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Predicting and mapping the location of an estimated population from a survey: an applied method

Cartographie d’une population estimée à partir d’une enquête: une méthode appliquée.
Philippe Gerber, Sébastien Fleuret et Marc Schneider


À partir d’une enquête réalisée en 2002 auprès de personnes âgées résidentes de la ville de Luxembourg (N = 903), ce texte présente une méthode originale visant à projeter spatialement les individus enquêtés âgés et leurs poids individuels respectifs, déterminés selon les standards de la théorie des sondages, afin de généraliser les résultats de l’enquête sur des aspects relevant de la santé des populations. Le principal enjeu de cette méthode est ainsi d’être en mesure d’agréger des informations individuelles (cartographie ponctuelle) de la totalité des personnes âgées pour produire une information discrétisée (cartographie surfacique) sur le bâti résidentiel de la capitale luxembourgeoise. Ce changement de dimension est obtenu par une procédure de projection spatiale aléatoire qui rend possible la cartographie des résultats de l’enquête à fine échelle et pour l’ensemble de la ville.

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1One frequent challenge, for estimating health and health services needs, is to be able to generalise results from case studies, in order to plan health policies at different scales, and especially the finest ones. In other words, it is about being able to switch from the individual scale (point mapping) to the scale of the group and further, to the level of the entire population (area mapping). A local area survey, that is designed to be reliable at ward level, uses a valid field instrument and is characterised by high response rates can be regarded as the‘gold standard’ (Twigg and Moon, 2002). Tackling this issue, this text presents a methodology for mapping a survey which achieves this dimensional change by using a map projection procedure linked with direct statistical weighted estimations.

2A broad theoretical background asserts the importance of the local spatial structure related to social, economics, health and wellbeing indicators (Kaplan, 1996; Curtis & Jones, 1998; Kearns & Gesler, 1998; Kawachi & Berkman, 2000; Hillemeier et al., 2003; Williams, 2003). We used this theoretical background to predict the localisation of an estimated population liable to health relevant problematics.

3In 2002, a survey on elderly was conducted in the city of Luxembourg. The primary results gave a global image of the living conditions of the elderly, but it appeared necessary to go further and, therefore, to generalize the results obtained from 903 individuals to the entire population. From a sample, and using weighting procedures (Deville, Sarndal, 1993), it is possible to give a global explanation of the survey results. But this procedure only gives a general vision. Yet it could be of great interest for urban and social planners to have a tool allowing a precise mapping of survey information.

  • 1 A concrete application is presented for example in Heady P., Clarke P. et al., 2003.

4Some attempts in this direction have already been made using techniques of synthetic estimation, deriving from the correlates of a particular behaviour or phenomenon from a large-scale survey or pre-existing study and applies those correlates to local data (Twigg and Moon, 2002). The most advanced forms of this techniques use multilevel modelling. Despite undeniable qualities1, multilevel-based estimations are constrained to delineated (administrative) areas. “Although large scale, well-designed studies (…) provide information on some of the more important health-related behaviours (…) they do not provide reliable estimates below the standard region or health authority level, respectively (Twigg & Moon, 2002). A third limitation was discussed by Twigg and Moon (2002) who have demonstrated that: “clearly the disparities between the estimates based on surveys and on multilevel synthetic estimation are of concern”. Finally, the synthetic estimations have an explicative goal: they are usefull to analyse, to predict, to simulate or to explain. But this tool is not the most appropriate while aiming at giving spatial representations.

5The method that we present in this text does not lack statistical estimation: the survey sample is statistically and spatially weighted. Proceeding with synthetic estimators would have added a second statistical estimation where we were looking for a geographical estimation, in other words, placing points on a map using spatial (not statistical) criteria. Moreover, the synthetic estimators tend to desagregate the informations, our will was to aggregate it in drawing maps.

6Thus we developed an original method based on the theoretical assumptions from the Chicago’s school of sociology (Grafmeyer, Isaac, 1979) leading to consider the city as a social-residential mosaic (Timms, 1971), and from the general law of spatial autocorrelation leading us to take into account euclidian and social distances between individuals showing similar profiles. In other words, this method consists in a spatial scattering taking into account (i) social and economic characteristics of the entire population (by calculating a mean distance on the basis of socio-economical profiles), (ii) characteristics of the elderly’s wellbeing, (iii) and the contribution of mapping technical knowledge.

