the person (physical capability, mood, etc.) and the walkability of her or his geographic life environments. Recent literature on the effect of trip purpose on walking separates recreational from utilitarian walking, [START_REF] Lee | Correlates of walking for transportation or recreation purposes[END_REF][START_REF] Owen | Understanding environmental influences on walking: Review and research agenda[END_REF][START_REF] Saelens | Built environment correlates of walking: A review[END_REF][START_REF] Spinney | Walking for Transport versus Recreation: A Comparison of Participants, Timing, and Locations[END_REF] and shows that utilitarian bouts are shorter, faster, and occur in denser environments [START_REF] Kang | Differences in behavior, time, location, and built environment between objectively measured utilitarian and recreational walking[END_REF]. With regard to utilitarian walking, other research separates commuting from multipurpose non-work trips [START_REF] Carse | The factors influencing car use in a cycle-friendly city: The case of Cambridge[END_REF][START_REF] Cervero | Travel choices in pedestrian versus automobile oriented neighborhoods[END_REF][START_REF] Feuillet | Built environment in local relation with walking: Why here and not there?[END_REF][START_REF] Menai | Walking and cycling for commuting, leisure and errands: relations with individual characteristics and leisure-time physical activity in a cross-sectional survey (the ACTI-Cités project)[END_REF], which are more flexible in time and space [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF]. The current study goes further, and investigates in greater depth the role played by trip purpose in non-work utilitarian walking. The research is based on the specific population segment of older adults. Due to the recent demographic shift, this group is gaining in importance, which triggers changes in the built environment to enhance and maintain daily mobility and independent lifestyles as people age [START_REF] Dumbaugh | Designing communities to enhance the safety and mobility of older adults: A universal approach[END_REF]. In addition to maintaining physical functioning and independent mobility, active travel (i.e. walking or cycling) in old age is further associated with reduced mortality rates [START_REF] Cerin | The neighbourhood physical environment and active travel in older adults: A systematic review and meta-analysis[END_REF], as well as lower risks of cognitive impairment, depression, dementia, cardiovascular diseases, and some cancers.

Shifting to a more active travel mode seems to provide greater overall health benefits to older adults than to younger individuals [START_REF] Cerin | The neighbourhood physical environment and active travel in older adults: A systematic review and meta-analysis[END_REF][START_REF] Mueller | Health impact assessment of active transportation: A systematic review[END_REF].

As stressed by Sugiyama and colleagues [START_REF] Sugiyama | Prospective Associations of Local Destinations and Routes with Middle-to-Older Aged Adults[END_REF], "aging in place" is a crucial component of the well-being of older adults, and-beyond the general idea of staying in a familiar neighborhood-it relies on older adults' ability to move outdoors and accomplish dayto-day activities as shopping, recreational activities, or engaging in social interactions with family and friends. The distance from home to engage in such types of activities typically decreases with age, which underlines the importance of the residential neighborhood environment in predicting short-distance, utilitarian walking trips [START_REF] Cerin | The neighbourhood physical environment and active travel in older adults: A systematic review and meta-analysis[END_REF].

Identifying the environmental attributes that facilitate utilitarian walking could contribute to inform urban planning interventions. Additionally, accounting for the purpose of walked trips (i.e. different types of errands or recreational activities), which may be influenced by different environmental attributes, would allow urban planners to target neighborhoods with specific characteristics.

It is well known that utilitarian walking is determined by trip characteristics such as the origin and destination, distance, and walkability of the environment [START_REF] Lee | Correlates of walking for transportation or recreation purposes[END_REF][START_REF] Moudon | Attributes of environments supporting walking[END_REF][START_REF] Owen | Understanding environmental influences on walking: Review and research agenda[END_REF]. However, the nature of the trip purpose itself may impose additional physical or time-space constraints on walking that need to be accounted for (specific clothing, goods to carry, opening hours, etc.). Transport research has long recognized the effect of trip purpose on the choice of travel mode [START_REF] Hatamzadeh | Walking Behaviors in Different Trip Purposes[END_REF][START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF][START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF], but there is little understanding of how trip purpose interacts with the other environmental or spatial determinants of utilitarian walking to shape active transportation patterns. Scheepers and colleagues [START_REF] Scheepers | Personal and Environmental Characteristics Associated with Choice of Active Transport Modes versus Car Use for Different Trip Purposes of Trips up to 7.5 Kilometers in The Netherlands[END_REF] reported an effect of the interaction between trip purpose and the level of urbanity on non-motorized travel. However, they considered an aggregate environmental typology and solely focused on the residential environment, thus providing only an incomplete picture of the linkage between exposure to environments during a trip, its purpose, and the mode of transport. There is also seldom any evidence of heterogeneity in the relationship between distance and utilitarian walking depending on trip purpose [START_REF] Dijst | Travel time ratio: The key factor of spatial reach[END_REF][START_REF] Hatamzadeh | Walking Behaviors in Different Trip Purposes[END_REF][START_REF] Susilo | How far is too far? Travel time ratios for activity participations in the Netherlands[END_REF][START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF], and no study has systematically examined the variations by trip purpose on the determinants of walking while accounting for both residence and destination environments.

