How building layout properties influence pedestrian route choice and route recall

Figures & data

Figure 1. An example of how a building layout is represented as a spatial network.

Figure 2. Generation of spatial networks: (a) a regular grid with 25 nodes arranged; (b) adjusting the regularity of the grid of nodes; (c) the Gabriel graph based on the nodes; (d) reduced Gabriel graphs with a lower average degree.

Figure 3. Distributions of building layout properties (the definition of properties can be found in Table 1).

Table 1. Summary of the measures of building layout and route properties.

Measurement	Factor	Definition	Purpose
	Randomness	The maximum ratio of the coordinate offset for each node compared to the original coordinate and the default distance between any two nodes(d)	To measure the regularity of the network
Building layout measurements	Average degree	The average number of edges per node in the network	To measure the connection between nodes
	Average path length	The average number of steps along the shortest paths for all possible pairs of network nodes	To measure the efficiency of transport on a network
	Relative distance	The ratio of the length of the chosen route and the shortest route among all possible routes	To measure how close the selected route is to the optimal route in terms of distance
	Relative number of turns	The ratio of the number of turns in the chosen route and the smallest possible number of turns across all possible routes	To measure how close the selected route is to the optimal route in terms of the number of turns
Route measurements	Relative accumulated angle change	The ratio of the accumulated angle change between consecutive links in the chosen route and the smallest possible value for this measure across all possible routes	To measure how close the selected route is to the optimal route in terms of the accumulated angle change
	Proportion of the path on the edge (edges are the outside limit of the building and contain all periphery nodes of the grid)	The number of periphery nodes passed by a route divided by the total number of nodes included in this route	To measure the tendency of people to follow the linear physical heterogeneities of the environment
	Large turn preference	The number of turn angles between consecutive links on a route that are greater than ${45}^{\circ }$ or ${90}^{\circ }$	To measure the preference of people choosing the turn with a greater angle

Figure 4. Still images of the virtual experiment as seen by participants on screen for the first task (a) and the second task (b).

Figure 5. Distributions of route properties as shown in Table 1.

Table 2. Statistical analysis of the behaviour of pedestrians walking along the periphery of spatial networks.

Effect	Estimate	SE	F	P
Intercept	−13.72	3.167	−4.3323	$1.4759\times {10}^{-5}$
Randomness	38.462	14.395	−2.6719	0.007543
Average degree	3.3221	0.87171	3.811	0.00013838

To distinguish participants completely following the periphery of the network, the response variable is a Boolean indicating whether the participants choose the path that is all on the edge of the building or not (1 for yes, 0 for no). Explanatory variables are the building layout properties randomness and average degree. Average path length is excluded from the model because of its high correlation with average degree (R = −0.6746, p = 0.00). P-values less than 0.05 are shown in bold. Positive parameter estimates correspond to it being more likely that participants choose to walk along the edge of the building.

Figure 6. Distributions of measures for route recall in the first task of the experiment. (a) shows the route similarity measure, (b) the difference in length, and (c) shows the difference in accumulated angle change between the initial route and the recalled route. Negative values in (b,c) indicate that the initial route was longer or had a higher value of the accumulated angle change, respectively.

Table 3. Statistical analysis of route similarity.

Effect	Estimate	SE	F	P
Intercept	11.386	3.0509	3.7321	0.00019
Average degree	−1.421	0.6035	−2.3545	0.018548
Relative distance	−2.889	1.4528	−1.9886	0.046741
Relative accumulated angle change	−0.41698	0.21033	−1.9825	0.047425

P-values less than 0.05 are shown in bold. Positive parameter estimates indicate it is more likely that participants select a route that is similar to the route they used to reach the destination and vice versa. We fit a Generalised Linear Model with binomial errors and a logit link function.

Table 4. Statistical analysis of distance using a standard linear model.

Effect	Estimate	SE	F	P
Intercept	0.20063	0.058337	3.4391	0.00064525
Average degree	0.0078684	0.01058	0.7437	0.45749
Relative distance	−0.19653	0.032982	−5.9588	$5.5988\times {10}^{-9}$
Relative accumulated angle change	−0.0046288	0.00495	−0.93511	0.3503

The response variable is the difference in distance between the initial and the recalled route. It is positive if the recalled route is longer and vice versa. The explanatory variable is the relative distance of the initial route participants chose compared to the shortest possible route. $P-\mathrm{values}<0.05$ are shown in bold.

Table 5. Statistical analysis of the accumulated angle change.

Effect	Estimate	SE	F	P
Intercept	0.30917	0.278	1.1121	0.26676
Average degree	0.060017	0.050418	1.1904	0.23461
Relative distance	−0.24322	0.15717	−1.5475	0.12255
Relative accumulated angle change	−0.12759	0.023589	−5.4089	$1.0968\times {10}^{-7}$

The response variable is the difference in accumulated angle change between the initial and the recalled route. It is positive if the recalled route has a higher value of the accumulated angle change and vice versa. The explanatory variables are the average degree of the building layout, the relative distance and the relative accumulated angle change of the initial route participants chose compared to the shortest possible route and the route with the smallest accumulated angle change. $P-\mathrm{values}<0.05$ are shown in bold.

Table 6. Statistical analysis of building layout preference.

Effect	Estimate	SE	F	P
Intercept	1.1173	0.2036	5.4878	$4.07\times {10}^{-8}$
Difference in randomness	−0.5049	0.2254	−2.2401	0.02508
Difference in average degree	0.1050	0.2256	0.4658	0.6414

The response variable is a Boolean variable indicating whether participants choose the destination in the building they entered (0 for no and 1 for yes). Explanatory variables are the difference in the randomness parameter and the average degree between the first building and the second building. $P-\mathrm{values}<0.05$ are shown in bold.

Figure A1. Still image of the virtual experiment as seen by participants on screen before route choice tasks start.

Figure A2. Route comparison of the first and second leg for the participants who selected different destinations in the second task of the experiment. Dashed horizontal lines show the mean of the data.