7The first part of this article is a summary of the objectives of the survey on elderly conducted in 2002 in the city of Luxembourg. The second part sets our method to get a geographical approximation of a population estimated from a survey sample. The third part presents the tests conducted to validate the procedure. Finally, we show examples of possible applications.

The survey ECL

8Originally, the survey ECL (Elderly, city of Luxembourg) aimed at collecting data about the health and the quality of life of the elderly with the assumption that health, standards of living, and social capital are therefore determinant factors (Gerber, 2006). Individuals were interviewed using a questionnaire tackling several aspects like composition of the household, the housing comfort, standard of living, perceived health, neighbourhood, access to public transportation, assistance and supports that the person felt able to mobilize…

9Finally a data base was produced on a sample of 903 elderly people, representative of the entire population of elderly in the city (namely 12615 people). Given the scale (infra-city) and the variations observed from one city-district to another, the sampling design was geographically stratified. Six areas (or “geographical strata”) were defined to account for the local heterogeneity of the socio-demographical composition in the different districts of the city (fig. 1) to guarantee the statistical inference, essential for the sampling procedure (Lindsey, 1973).

10Thus the sampling was random-based, but controlled by geo-based criteria. Afterwards, a raking procedure permitted to give a relative weight to each interviewed individual according to his representativeness in terms of all the criteria presented on the table 1. Indeed we wanted to calibrate our estimations with the information enclosed in the population file with regard to the bias detected by the analysis of the non-responses (for more details about the explanation of non-response, see Gerber, Bienvenue, 2004). The calibration estimator (Deville et al., 1993) arising from this raking procedure is asymptotically equivalent to a regression estimator. Thus the estimation of a population Y is given by:


ŶHT = Y estimated with the Horvitz-Thompson (1952) estimator,

wk= weighting estimation

k= variable from the survey, and matrix calculation with X = matrix of all the variables used in the weighting procedure and is estimated with the Horvitz-Thompson (1952) estimator.

11The sum of the 903 relative weights is equal to the total population of elderly in the city of Luxembourg (see Gerber, Bienvenue, 2005 for more details about the results of weighting procedures).

Figure 1: Constitution of the 6 geographical strata in the city of Luxembourg.

Figure 1: Constitution of the 6 geographical strata in the city of Luxembourg.

Tab. 1: Criteria of representativeness for the calculation of the relative weight.

12The results of the survey were processed to a principal component analysis and a hierarchical ascending classification, based on eight social and three demographic quantitative indicators on elderly (see Gerber, 2006 for the construction of the variables, and table 2).

Principal component analysis

Factor 1

Factor 2

Factor 3

Factor 4


Objective health status






Subjective health status






Home care availability






Subjective comfort






Available supports






Household size






Standard of living






Objective comfort (facilities)












Institutionnal assistance received






Relational assistance received












Variance components






Tab. 2: Quantitative Variables used in the Principal component analysis.

13By doing so, we came to a hierarchy of factors essentially structured by: the perceived health and subjective wellbeing; the standards of living; the conveniences and the age. From this analysis, 5 profiles were determined with a hierarchical cluster analysis (see fig. 2):

  • Profile 1 (9.3 % of the elderly): “aged persons with very limited autonomy”,

  • Profile 2 ( 25.1 % of the elderly): “aged & lonely person with low income and low level of support”,

  • Profile 3 (9.6 % of the elderly): “aged & lonely person with high income”,

  • Profile 4 (19.5 % of the elderly): “aged and healthy persons with good living conditions”,

  • Profile 5 (36.5 % of the elderly): “young elderly”.

Fig 2: Socio-residential profiles and individual elderly profiles and classification

Geographical approximation

14These profiles can be useful for turning public policies toward services adapted to the different types of needs of the elderly. However, to go further, it appears necessary to be able to localise areas where some characteristics are so clustered that an intervention is needed. For example in case of a high amount of lonely elderly with weak health in a neighbourhood. Therefore, we developed a geographical approximation based on the consideration that the neighbourhood of the individual is fundamental. But according to Grasland et al. (2000), we consider as a mistake “to reduce the production of continuous maps of social phenomena to a classical problem of estimation of a surface derived from a sample of points for which exact value is known.” Thus we developed a method using a combination of complementary criteria.