Various classifications of trip purpose have been used in travel studies [START_REF] Engstrom | Private enforcement's pathways: Lessons from qui tam litigation[END_REF][START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF]. These range from using three or four classes (i.e. work, study, or shopping) [START_REF] Hatamzadeh | Walking Behaviors in Different Trip Purposes[END_REF][START_REF] Larranaga | The relationship between built environment and walking for different trip purposes in porto alegre, Brazil[END_REF][START_REF] Scheepers | Personal and Environmental Characteristics Associated with Choice of Active Transport Modes versus Car Use for Different Trip Purposes of Trips up to 7.5 Kilometers in The Netherlands[END_REF][START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF], to more-refined categorizations (i.e. shopping, appointments, personal, college, free time, visiting, work, or school) [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF][START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF][START_REF] Manaugh | What makes travel "local": Defining and understanding local travel behaviour[END_REF][START_REF] Millward | Active-transport walking behavior: Destinations, durations, distances[END_REF][START_REF] Susilo | How far is too far? Travel time ratios for activity participations in the Netherlands[END_REF]. Some authors contrast activity types between major anchor points (e.g. home, work) and minor locations (e.g. restaurants, banks, shops, etc.) [START_REF] Flamn | The concept of co-creation[END_REF], while others distinguish between mandatory and discretionary activities, between fixed and flexible activities [START_REF] Hägerstraand | WHAT ABOUT PEOPLE IN REGIONAL SCIENCE?[END_REF], or between habitual, planned and spontaneous in space and time [START_REF] Gärling | Reintroducing attitude theory in travel behavior research: The validity of an interactive interview procedure to predict car use[END_REF]. Building on timegeography [START_REF] Dijst | Time Geographic Analysis[END_REF], transport [START_REF] Flamn | The concept of co-creation[END_REF][START_REF] Hägerstraand | WHAT ABOUT PEOPLE IN REGIONAL SCIENCE?[END_REF][START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF], activity-based approaches [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF], and epidemiology [START_REF] Hatamzadeh | Walking Behaviors in Different Trip Purposes[END_REF][START_REF] Larranaga | The relationship between built environment and walking for different trip purposes in porto alegre, Brazil[END_REF][START_REF] Millward | Active-transport walking behavior: Destinations, durations, distances[END_REF][START_REF] Scheepers | How combined trip purposes are associated with transport choice for short distance trips. Results from a crosssectional study in the Netherlands[END_REF][START_REF] Scheepers | Personal and Environmental Characteristics Associated with Choice of Active Transport Modes versus Car Use for Different Trip Purposes of Trips up to 7.5 Kilometers in The Netherlands[END_REF][START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF] research lines, we opted for a categorization of non-work trip purposes that could constrain or enhance walking among older adults (Table 1).

In this study, we explore three hypotheses, based on precise geographical information about participants' regular destinations, the corresponding transportation mode, and the trip purpose: First, ceteris paribus, trip purpose is an independent correlate of utilitarian walking (H1).

Second, the associations between environmental attributes surrounding participants' destinations and walking vary by trip purpose (H2): depending on the purpose, individuals might be more or less sensitive to the walking-friendly attributes of neighborhood environments. Third, the association between the distance travelled and walking varies depending on the trip purpose (H3), as the barrier effect of distance on walking may vary according to the type of activity realized at the destination.

Methods

2.1.Population

Our data is taken from a cross-sectional study in Luxembourg, initiated within the CURHA project (Contrasted Urban contexts and Healthy Ageing) (Kestens et al., 2016a). In total, 471 participants aged 65 years and above were sampled between April 2015 and January 2016. The sample was assembled randomly from Social Security files and stratified by age and gender, and along spatially contrasted strata representing different degrees of urbanity (Figure 1). Each participant completed two face-to-face questionnaires: the LuxCohort questionnaire focusing on self-reported socio-demographic data, health, well-being, perception of residential neighborhood, and overall physical activity habits; and the VERITAS questionnaire (Visualization and Evaluation of Route Itineraries, Travel destinations, and Activity Spaces) (Chaix et al., 2012b), allowing identification and geolocation of the participants' regularly visited destinations and associated transport modes. The actual routes traveled between residence and destinations were not reported.

Measurements

Utilitarian walking. In the VERITAS survey, participants reported their usual mode of transport to reach each regular destination.

Regularly visited destinations and trip purposes. The term "destination" refers to a nonresidential location visited by a participant to perform an activity, and "trip purpose" refers to the main activity performed at the given location. During the VERITAS survey, participants were invited to report and geolocate regular destinations visited for 19 different purposes. We subsequently re-ordered these into eight categories based on the classification detailed in Table 1. Details of the number of items per category and the walking probability are presented in Table 2. Due to the small number of reported locations, work as trip purpose was not analyzed, and free-time sports and non-sports activities were merged.

Environmental measurements. Exposure to multiple environments was assessed within buffered line-based network buffers [START_REF] Oliver | Comparing circular and network buffers to examine the influence of land use on walking for leisure and errands[END_REF], computed around the residence of the participants, their regular destinations, and the shortest route between locations. The buffer size was set at 30 meters from the street segments reachable within a 10-minute walk. Walking speeds were adjusted for uphill and downhill directions: with final values from 4.4 km/h for a slope of 0-2 percent, to 2.0 km/h for a slope greater than 10 percent [START_REF] Carre | Sequences pietonnieres et mesure de l exposition au risque[END_REF] (Appendix 1). The 30 meter threshold was chosen in order to include adjacent plots and buildings, while avoiding inaccessible ones. We merged exposure areas (buffers) around the place of residence, around each regular destination, and around the shortest route between the residence and each destination; overlaps between buffers were removed. Five environmental variables were computed based on past evidence concerning the main components of the built environment influencing travel behaviors, as suggested by [START_REF] Ewing | Travel and the built environment[END_REF] and based on the increasing interest in research about the effect of greenness on walking [START_REF] Sarkar | Exploring associations between urban green, street design and walking: Results from the Greater London boroughs[END_REF]: number of amenities, diversity of amenities, street connectivity, number of public transport stops, and an index of greenness (see Table 3). All the environmental variables were estimated using ArcMap 10.5 and PyScripter 3.2 software programs.

