## 4 Methodology
### Index of Social Transport Needs  
Based on previous methodologies [54; 57; 58], the Index of Social Transport Needs (ISTN) incorporated socioeconomic and housing dimensions, following the wide evidence that social transport needs are different according to income, age, vehicle ownership, gender or education [59; 60; 37; 61; 62]. Transport disadvantage has a greater impact on particular categories that include the elderly, people with health problems, low incomes groups, those living in conditions of poverty, unemployed or disabled people [63; 64; 65; 66; 25; 31; 59; 26; 67; 68]. The ISTN incorporated nine transport disadvantage indicators with their variables: disability; educational level; elderly; childhood; unemployment; illiteracy; low income; vehicle ownership and gender. The combination of the variables of these indicators provides an index of social transport needs, produced with the most important explanatory factors of transport disadvantage. Interestingly, gender was incorporated through the variable \"female-headed households\". Gender has a decisive influence on possibilities for moving through the non-central regions of the metropolis, as well as on ways of linking with the main metropolitan activities [55; 57; 63]. In the case of the metropolis in developing countries, [PERSON] and [PERSON] [41] showed that female-headed households make less use of the car and spend less on transportation than male-headed households, due to the prevailing conditions of poverty and the greater deficiencies in the public transport systems. The ISTN were calculated as the weighted sum of these variables within the GS. Equation (3) shows the algorithm used to compute this. It was normalized adapting Equation (2). Equation (3). Index of Social Transport Needs (ISTN)  
\[\text{ISTNj}=\sum_{\text{i=1}}^{8}S_{\text{ij}}\times W_{\text{i}} \tag{3}\]  
where \(\text{ISTNj}\) = Index of Social Transport Needs at GS j; \(S_{\text{ij}}\) = Social indicator i at GSj; \(W_{\text{i}}\) = Weight of the social indicator i. The weighted values of socioeconomic and dwelling variables are listed in Table 3.  
Principal component analysis (PCA) is a statistical technique usually used in academic studies concerning the social dimension of transport [68; 69; 70; 71], as well as in the evaluation of social public policies in Mexico [72]. The PCA describes correlations between a set of variables by creating new components that propose weights for the original variables. The purpose of the PCA is to obtain a small number of linear combinations of the dataset that account for most of the variability in the data. Each component can be interpreted as one part of the social transport needs. A negative value means that this variable negatively affects the phenomenon. The variability of the original data is an indicator of the analysis performance. The higher the variability, the better the components account for the phenomenon. The component calculated in this study accounted for 76% of the social transport needs. Table 3 shows the factors which better explain transport-related social needs (TSN) in the city. Principal component analysis (PCA) was inputted with 214 socioeconomic and dwelling variables for the 1834 GS [73]. The PCA reduced the dimensionality of the social data set. The fraction of variance explained by the first principal component accounted for 76%. The weights of the first principal component rotated matrix of PCA referred to transport disadvantage. The weights of the main component variables shown in Table 3 totaled 1.0, as they were previously normalized to be included in subsequent calculations. The weight values represent the contribution of each indicator to the social needs of transport in the GMA. These are valid only for the analyzed data set. As shown in Table 3, the weight assigned to \"vehicle ownership\" represents only 6% of the indicators related to the disadvantage of transport for each GS.