The method

  • 2 We tested this tool by mapping the location of elderly over 60 from the survey and from the census (...)

15Nowadays, the Geographical Information Systems (GIS) contain a lot of tools that are easily available like the “kriging” or “smoothing”. These tools allow spatial estimations of a random projected population. However the cartography that arises from using one or the other is not satisfactory2 because it is not adapted to our problematic. For example, the kriging is based on isolines and is thus not adaptable to the borders of the census tracks (Arnaud, Emery, 2000). Moreover the kriging is a tool for continuous variables but we also need to deal with discrete variables (for example, it is not appropriate to map a qualitative taxinomy using kriging). Another method could be used to produce spatial estimations: Kernel Density Estimation (KDE: Silverman, 1986). This method is useful to estimate a continuous density (spatially) from observed data (survey), especially in social sciences studies (Waller, Gotway, 2004). The benefit of such a method based on an estimation of a probability density is to make a mapping subsequently possible. However, the application of the KDE to our problematic suffered some limitations.

16First, this method does not keep the memory of the individual initial information but creates a ratio which erases the attributes of each individual to the detriment of any spatial allocation. Now, our goal is (i) to restore an individual information with regard to social demographic constraints and characteristics, and (ii) to proceed to a spatial diffusion of this information with regard to spatial constraints and characteristics.

  • 3 When « border effects » arise in KDE method, this can be weakened in a way that does not remain an (...)

17The second limitation of the KDE is the apparition of border effects3 located at the periphery of the study area. This bias does not appear in the chosen methodology that we will present hereafter.

18In our approach, the value of each individual relative weight in the sample determines the estimated number of individuals that we want to project randomly over a residential controlled area to obtain a geographical approximation of the entire elderly population, point by point, individual by individual. For example, if an individual X with a common profile is representative of 16 individuals of the estimated entire population, we will generate 16 points that we will randomly localize over the controlled area. These 16 points will have the same characteristics as the point of origin. Likewise, another individual with a lower weight would, for example, only generates 2 points around him. This procedure is called “projection”. In our case study in Luxembourg, the average weight is 13.953. This weight has to be considered as a multiplier factor used to calculate an estimation of the global population from the sample of 903 individuals.

The projection: how and where? The method step by step

19The GIS offers an automatic task for random localisation. However, according to our theoretical postulates (neighbourhood effects and importance of the local spatial structure), we had to proceed to a random projection of theoretical individuals within a controlled perimeter. Moreover, according to Grasland & al. (2000), we stipulate that “all the interactions are captured by an effect of the distance”. And accepting Tobler’s first law of geography we state that “Everything is related to everything else, but closer things more so”. So we had to define the perimeter of projection regarding the distance between one individual and his neighbours. The goal was to ensure that each individual of the sample generates a random localisation only over areas having a similar profile to his residential area.

20We decided to control 3 criteria to define the proximity between each individual in a contextual frame (see figure 3, steps 1, 2 and 3), according to the concept of neighbourhood developed in health geography (Kawachi & Berkman, 2003; Flowerdew, Manley and Sabel, 2008):

  • the limits of the 6 geographical units (strata, see figure 1.C) used for the sampling.

  • the 5 types of elderly (individual profiles, results of the principal component analysis on the survey data) (see figure 2).

  • a socio-residential profile that we estimated using principal component analysis, according to urban factorial ecology (Berry, Kasarda, 1977). This method allowed us to define five socio-residential profiles based on 45 variables calculated from the census 2001 (see Gerber, Pruvot, 2005). But as the city of Luxembourg is small (80 000 inhabitants), a subdivision in 5 profiles did not guarantee the representativeness of the smallest areas. That is why we decided to use only 2 profiles (see figures 2 and 3.2). In the case of a study on a city, with a bigger population, it would be possible (and useful) to use a greater number of profiles to ensure more accuracy and reliability.

Fig 3: The complete procedure of the random projection areas.

21To summarize, we use 60 probabilities (figure 3.C) to calculate 60 homogeneous groups for a random projection. All these criteria are overlapping.