Distance to activity places. The street network distance from the place of residence to each destination was calculated using the shortest route. Distance was computed as a continuous time-distance variable based on walking speed.

Individual covariates. Several socio-demographic factors were considered: age (continuous), sex, education (none, primary, secondary, or post-secondary), marital status (living alone or living as a couple), and having a valid driving license. A composite score of physical health was computed based on the Medical Outcome of the 36-Item Short Form Health Survey (SF-36). [START_REF] Health | 36-Item Short Form Survey (SF-36) Scoring Instructions[END_REF] Mental health was evaluated using the geriatric depression score and categorized as either "no depression," or "suggestive, to indicative of depression." Neighborhood self-selection [START_REF] Handy | Self-selection in the relationship between the built environment and walking: Empirical evidence from Northern California[END_REF][START_REF] Mccormack | In search of causality: a systematic review of the relationship between the built environment and physical activity among adults[END_REF]Van Dyck et al., 2011) was evaluated using three variables. Participants reported whether when they moved to their current residence they considered it important to live in a neighborhood that was i) pleasant to walk in, ii) well served by public transport, and iii) convenient for driving (ease of parking, not too much traffic, good accessibility by car).

Statistical analyses

Analytical sample. From the initial sample of 471 participants and 5,080 geolocated activity places, we excluded 94 participants who reported physical limitations to walking more than 100 meters, 6 participants who reported no residence or destinations, and 21 participants for missing values. Of the 4,179 remaining destinations, 53 were located outside Luxembourg and were ignored. As we focus on utilitarian walking, we only considered regular destinations within a 60-minute walking distance from of each participant's residence. The final sample includes 342 participants and 2,433 destinations.

Regression models. Considering each destination of participants with the corresponding mode of transport as the unit of analysis, we modeled the probability of reporting walking as the usual way to reach a destination. To evaluate associations between environment, trip purpose, distance, and walking, we estimated several multilevel logistic models, using Laplace approximation from the Glimmix procedure in SAS 9.4.

Since individuals reported multiple destinations, random effects account for the withinindividual correlation in travel mode choice. Individual covariates were tested separately as potential confounders and excluded when not significant (p-value >0.05), except for age and sex, which were retained in all models. Each variable was first examined separately in a bivariate regression with the Loess procedure (SAS 9.4) to visualize the shape of the relationship between each effect and walking, and to identify potential nonlinearities. Different continuous modeling approaches were tested, including linear, quadratic, and linear spline with two or three knots [START_REF] Lamb | Categorisation of built environment characteristics: The trouble with tertiles[END_REF]. Models were compared using the Akaike Information Criteria (AIC). We then tested the association between trip purpose and walking (H1), accounting for distance, environmental variables, and confounding factors in the same model (see Model A). Lastly, we tested one by one the potential multiplicative interactions between trip purpose and i) each environmental variable (H2), and ii) distance to the residence (H3). Only statistically significant interaction terms were retained after a type III test of fixed effects (Wald Chi² p-value <0.01) comparing the models with and without interactions (see Model B). A parsimonious modeling approach was chosen, thus environmental quadratic transformations or spline knots were removed from the full model when not significant (p-value <0.05), either as an independent effect on walking or as an interaction effect with trip purpose.

Results

The regular destinations, study population, and environmental characteristics are presented in Table 2, Table 4, andTable 5 respectively. Some 47 percent of the participants were female, 52 percent reported having a secondary education level, and 34 percent were living alone.

Participants reported a mean number of 7.11 (SD: 3.94) destinations. Among the 2,446 destinations, 41 percent were reached by walking. "Personal" trip purpose was the most prevalent category (24 percent), followed by "daily shopping" (16 percent), and "health appointment" (16 percent). "Visit to family and friends" and "daily shopping" were the most walked activities (52 and 46 percent, respectively). Out of all the destinations, 53 percent were located within a 20-minute walk of the place of residence. The mean time-distance from the residence to all destinations reached by walking was 11 minutes (SD=9.52). The mean timedistance walked varied from 13 minutes (SD=10.90) for the "health appointment" trip purpose, to 9 minutes (SD=5.86) for "heavy goods shopping." These results are in line with the 10minute buffer size defined around each residence and destination.

Among the confounding factors tested, education level, marital status, geriatric depression score, having a valid driving license, and neighborhood self-selection related to public transport services and car use, were kept in full model.

Distance, environment, and walking

Table 6 presents the associations between distance, environment, and walking, after adjusting for confounding factors. Looking at the environment, the odds of walking were positively associated with the number of amenities (β=0.006; SE=0.002) and negatively associated with the number of public transport stops (β=-0.030; SE=0.013) (Model A). Street connectivity ranging from 0 to 8 intersections was positively associated with the odds of walking (β=0.176; SE=0.059) while above 8 intersections, we observe a negative correlation coefficient β=-0.015 (β=0.176-0.191; with 0.176 indicating the slope before the knot and 0.191 indicating the difference in slopes before and after the knot). An increase of 5-minutes in the walking distance from the place of residence is strongly negatively associated with walking (β=-0.189; SE=0.010) (Model A).

