Experimental procedure
The research procedures reported in this paper were carried out in accordance with Swiss Federal Act on Research involving Human Beings and Nanyang Technological University’s policy on Research Involving Human Subjects and were approved by ETH Zurich Ethics Commission (approval no. EK 2018-N-94, 18 January 2019) and by the Institutional Review Board of Nanyang Technological University (reference no. IRB-2019-04-025, 23 May 2019).
This study has been pre-registered prior to data analysis (https://osf.io/q5hnk/).
The experiment was conducted during the period from June to December 2019 in the courtyard of National Institute of Education on the campus of the Nanyang Technological University, Singapore. Students, staff and visitors of the University constitute the sampling population. Participants were recruited through posters, placed on campus, advertising the study. Eligibility requirements listed ages of 21 to 55 years, an overall physical fitness level necessary for walking in outdoor environments and an absence of medical conditions preventing prolonged walking in outdoor spaces.
For each experimental session a 1.5 h time slot was reserved. Participants arrived at a predefined instruction spot located in the outdoor environment, protected from direct sunlight. After studying the information sheet and providing their informed consent, the participant was asked to fill the pre-experiment survey (can be found in pre-registration) containing questions on socio-demographic characteristics of the participant, his/her attitude towards Singapore’s environment and his/her lifestyle. Upon finishing the survey, a physiological wearable sensor (wristband) Empatica E4 was attached to each participant for the purpose of physiological monitoring (data not reported in this paper). The participant was asked to read a short story (for the purpose of recording their baseline physiological signals measured by Empatica E4), after which instructions for the experiment followed. After the participant confirmed his/her readiness, an action camera was put onto her/his chest, to serve the purpose of registering the decisions and the environmental events during the experiment, e.g. start and end of each trial or appearance of the sun.
The participant was directed to the start of the experiment and informed once again about the procedure of the experiment. The participant had to make choices which were given in a choice set booklet (see Appendix A for the choice set booklets given to participants). Trial 0 served the purpose of exploring the environment, in it the participant was asked to walk around the lawn and reach the target. Subsequent trials (trials 1 to 13) were asking participants to reach the target with the paths specified by arrows in the booklet. The target of the previous trial served as the origin of the current one. The participant was asked to visually identify the target and path options in the environment at each decision point. Next, the participant was asked to make decisions based on his/her own preferences, as there was no correct or incorrect choice. The participant was informed, that he/she was not tested for the speed of trial completion. Participants were provided a water bottle to avoid dehydration and were explicitly asked to make use of it at their own discretion. The experimenter has left the participant to complete the trials and was observing the participant from a distance without giving additional instructions. Participants were asked to indicate their need for any help by standing still and raising their hand. Participants, who required intervention of experimenter in their walking trials due to environmental conditions (rain), confusion of paths or other reasons, were dismissed from the analysis reported in this paper. Upon finishing the last trial, the participant was met by the researcher and led back to the instruction location, where sensors were detached. The participant was then asked to fill in a post-participation survey, containing questions on the overall state of the participant, as well as on their motivation for each of the chosen paths, evaluation of climate sensation, perception and acceptance during the trials. After completing the experimental procedures, the participants were debriefed and compensated for their participation with 20 Singapore dollars in cash. Neither recruitment, nor instruction materials included an explicit formulation of the research question of this behavioural study to minimize the bias in their behaviour. Instead, the goal of the study was formulated as follows: ’The goal is to investigate navigational attributes, or features, of outdoor ambulation in a variety of environments within Singapore. In addition we plan to focus on the environment’s influential factors’.
In total 74 participants took part in the experiment. Of them 4 had missing data or could not complete the experiment due to rain, 3 were dismissed due to failing the dummy trial, 9 took unspecified paths or had other navigational problems, which required intervention by the experimenter, 2 participants managed to self-correct their incorrect paths without the experimenter’s intervention, but were still dismissed from the analysis in this study.