  • 4 The Euclidian distance is preferred to a Manhattan distance because the calculation applies to an e (...)

22The fourth step of the procedure consists of drawing a circular zone (called buffer in the GIS) around each individual location. To calculate the radius of the buffer, we measure the distance between each individuals of a same homogeneous group of randomisation as shown on the figure 4 (also appearing in fig. 3, step 4). This map shows an example of individuals who belong to the geographical stratification number one and to the individual profile “aged with low autonomy” and to the less deprived socio-residential profile. This group encounters 3 individuals. We measure the distances between them. The mean of theses distances gives the radius. In this calculation, an euclidian distance matrix from each point concerned is used to define a proximity distance4.

Figure 4: Calculation of an average distance between individuals.

23The next step of the method consists in determining the projection area. Using a GIS (Arcgis), we draw circular buffers around the 903 individuals of the sample. Then we want to determinate a random localization in these buffers of the population estimated by the weighting procedure.

24But for some evident reasons, we can not spread the estimated points everywhere:

  • because the sampling was spatialised, we have to check that each individual generates points situated within the limits of his/her geographical strata.

  • we also need to ensure that the points are generated on residential areas (not in the middle of unpopulated areas).

25Doing so, we define a theoretical “projection area” (see figure 5 and also figure 2, step 4), relevant for each individual. Now we can begin the theoretical projection and obtain a geographical approximation of the entire population with all the data collected in the survey.

Figure 5: Theoretical projection area.

Limitation and validation

26With this method, we aim to map the results of the survey at a finer scale than the 6 geographical strata used for the sampling. In the preliminary phase of definition of the 6 geographical strata, the confidence interval was validated by using weighting tests (cf. Gerber & Bienvenue, 2004). Despite this, it appears impossible to calculate confidence intervals after the projection of the theoretical population generated from the survey, neither at the scale of 24 administrative districts, nor at the scale of the 79 census tracts. Indeed, the projection is achieved at the individual scale, while the calculation of a confidence interval applies on clusters. However, it is essential to validate our methodology. It can be done by a crossed comparison of the results of the survey with available and comparable data from the population census.

27Thus, as validation test, we present in the next pages some applications which could be useful for targeting policies. But before beginning the mapping process, we had to check out the validity of the method. Therefore, we compare the estimated population with the official census data at different scales.

Comparison with the census

28According to the topic of the ECL survey, we decided to compare the number of elderly people enumerated in the 24 administrative districts of Luxembourg City in the reality (census data) with our estimated population. We obtain a Pearson correlation coefficient of 0.82 (significant < 1%). Then we do the same at a finer scale, the 79 census blocs, the chi square remains significant but the Pearson correlation coefficient (significant < 1%) gives a weaker score of 0.42. At this stage, the method seemed to be appropriate but we needed to increase the score (regression coefficient).

  • 5 Three criteria were considered to calculate the proximity between each individual. These criteria a (...)

29Therefore, we add another restriction to the conditions of random projection: the density of elderly (figure 2, steps 5 and 6). We define 3 classes of density and then we repeat the whole procedure. This time, the theoretical localisation area is delineated by 3 criteria5 (figure 6, also figure 2, step 6):

  1. The 6 geographical strata from the sampling,

  2. the residential area,

  3. the class of density.

Figure 6: Theoretical projection area based on density.

30The figure 6 illustrates the restrictions added in the delineation of the projection area (i.e. density of elderly represented in 3 classes). The individual X will generate points only in residential area corresponding to its class of density (here the class 3).

31With this geostatistical supplement in the validation control, the Pearson correlation coefficient (significant < 1%) improves from 0.42 to 0.82 at the scale of the 79 census tracks.


  • 6 The values represented on maps using can be discrete or continuous

32Among others interests, a method makes sense when its applications are useful. To validate the utility of our projection’s methodology, we present below three possible and concrete applications6. The first example is a mapping of perceived health. Numerous countries do not produce any general statistics on self-related health. The only available information in the elderly population are from surveys and are generally limited to a regional scale. Using our methodology, we can afford a map at the infra municipal scale.

33This map (figure 7) estimates elderly people perceiving their health as ’bad’ or ’very bad’. This estimation is based on the answers to the question: “generally, would you say that your health status is: very bad, bad, good, very good, or excellent?” in the ECL survey.