Trip purpose and walking

The probability of walking was found to vary according to the trip purpose, with the highest value for "visit activity" (52 percent) and the lowest for "heavy goods shopping" (17 percent) (Table 2). Even after accounting for confounding factors, environment and distance, a strong association remained between trip purpose and walking (p <0.001) (Model A). The odds of walking to "visit to family and friends" were higher (β=0.966; SE=0.338) than the odds of walking to conduct "personal activities." The odds of walking to a "heavy goods shopping" destination were much lower (β=-1.826; SE=0.324).

Interactions between trip purpose and environmental attributes are non-significant. However, a strong heterogeneity is observed for the association between distance and walking depending on the trip purpose (Wald Chi² test p <.001) (Model B). Figure 2 presents the odds ratios of walking to a destination located 15 minutes from the place of residence compared with 10 minutes, by trip purpose. The odds ratio of walking to "restaurant" destinations was 0.513 (95% CI: 0.428; 0.615), while for a "heavy goods shopping" destination it was 0.174 (95% CI: 0.097; 0.311). Overall, the odds of walking were low for "heavy goods shopping" and "daily shopping," and high for "restaurant," "visit to family and friends," "free time," and "appointment" (health related or not).

Discussion

The decision to walk depends on the trip purpose, irrespective of the distance and environment

The trip purpose remains a major correlate of walking, after controlling for environment, distance, and confounders. "Heavy goods shopping" was negatively associated with walking compared with "personal" activities, which is highly understandable as the former implies carrying heavy bags, thus favoring car use. Also in line with our first hypothesis, "visit" to family and friends was positively associated with walking; it does not imply specific time-space or physical constraints that affect the travel mode. Our results contribute to existing knowledge by analyzing a more detailed trip purpose typology, which offers opportunities for future generalizations by replication [START_REF] Davis | Getting out and about in older adults: the nature of daily trips and their association with objectively assessed physical activity[END_REF][START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF].

Walking is associated with multi-place environmental exposure

Three reviews have recently examined the role of different aspects of the built environment on active travel among older people [START_REF] Barnett | Built environmental correlates of older adults' total physical activity and walking: A systematic review and meta-analysis[END_REF][START_REF] Carlin | A life course examination of the physical environmental determinants of physical activity behaviour: A "Determinants of Diet and Physical Activity" (DEDIPAC) umbrella systematic literature review[END_REF][START_REF] Cerin | The neighbourhood physical environment and active travel in older adults: A systematic review and meta-analysis[END_REF].

Our results are consistent with numerous studies on walking among the elderly [START_REF] Borst | Influence of environmental street characteristics on walking route choice of elderly people[END_REF][START_REF] Cerin | The neighbourhood physical environment and active travel in older adults: A systematic review and meta-analysis[END_REF][START_REF] Li | Multilevel modelling of built environment characteristics related to neighbourhood walking activity in older adults[END_REF][START_REF] Maisel | Impact of older adults' neighborhood perceptions on walking behavior[END_REF][START_REF] Siu | Built environment and its influences on walking among older women: Use of standardized geographic units to define urban forms[END_REF][START_REF] Tamura | Spatial clustering of physical activity and obesity in relation to built environment factors among older women in three U.S. states[END_REF][START_REF] Van Cauwenberg | Environmental factors influencing older adults' walking for transportation: a study using walk-along interviews[END_REF], 2011), and show a positive relationship between street connectivity and utilitarian walking among those with a low street connectivity (up to eight intersections within buffered line-based network buffers around the place of residence, the destination, and the shortest route). The rationale is that greater street connectivity promotes walking (Chaix et al., 2014;[START_REF] Rosso | The Urban Built Environment and Mobility in Older Adults: A Comprehensive Review[END_REF][START_REF] Saelens | Built environment correlates of walking: A review[END_REF] by providing more routes within a neighborhood, more direct paths, and shorter walking distances to destinations. However, some studies have obtained mixed results [START_REF] Barnett | Built environmental correlates of older adults' total physical activity and walking: A systematic review and meta-analysis[END_REF][START_REF] Nagel | The relation between neighborhood built environment and walking activity among older adults[END_REF][START_REF] Satariano | Lower-Body Function, Neighborhoods, and Walking in an Older Population[END_REF][START_REF] Wang | Site and neighborhood environments for walking among older adults[END_REF], which could explain the slightly negative correlation observed with street connectivity above eight intersections.