Data processing
The raw datasets resulting from the experiments consist of the video shot on the camera mounted on the participant’s chest, physiological signals originating from the Empatica E4, responses to pre- and post-experimental survey, microclimate data recorded by two Kestrel 5400 portable weather stations installed in the sun and in the shade. In the current paper the data extracted from video recordings was used.
The video-recording of each participant was processed by student research assistants according to a protocol by entering all events from the video into a spreadsheet of a predefined structure. Times on the video, wristband and experimenter’s smartphone were synchronized by matching the synchronization events on the video with camera’s time. The following events were coded by participants:
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1.
Decision event: start by participant of a particular trial.
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2.
End of trial event: participant stepping on the target of the current trial.
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3.
Sun presence event: alteration of sun from one state to another. States are:
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(a)
full sun (sharp shadows are visible on the ground);
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(b)
cloudy sun (soft shadows are visible on the ground);
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(c)
no sun (sun is behind the clouds and no shadows are visible on the ground).
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(a)
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4.
Sun exposure event: alteration of exposure to sun from one state to another. States are:
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(a)
No shade (participant walks on the surface exposed to the sun).
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(b)
Tree shade (participant walks on the surface covered by the shadow cast by the tree).
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(c)
Building shade (participant walks on the surface covered by the shadow cast by the building).
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(a)
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5.
Water intake event: it appears at recording that participant is drinking water.
For each of the event the following attributes are recorded:
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1.
Event code;
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2.
Time of event;
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3.
XY-coordinates of approximate location of event probed with the mouse click in the realistic model of the space and sun position (described in the next section);
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4.
For decision events only: indicator of whether option A path was chosen by participant.
All the decisions and end of trial events were cross-coded by two student research assistants and checked for agreement of decision label, sun presence and timing. Data coding disagreements (events disagreeing in decision label, in sun presence or in start or end time by more than 5 seconds) were resolved by a third person (experimenter).
Events data was used in the current study and provided information on decisions made by participants and on the presence of the sun at the moment of decision (determining whether decision is considered as treatment one). Timing information of decision events was used for calculation of the sun-shade composition of the path options by adjusting the sun position in the model described in the following section.
Events diverging from the standard experimental procedure (e.g. intervention of experimenter or participant making a shortcut), or potentially ambiguous events (e.g. uncertainty regarding presence of the sun) were recorded by data coders in the notes file, which was then reviewed by the experimenter and which informed the consequent treatment of the participant’s data (e.g. dismissal from the analysis).
Calculation of the sun-shade composition of the path options
The 3D model of experimental area was created and imported into a Unity 3D game engine and visually validated for the realistic reproduction of the shading of the walking paths (see Appendix B for a comparison of video shots and reproduction of them in the model).
All the path options were incorporated into the 3D model as the polygons covering the walking surface. As the paths along the building are 6 m wide, they were divided in 5 strips (each 1.2 meters wide). Thus, each path option had 5 polygons (path strips) assigned to it. When calculating the sun-shade composition of the path options at particular trial, the time information from the event files was used to adjust the sun position in the model. Then the rays covering each polygon of a path option (on a grid of 0.1 (times) 0.1 m) were shot in a direction towards the sun. The intersection of each ray with tree or building was detected and then the fractions of rays not hitting anything, hitting a tree and hitting a building were considered as the fractions of the sun, tree shade and building shade on a particular path option polygon. The intersection of the rays with the tree were detected as their intersection with the convex hull around the tree crone, thus the tree shades rendered by Unity 3D and those considered in calculation of sun-shade composition of path options may differ slightly. For each path option, the polygon (strip) with the lowest fraction of the sun was considered as representative of the overall sun-shade composition of the path option. Building shade that covered less than 15% (i.e. less than 0.9 m) of the wide paths along the buildings was denoted as insufficient to be considered by the participants and path options with such shading pattern were parameterised as having no building shade.
