2.5 Statistical modelling

The variable of interest–FoS–is an ordinal variable, measured, as previously mentioned, on the following 4-point Likert scale: feel very unsafe (0), feel little unsafe (1), feel reasonably safe (2), feel very safe (3). Therefore, the ordered logistic regression [32] was employed for the analysis. In this regression, explanatory variables (or predictors) "push" the dependent variable, either upward or downward, to adjacent categories [33, 34].

To identify the impact of different PSL attributes on FoS, we used PSL attributes and controls (see S4 Appendix) as predictors for FoS in a set of nested models. The first model included PSL attributes only. In the second model, we appended dichotomous city variables (dummies) to account for unobservable inter-city differences, not captured by other variables. Lastly, in the third (augmented) model we appended social demographic, temporal and environmental factors (see S4-S7 Appendices).

To run the models, we coded the categorical variables as indicators, i.e., assigned the value of 1 if the category of interest is compatible with the observation (otherwise 0), thus making it possible to test the effect of a specific category, such as the city in which the measurement was taken, on the regression results [35]. The estimated models are represented by the following equations:

where:

y_i = logp(FoS≤j)p(FoS>j) with p(FoS≤j)p(FoS>j) the odds of FoS being less than or equal to a particular value category;

i (1, …, 25,940) = observations in the whole dataset;

j (0, …, 3) = assessment categories provided for each PSL variable;

l (1, …, 257) = assessment points;

s (1, …, 380) = observers;

p refers to probability;

p(FoS≤j) is the cumulative probability of FoS being less than or equal to a specific category, where j = 0, …, 3 since p(FoS = 4) = 0;

PSL = vector of subjective PSL assessments, which include illumination, light color temperature, light uniformity and glare (see Table 1), while β is their vector of corresponding regression coefficients;

CITY = vector of cities dummies (see Table 1); γ is their vector of corresponding regression coefficients;

SOC = vector of socio-demographic attributes, which include age group, gender, country of birth and education (see Table 1); δ is their vector of corresponding regression coefficients;

ENV = vector of environmental dummies, which include traffic intensity and vegetation density (see Table 1); η is their vector of corresponding regression coefficients;

TEM = vector of temporal dummies, which include the month and time of the measurement (see Table 1); θ is their vector of corresponding regression coefficients; and α is vector of intercepts estimated by the models.

The analysis was performed in the open source "R" software, using its polr function from the "MASS" library.