We observed a slightly positive association between the number of amenities and walking, while no relationship was observed with the diversity of amenities [START_REF] Cerin | Effects of built environment on walking among Hong Kong older adults[END_REF][START_REF] Chudyk | Destinations matter: The association between where older adults live and their travel behavior[END_REF][START_REF] Rosso | Neighborhood amenities and mobility in older adults[END_REF]. Other studies among older adults have reported positive associations between walking and the perceived access to amenities [START_REF] Cerin | Ageing in an ultra-dense metropolis: perceived neighbourhood characteristics and utilitarian walking in Hong Kong elders[END_REF][START_REF] Cerin | Effects of built environment on walking among Hong Kong older adults[END_REF][START_REF] Salvador | Practice of walking and its association with perceived environment among elderly Brazilians living in a region of low socioeconomic level[END_REF], or objective measurements of density or the number of amenities [START_REF] Chudyk | Destinations matter: The association between where older adults live and their travel behavior[END_REF][START_REF] Etman | Characteristics of residential areas and transportational walking among frail and non-frail Dutch elderly: does the size of the area matter?[END_REF][START_REF] Hirsch | Destinations That Older Adults Experience Within Their GPS Activity Spaces[END_REF], or with the use of walking scores. [START_REF] Frank | Healthy Aging and Where You Live: Community Design Relationships With Physical Activity and Body Weight in Older Americans[END_REF][START_REF] King | Aging in neighborhoods differing in walkability and income: Associations with physical activity and obesity in older adults[END_REF][START_REF] Wasfi | Place matters: A longitudinal analysis measuring the association between neighbourhood walkability and walking by age group and population center size in Canada[END_REF]. However, only a few researchers have examined these associations within both residential and non-residential neighborhoods [START_REF] Chaix | The "Residential" Effect Fallacy in Neighborhood and Health Studies[END_REF][START_REF] Chaix | A GPS-Based Methodology to Analyze Environment-Health Associations at the Trip Level: Case-Crossover Analyses of Built Environments and Walking[END_REF][START_REF] Hirsch | Destinations That Older Adults Experience Within Their GPS Activity Spaces[END_REF][START_REF] Howell | Residential or activity space walkability: What drives transportation physical activity?[END_REF]Karusisi et al., 2014;[START_REF] Perchoux | Accounting for the daily locations visited in the study of the built environment correlates of recreational walking (the RECORD Cohort Study)[END_REF][START_REF] Tribby | Assessing built environment walkability using activity-space summary measures[END_REF], and have reported differing results from the varying methods used. Hirsh and colleagues found no association among older adults between physical activity and the density of destinations measured within both "all-modes" and "pedestrian and bicycling" GPS-defined activity spaces [START_REF] Hirsch | Destinations That Older Adults Experience Within Their GPS Activity Spaces[END_REF]. By contrast, using trip-level data, Chaix and colleagues observed a positive association between walking and the density of services at the trip origin and the trip destination separately [START_REF] Chaix | A GPS-Based Methodology to Analyze Environment-Health Associations at the Trip Level: Case-Crossover Analyses of Built Environments and Walking[END_REF].

The negative association between the number of public transport stops and utilitarian walking was unexpected. In their meta-analysis, Barnett and colleagues observed significant evidence among older adults of a positive association between access to public transport and total walking [START_REF] Barnett | Built environmental correlates of older adults' total physical activity and walking: A systematic review and meta-analysis[END_REF]. Access to public transport stops provides an opportunity for less car use, and tends to increase the overall level of physical activity by fostering active mobility to and from public transport stops. However, since the survey only allowed participants to report one unimodal transport mode, we were unable to evaluate a potential fine-grained increase in walking, measured as walking time or walking frequency.

Further, no interaction between environment and trip purpose was observed, which invalidates our second hypothesis: the associations between walking and the number of amenities, public transport stops, or street connectivity do not depend on the trip purpose. This contrasts with the results obtained by Manaugh and colleagues who found that the variance of walking explained by residential-based walkability measurements changed in accordance with the trip purpose (i.e. shopping vs. school) [START_REF] Manaugh | Validating walkability indices: How do different households respond to the walkability of their neighborhood?[END_REF]. Scheepers and colleagues observed that shopping trips realized within urban centers were the most likely to lead to active transport, compared with other trip purposes and other urbanity types [START_REF] Scheepers | Personal and Environmental Characteristics Associated with Choice of Active Transport Modes versus Car Use for Different Trip Purposes of Trips up to 7.5 Kilometers in The Netherlands[END_REF]. While their study classified residential neighborhoods by the degree of urbanity, we examined multiple environmental factors measured around both residence and regularly visited destinations. Our results suggest that among older adults in Luxembourg, the influence of micro-scale environments on walking does not vary by purpose.

Distance remains the key factor for walking and varies with the trip purpose

In the vast body of literature on transport mode determinants, distance is the key determinant of walking, and our study is no exception. Nevertheless, there is much less research explicitly devoted to interaction effects. Our results confirm our third hypothesis that there is a multiplicative interaction between trip purpose, distance, and walking. We observed similar results using trip-level analyses categorized by purpose; with shorter distances and durations for meals and shopping [START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF]. Our sorting by trip purpose suggests that the likelihood of walking for mandatory activities such as "daily shopping," "heavy goods shopping," or "personal" decreases as the distance increases. The underlying mechanism could be that the physical constraint of carrying goods is reinforced with distance, favoring car use even for short journeys. This is consistent with studies on the modifying effect of distance, showing that distance tends to reinforce associations with some walking inhibitors [START_REF] Panter | Attitudes, social support and environmental perceptions as predictors of active commuting behaviour in school children[END_REF][START_REF] Perchoux | Neighborhood educational disparities in active commuting among women: the effect of distance between the place of residence and the place of work/study (an ACTI-Cités study)[END_REF]. More discretionary activities such as "free time," "restaurant," and "visit to family and friends" are more likely to involve walking with increasing distance.

These activities are usually characterized by low physical constraints and high flexibility in terms of space and time, which may give older adults the opportunity to engage in such activities in optimal conditions (e.g. good weather, good mood, feeling physically well, having time, etc.) and thus diminish the barrier effect of distance on walking. The relatively high probability to walk to health appointment locations seems notably peculiar with regard to our hypothesis that feeling unwell or being ill would be associated with a low probability to walk, and even more so with increasing distance.

