2.4. Map Algebra to Identify Potentially Accessible Areas

Map algebra constituted our main strategy for obtaining one output layer from the combination of several input layers processed through an algorithm. To compute the accessibility of different neighborhood sectors, we calculated a weighted sum of the layers (representing each of our variables). This process combined a series of steps. First, we homogenized our data format by converting every layer into a regular grid or 5 m raster format (due to the study’s fine scale) and then normalized the criteria by reclassifying the input raster values into a common rating scale. When the input criteria layers used different numbering systems, i.e., with different units (percentages, distances), each cell (pixel) of each criterion had to be reclassified using a common scale. The study of accessibility in urban contexts is a multifaceted topic, and the generality of the term accessibility has led to there still being no consensus in the scientific literature on how to qualify it precisely [59]. Our model used five levels of accessibility (very low, low, moderate, high, and very high), levels based on the availability and proximity to a service, commerce, or a bench, and the difficulty of the travel due to slopes and gradients, which allowed us to perform arithmetic operations using values that had originally been of different types (Table 2). Subsequently, each variable (input layer) had to be weighted by its percentage of influence, which was assigned to it according to the characteristics of the profile of the population studied. The choice of weighting criteria for each variable was based on the available literature studying the relationship between neighborhood physical environmental attributes and older adults, which is developed in detail in Section 2.4.1 (e.g., [4,60,61]). Once the weighting criteria were established, and validated collectively by the team, a weighted linear combination or weighted sum analysis was applied, illustrated by Equation (1) [62], in which the cell (pixel) values of each input layer (variable) were multiplied by their respective weighting coefficient and these results were summed to produce a final output layer representing the potential accessibility of the neighborhood.

Weightings for calculating accessibility levels for each older adult profile.

Note: Rank corresponds to the values (meters and percentages) determined for the accessibility calculations for each variable. * Services and facilities, for the calculation of Profile 2, were divided into health services (health centers, specialized health facilities, and pharmacies) and other services and facilities (see Table 1).

The weighted sum is illustrated in the following equation:

where PA is the potential accessibility, n is the total number of variables, r_i is the variable or input layer, and w_i is the weight assigned to each variable or input layer.

Although the major contribution of the literature on social gerontology is its emphasis on the diversity of ways of aging, the literature combining quantitative research on living environments and aging [63,64] does not seem to dwell on this. Although some qualitative spatial research methods appear in studies on aging [65], few have compared the perceptions of different groups, such as various ethnic groups or people with disabilities [49,66].

The benefit of distinguishing several population profiles (in our model, three) is taking advantage of both types of approaches, namely quantitative and qualitative. The weighting given to each variable for calculating accessibility according to each of these profiles is, therefore, not necessarily representative of every individual due to our study’s experimental nature (Table 2). It should be noted that the choice of weighting for each variable was based on the available literature where the needs and/or physical and health characteristics of each profile are reported.

Because the presence of nearby services and facilities that promote physical activity among a neighborhood’s older adults represents one of the most important aspects found in the relevant scientific literature [31,33,43], this variable was given a higher weighting (45%) than the others; we considered five groups of services and facilities (Section 2.2.3). We considered that gradients (10% weighting) did not present a disadvantage to healthy older adults, and we assumed that they would have many more leisure and recreational outings, and therefore benches would be a more important variable for them (45% weighting).

Although physical activity is a recognized element in the prevention and management of many chronic diseases associated with aging [43,67], levels of physical activity tend to decrease progressively with age [60,68]. Diabetes among older adults is an increasing worry in Western countries [69]; in France, a quarter of type 2 diabetics are over 75 years old, with an associated lower life expectancy and excess mortality [70]. Therefore, for this group of older adults who need recurrent medical treatment, the presence of nearby health services (health centers, specialized healthcare, and pharmacies) was given greater importance (40% weighting) than other services and facilities (municipal facilities and services, social and cultural facilities, shopping, and school and childcare facilities) (10%), the presence of benches (30%), and the gradients of the neighborhoods (20%).

As adults age, they may experience a decline in their ability to walk safely, so some use assistive devices such as canes or walkers [71]; therefore, the ability to move around the community safely and easily plays a key role in the lives of people who use mobility devices [49,61]. Although the sense of use of mobility or assistive devices may have a negative effect (ageism) on self-representation as “old” due to others’ views equating it with the limitations of old age [72]. The mobility of these older adults will be strongly influenced by travel conditions [61]; a lower slope correlates with greater overall participation (40% weight), the presence of various public and commercial services in the neighborhood correlates with greater participation in recreation and cultural activities [73] (30% weight), and the presence of resting places (benches) in parks, on trails, and in stores correlates with greater motivation to get out and walk longer distances [41,49] (30%).