The length of the path options was calculated as the sum of the lengths of their segments. These were measured with the use of a laser distance meter by two researchers one operating the meter and another holding a mark at which laser was shot. An average of three repeated measurements was taken as a length of path segment. Additionally, the distance from each tree to selected anchor point in the area was measured and 3D tropical trees were placed in corresponding locations in the 3D model. The dimensions of each tree were adjusted to closely match the shading recorded by the chest-mounted action camera during the experiment in two different seasons. See Supplementary materials for comparison of the 3D model with the camera shots.
The length of the sun-lit stretch, tree shade and building shade along the option was calculated as the length of the path multiplied by the fraction of each component (calculation of which is described in the paragraph above).
Hierarchical model of the choices
We define the following cost function of the path option:
$$begin{aligned} c^{(A)}_{ji} = beta _{j}[a^{text {sun}}_{ji} + (1-rho )a^{text {tree}}_{ji}]+ a^{text {shade}}_{ji} + rho a^{text {tree}}_{ji}, end{aligned}$$
(1)
where (a^{text {sun}}_{ji}), (a^{text {tree}}_{ji}) and (a^{text {shade}}_{ji}) are the metric distances in the sun, in the tree shade, and in the building shade respectively, of path option A of trial i presented to participant j. (beta _j > 0) is the participant specific distance-inflating coefficient (cost factor) of walking under the sun, (rho in [0, 1]) is the parameter of shade intensity (relief) associated with tree shade, common to all the participants. Assuming an equivalent definition for the cost of option B ((c^{(B)}_{ji})), the difference in the option costs is:
$$begin{aligned} Delta c_{ji} = c^{(A)}_{ji} – c^{(B)}_{ji}. end{aligned}$$
(2)
The probability of choosing path option A (p(y_{ji}=1)) is modelled by logistic function widely used in dichotomous choice models37:
$$begin{aligned} p(y_{ji}=1|Delta c_{ji};beta _j, rho , tau _k) = frac{1}{1+exp (Delta c_{ji}/tau _k)} end{aligned}$$
(3)
where (tau _k) is the cost-difference-scaling coefficient specific to a choice set (k in {1, 2}).
The hierarchical model of the participant choices described in the Eqs. (1, 2 and 3) has the following prior belief distributions of the model parameters:
$$begin{aligned} {begin{matrix} &{} d, e sim text {Normal}(0, 1) \ &{} beta _j sim text {Gamma}(exp [d+e], exp [d-e]) \ &{} tau _k sim text {Gamma}(12.5, 50) \ &{} rho sim text {Beta(1, 1)} end{matrix}} end{aligned}$$
(4)
Here the chosen way of parameterisation of distribution of (beta _j) helps to avoid high correlation in parameters of (text {Gamma}) distribution, allowing the NUTS Hamiltonian Monte Carlo sampler to explore the parameter space more efficiently, to prevent divergence and help faster convergence.
The prior for (tau _k) is chosen such that (E[tau _k]=0.2) – an approximate average down-scaled (by factor of 0.01) length difference between the path options.
The full diagram of the model is provided in Fig. 4.
Figure 4
Graphical representation of the hierarchical model of path choices. All variables are continuous except binary (y_{ji}). Observed variables are shaded, unobserved are not shaded. Of unobserved variables, stochastic ones are single-bordered, deterministic are double-bordered. The figure is generated with use of package daft v0.1.0 (https://docs.daft-pgm.org/en/latest/) for Python v3.7.7.
Markov chain Monte Carlo estimation of the model parameters
We have used the PyMC338 probabilistic programming framework for Python to estimate the parameters of the model. We have used the standard No-U-Turn Sampler47, which is based on the principles of Hamiltonian Monte Carlo sampling. The number of chains used is 4, the number of tuning steps is 2000, the number of samples is 10,000 per chain. These parameters achieved a rank-normalized (hat{R}=1.0) and effective sample size (>2500) for all parameters. Thus, there is no indication of lack of convergence of the MCMC sampler.