Overall, individuals seem to have a different sense of an "acceptable distance" [START_REF] Rahul | A study of acceptable trip distances using walking and cycling in Bangalore[END_REF] for walking, depending on the trip purpose [START_REF] Hatamzadeh | Walking Behaviors in Different Trip Purposes[END_REF]. The acceptable distance by trip purpose was also investigated in relation to travel time and activity duration. Travel time (and thus transport modes) was found to be positively related to activity duration [START_REF] Kitamura | Traveler Destination Choice Behavior: Effects of Time of Day, Activity Duration, and Home Location[END_REF], but the travel time/activity duration relationship varied by trip purpose [START_REF] Susilo | How far is too far? Travel time ratios for activity participations in the Netherlands[END_REF]. Mandatory activities showed a more unfavorable balance between travel time and activity duration than discretionary activities [START_REF] Dijst | Travel time ratio: The key factor of spatial reach[END_REF].

Strengths and Limitations

The relationship between trip purpose and transport modes has been little investigated in place and health research, while it is well known within transport research. Using a multi-places exposure approach, we investigated the environmental attributes around the place of residence and the shortest route to regularly visited destinations among older adults. Systematically testing the interactions between utilitarian walking and distance, environment, and trip purpose constitutes one of the very few attempts to disentangle how space-time and physical constraints imposed by trip purposes may modify the influence of well-known walking correlates [START_REF] Scheepers | Personal and Environmental Characteristics Associated with Choice of Active Transport Modes versus Car Use for Different Trip Purposes of Trips up to 7.5 Kilometers in The Netherlands[END_REF][START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF]. Limitations include the fact that both visited locations and the usual mode of transport were self-reported. In addition, environmental conditions at the trip origin were disregarded, as we did not have data about the activity chaining and the actual path between locations. We also ignored the potential confounding effect of the transport mode used during the previous or next trip in the chain [START_REF] Chaix | A GPS-Based Methodology to Analyze Environment-Health Associations at the Trip Level: Case-Crossover Analyses of Built Environments and Walking[END_REF], or of the activity undertaken at the origin [START_REF] Scheepers | How combined trip purposes are associated with transport choice for short distance trips. Results from a crosssectional study in the Netherlands[END_REF]. Further, the time spent in each destination and the frequency of visits were not considered, although they could weight the environmental exposure of a trip. We did not distinguish between residential and nonresidential environments, since 52 percent of destinations were located within a 20-minute walk of the residence and this would have resulted in overlaps of the exposure areas (i.e. buffers).

However, this might have led to a misestimation of the associations between environment and walking, as associations between the residential/trip-origin environment and nonresidential/trip-destination environments may differ [START_REF] Chaix | The "Residential" Effect Fallacy in Neighborhood and Health Studies[END_REF][START_REF] Lee | The attributes of residence/workplace areas and transit commuting[END_REF].

Lastly, although we attempted to reduce self-selection in the transport modes available to a person by including environmental preferences at the time of moving to a residential neighborhood, selective daily mobility bias [START_REF] Chaix | GPS tracking in neighborhood and health studies: A step forward for environmental exposure assessment, A step backward for causal inference?[END_REF][START_REF] Perchoux | Residential buffer, perceived neighborhood, and individual activity space: New refinements in the definition of exposure areas -The RECORD Cohort Study[END_REF]) cannot be ruled out.

The importance of walking purpose in place and health studies

Recent work has pushed the boundaries of place and health research by accounting for individuals' daily mobility while evaluating neighborhood effects on health [START_REF] Perchoux | Conceptualization and measurement of environmental exposure in epidemiology: Accounting for activity space related to daily mobility[END_REF][START_REF] Shareck | Considering daily mobility for a more comprehensive understanding of contextual effects on social inequalities in health: A conceptual proposal[END_REF]. This breakthrough has been supported by the increased use of Global Positioning System (GPS) data, and has opened up new possibilities to refine the assessment of daily exposure, visited locations, and transport mode [START_REF] Brondeel | Using GPS, GIS, and Accelerometer Data to Predict Transportation Modes[END_REF][START_REF] Chaix | GPS tracking in neighborhood and health studies: A step forward for environmental exposure assessment, A step backward for causal inference?[END_REF][START_REF] Kerr | Erratum: Using global positioning systems in health research: A practical approach to data collection and processing[END_REF]Kestens et al., 2016b). While the current study does not question the potential benefits of such types of data, our results stress the importance of taking into account the purpose of conducted activities [START_REF] Kestens | Contextualizing Context": Reconciling Environmental Exposures, Social Networks, and Location Preferences in Health Research[END_REF]. GPS data allows us to answer the "where and when" [START_REF] Kestens | Contextualizing Context": Reconciling Environmental Exposures, Social Networks, and Location Preferences in Health Research[END_REF](Kestens et al., , 2016b)), but it gives few meaningful insights into the "why" and "what for," or more specifically, the type of activities performed. The physical and space-time constraints that apply to the realization of an activity at a specific location may have an impact on the transport mode choice, and modify the influence of transport-related correlates. Some authors have further recognized the role played by "social relations" and "social networks" in the spatial distribution of activity places, travel behavior, and transport modes [START_REF] Axhausen | Activity spaces, biographies, social networks and their welfare gains and externalities: Some hypotheses and empirical results[END_REF][START_REF] Axhausen | Social networks, mobility biographies, and travel: Survey challenges[END_REF][START_REF] Carrasco | Collecting social network data to study social activity-travel behavior: An egocentric approach[END_REF][START_REF] Kestens | Contextualizing Context": Reconciling Environmental Exposures, Social Networks, and Location Preferences in Health Research[END_REF][START_REF] Perchoux | Conceptualization and measurement of environmental exposure in epidemiology: Accounting for activity space related to daily mobility[END_REF]. Accounting for the actual nature of the activity performed at a given location-and why, and with whom-would allow examination of the transport mode choice as part of a behavioral continuum in space and time, and not only as an isolated activity. In this sense, our study puts into perspective the importance of "walking purpose," which can be assessed with GPS combined with body-worn cameras [START_REF] Carlson | Validity of PALMS GPS scoring of active and passive travel compared with SenseCam[END_REF] prompted recall interviews (Chaix et al., 2012a), travel surveys [START_REF] Kestens | Using experienced activity spaces to measure foodscape exposure[END_REF][START_REF] Setton | The impact of daily mobility on exposure to traffic-related air pollution and health effect estimates[END_REF], map-based questionnaires (Chaix et al., 2012b;[START_REF] Shareck | Examining the spatial congruence between data obtained with a novel activity location questionnaire, continuous GPS tracking, and prompted recall surveys[END_REF], or travel or activity diaries [START_REF] Chudyk | Destinations matter: The association between where older adults live and their travel behavior[END_REF].