34We can clearly see geographical variations in the rate of elderly with a bad or very bad health perception (the scale is the one of the census blocks). The southern part of the city appears to be disadvantaged and 2 areas should benefit of a particular attention: Train station and Gasperich.

Figure 7: Rate of Elderly reporting bad health perception.

35The second example presented below is a mapping of the amount of supports (family, friends, neighbours…) that an elderly person can count on if help is needed (figure 8). It is a representation of an aspect of the social capital summarized by the resources that everyone is able to mobilize.

Figure 8: Number of available supports for elderly.

36A large literature has provided evidence that this capital is very important for supporting elderly living at home (i.e. Pin & al., 2003; Martel & Legaré, 2001; Andrew, 2005). We see on the figure 8 that the centre of Luxembourg City offers less convenience than outlying districts. So that’s probably in the central part of the city that the support provision should be enhanced.

37For the last example, we managed to map the spatial distribution of one of the 5 profiles calculated from the ECL survey results, after the principal components analysis and hierarchical ascending classification (figure 9).

Figure 9: Rate of deprived Elderly.

38This map shows the results for the profile “aged & lonely person with low income and low level of support”. People presenting this profile are very vulnerable and potentially candidate for a support program. Such a map can help to determine priority areas for these programs.


39We obtained significant results and it appears like another evidence of the necessity of considering the local context in the research concerning health in geography. Using mixed criteria, we have defined theoretical neighbourhood around individuals who were presenting similar profiles. Where numerous studies have focused on the search of relations between area of residence and health above and beyond individual level risk factors (Jones & Duncan, 1995; Yen & Kaplan, 1999, Frohlich & Al, 2001; Macintyre, Ellaway, 2002), or on the suggestion that some neighbourhoods are healthier than others (Diez-Roux et al., 2001), we made another choice. This choice was to considerate as prerequisite the existence of strong and joint relations between individual profiles, geographical context and health and wellbeing variables. We linked individual data with characteristics of the neighbourhood. Indeed, compositional data were used to determinate homogeneous groups of projections and contextual criteria were used to determinate areas of projections. Thus, our projection method generates a random localisation of individuals according to, simultaneously, contextual data (social residential profiles) and compositionnal data (individual profiles) in a dimension of proximity (defined by the radius of the buffers). This method allows the reconstruction of a virtual population whose caracteristics are very close to those of the real population. For the future, it will be of great interest to test this method on other field. Therefore one condition can not be ignored. Prior to the projection attempts, the survey panel must be spatially stratified.

40With respect to this condition, the results obtained present a relatively simple way to map data related (among other things) to wellbeing or health elderly. This method allows a spatial agregation and the generalisation of results obtained from a representative sample. Thereby it becomes possible to give, at a fine scale, a spatial representation of data that, since here, could only be analysed in their globality. And the fact that we finally needed (more than we wanted) to use simultaneously contextual and compositional data to obtain the best results, is a new argument to the debate on the relation between health and place.

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1 A concrete application is presented for example in Heady P., Clarke P. et al., 2003.

2 We tested this tool by mapping the location of elderly over 60 from the survey and from the census data.

3 When « border effects » arise in KDE method, this can be weakened in a way that does not remain an intrinsic limitation of the method, but therefore complementary calculations are needed (e.g. Bailey and Gatrell, 1995).

4 The Euclidian distance is preferred to a Manhattan distance because the calculation applies to an estimation of proximity, and not to the measure of the cumulated length of a network links.

5 Three criteria were considered to calculate the proximity between each individual. These criteria are different from those used here to control the projection area.

6 The values represented on maps using can be discrete or continuous

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Philippe Gerber, Sébastien Fleuret et Marc Schneider, « Predicting and mapping the location of an estimated population from a survey: an applied method », Cybergeo : European Journal of Geography [En ligne], Systèmes, Modélisation, Géostatistiques, document 494, mis en ligne le 22 mars 2010, consulté le 23 septembre 2020. URL : ; DOI :

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Philippe Gerber

CEPS/INSTEAD, Luxembourg,

Sébastien Fleuret

CNRS, ESO-Angers, Carta, Université d’Angers, France,

Marc Schneider

CEPS/INSTEAD, Luxembourg,

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