From a policy perspective, understanding the distribution of walking by purpose could be translated into public health initiatives. For instance, strategies for designing walkable neighborhoods could account for the type of activities that are found in each area. This is all the more important with regard to increasing the cost-effectiveness of public health and land use planning interventions, as budgets are limited and interventions are rarely implemented homogeneously over space. Another implication would be to design interventions among older adults aimed at increasing walking for specific trip purposes only, such as free-time and recreational activities, or visits to relatives and friends. Further studies into the spatial dependency of these walking-friendly trip purposes, and how destinations cluster over space (or not), would thus geographically inform such interventions. This would constitute a "lowhanging fruit" strategy compared with targeting other destinations, such as supermarkets, which are less walkable destinations independent of the surrounding environment [START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF], and more likely to be reached by motorized transport, even over short distances.

Conclusion

The current study contributes to the overall understanding of utilitarian walking among older adults. By bridging concepts from time-geography, transport, and epidemiology, we examined the role played by trip purposes on utilitarian walking, and the potential interactions with wellknown walking correlates-including environment and distance-in shaping active transportation patterns. We have shed light on the differential barrier effects of distance on utilitarian walking by trip purposes. Trip purposes characterized by low physical constraints and high flexibility in space and time seem to be less influenced by the barrier effect of distance on walking. While place and health studies increasingly address both the "where" and "when" of travel behaviors, this study additionally stresses the importance of the trip purpose to address "why" and "for what" people walk.

Table 1. Trip purposes and their potential time-space and physical constraints 762

Trip purpose

Comments on the potential space-time and physical constraints Personal (e.g. banking, filling station, dry cleaning, etc.) [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF] Personal activities have been defined as "getting a service done or completing a transaction" [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF]. This category can encompass various activities, with low to medium physical constraints that inhibit utilitarian walking. While mandatory, these activities are relatively flexible in space, but limited in time by the opening hours of facilities.

Free-time activity (e.g.

entertainment,

theater, sport, church, library, exercise) [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF] Free-time activities have been defined as "non-task-oriented activities" [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF]. With regard to distance and duration, recreational activities (both "go to gym/exercise/play sports" and "rest or relaxation/vacation") were the trip purposes with the highest probability to walk compared with other trip purposes (work, study, shopping, social event, and meals) [START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF].

Walking distance and duration were also higher for recreation purposes than for other categories. We believe that an additional distinction between sports and non-sports activities is meaningful. Non-sports activities during free time are likely to be flexible in space and time.

Sports activities may require specific clothing and equipment that could inhibit utilitarian walking [START_REF] Scheepers | How combined trip purposes are associated with transport choice for short distance trips. Results from a crosssectional study in the Netherlands[END_REF]. Looking at physical constraints related to energy expenditure, walking to or from a sports facility may be considered as either a warm-up/stretching exercise, or an excess expenditure of energy that is in competition with the sports activity itself, and should thus be avoided.

Shop

Locations at which to "buy concrete things" [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF]. Shopping is a mandatory activity that responds to specific physical needs.

Different types of shopping places might, however, relate to different degrees of physical and spatial constraints.

Daily shopping: Shopping for small goods or the provision of daily requirements does not imply specific physical or temporal constraints.

The flexibility in space and time of this activity, as well as the numerous shops in high accessibility neighborhoods, should facilitate utilitarian walking.

Heavy goods shopping: heavy goods shopping is usually realized in large stores, new commercial areas, and malls. Walking would require carrying heavy bags on the way back home [START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF][START_REF] Perchoux | Accounting for the daily locations visited in the study of the built environment correlates of recreational walking (the RECORD Cohort Study)[END_REF][START_REF] Scheepers | How combined trip purposes are associated with transport choice for short distance trips. Results from a crosssectional study in the Netherlands[END_REF], and carrying heavy goods has been identified as the most common reason for car use on short trips [START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF]. Moreover, these activity locations are absent from high neighborhood accessibility areas due to the need for large parking areas and ease of car accessibility [START_REF] Krizek | Neighborhood services, trip purpose, and tour-based travel[END_REF].

Health appointments

Visiting a medical doctor is mandatory and usually associated with being, or perceiving oneself as being sick, which might negatively influence the ability to walk. "Feeling unwell" has been reported as an importance motive for car use [START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF].

Other appointments

Appointments are usually fixed in space and time, and being "short of time" has been rated as the third main reason for using a car (Mackett, (hairdresser, meeting, etc.) 2003). However, it is unlikely that non-medical appointments require a large amount of energy expenditure or physical constraints.

Therefore, if there is reasonable time to travel to or from the appointment location, utilitarian walking should be possible.

Visiting family and friends

Visiting relatives and friends, per se, is a discretionary activity, flexible in space and time, and should not require specific space-time or physical constraints. However, Mackett and colleagues observed that carrying "heavy goods" was the first reason to use a car for social trip purposes [START_REF] Mackett | Why do people use their cars for short trips? Transportation[END_REF].

Restaurant

(e.g. café, restaurant, bar, etc.)

Eating or drinking activities are discretionary, flexible in space and time, and should not imply specific space-time or physical constraints that limit utilitarian walking to or from a location. Some evidence shows that visiting "restaurants or bar" ranks as the fourth destination most likely to be reached by walking (single episode trip only) [START_REF] Millward | Active-transport walking behavior: Destinations, durations, distances[END_REF]. However, Yang and Diez-Roux observed that 36 percent of walking trips were more than 10 minutes in duration and 5 percent more than 30 minutes [START_REF] Yang | Walking distance by trip purpose and population subgroups[END_REF] Finally, the potential walking areas are computed as an area that each surveyed participant would reach by walking from a starting point (i.e. place of residence or place of activity) within 10 minutes (20 minutes to go and return from an activity). Services areas are created by using ArcGIS network Analyst. The polygons which form the services areas will be the study unit areas.

Figure captions Figure 1 .Note 1 :Note 2 :

 captions112 Figure captionsFigure 1. CURHA LuxCohort study area

Figure 2 .Note 2 :

 22 Figure 2. Total interaction effect on walking between trip purpose and distance to the place of residence (N=2,446)

Table 4 . Socio-demographic characteristics of the participants (N=342)

 4

	, which

764

Table 5 . Environmental characteristics measured around the place of residence, each regularly visited destination, and the shortest route (N=2446)

 5

	Variables	Mean (SD)	1 st Quartile	2 nd Quartile	3 rd Quartile
	Number of amenities	78.92 (86.68)	17	37	100
	Diversity of amenities	0.77 (0.16)	0.78	0.82	0.84
	Number of public transport stops	23.83 (14.90)	13	22	30
	Street connectivity	19 .12 (17.46)	5	13	30
	Greenness index	0.17 (0.19)	0.10	0.15	0.23

Acknowledgments

The CURHA project (Contrasting Urban Environments and Healthy Ageing: The International Longitudinal CURHA Study) is an international study conducted in Luxembourg (LISER -Luxembourg Institute of Socio-Economic Research), Canada (CRCHUM -Centre de Recherche du Centre Hospitalier de l'Université de Montréal) and France (INSERM -Institut National de la Santé et de la Recherche Médicale). It is cofounded by FNR (Fonds National de la Recherche, INTER/JCRA/12/6542889), IRSC (Institut de Recherche en Santé Canada TEA-124969), and FRSQ (Fonds de Recherche du Québec, #28837). We are grateful to the people in LISER from Survey Team.

Diversity of amenities

Index ranking from 0 to 1, based on a formula from Youssoufi [START_REF] Youssoufi | Satisfaction residentielle et configurations spatiales en milieu periurbain[END_REF], applied to Luxembourg by [START_REF] Glaesener | Neighborhood green and services diversity effects on land prices: Evidence from a multilevel hedonic analysis in Luxembourg[END_REF] To compute the potential walking areas of elderly, it is important to take into account certain relevant characteristics of their environment that require additional effort when walking. Thus, topography has a direct impact on the pedestrian movement of elderly, who will get tired more quickly when facing a significant slope, whether on uphill or downhill. To integrate this type of constraints, a GIS is mandatory. In our case study, we have used ArcGIS Desktop 10.5 and proceeded as follows.

Construction of a pedestrian network.

The pedestrian network is built from trails and roads network taken from topo-cartographic database (BD-L-TC, provided by Luxembourgish Administration of Cadastre and Topography). This network has been complemented by the digitization of zebra crossing, footbridges, underground passageways. In addition, all open spaces such as places, squares and parking have been converted from polygonal to linear objects, which makes it possible to integrate them in the pedestrian network.

From Digital Elevation Model (DEM) to a network integrating slope

A DEM was generated based on the contours and height spots from topo-cartographic database. Then, altitudes are assigned to each vertices of the different arcs composing the pedestrian network. Each segment was cut beforehand at equidistant intervals of 60 meters maximum. In many cases these segments of the network have both downward and upward slope. In that case, an average slope on these segments is calculated using the following formula:

) 100

where 𝑥̅ _up : average slope uphill (in °)

𝑥̅ _down : average slope downhill (in °) l_up : slope length uphill on a section l_down : slope length downhill on a section L : total length of a section

Determination of the speed of the pedestrian

The walking speed through the network, and consequently the travel time is determined by the slope previously computed according to Julien and Carré (2003) and real-life experiments conducted by Nadja Victor (Victor, 2015) in her PhD thesis (table 1).