Social cartography and satellite-derived building coverage for post-census population estimates in difficult-to-access regions of Colombia

Figures & data

Figure 1 Maps showing percentage of expected properties from the census frame that were actually enumerated by census workers: rural and urban areas, Colombia 2018

Notes: Left-hand panel: In rural areas, census enumeration areas in which 90 per cent or more of expected properties were enumerated during census fieldwork are shown in green, areas where 0–90 per cent were enumerated are shown in orange, and areas where no property was enumerated are shown in grey. Right-hand panel: In urban areas, colours are the same as for rural areas, but the indicator was the percentage of expected dwellings in a census enumeration area.

Source: The methodology for determining census coverage is described by DANE (2022a). The image is taken from the Geovisor tool used by DANE to monitor census coverage.

Figure 2 Maps of the study area in Colombia, 2018, showing two important predictor variables: Left-hand panel shows community-based estimates of population size in each enumeration area; Right-hand panel shows remotely sensed building coverage for 90 m pixels

Source: National boundaries were obtained from Global Administrative Areas (GADM 2019) and the subnational boundaries from DANE (2022b). The maps were created using ESRI ArcGIS pro v.2.5. Community-based estimates of population size in each enumeration area were obtained from social cartography workshops. Remotely sensed building coverage for 90 m pixels was obtained from World Settlement Footprint 3D.

Figure 3 Directed acyclic graph (DAG) showing relationships between data (squares) and parameters (circles)

Notes: The hierarchical model structure has a sub-model to estimate counts of buildings (B) that feeds into a sub-model of population (P). Solid lines indicate stochastic relationships, while dashed lines indicate deterministic relationships. Black-filled nodes were not included in every model. Key parameters included people per building ($\rho$) and buildings per hectare ($\theta$). Parameters and data are defined in Tables 1 and 2.

Source: Authors’ own.

Table 1 Definitions of symbols for data

Symbol	Definition	Source
d	Index: Department (administrative unit)	Colombia administrative boundaries
m	Index: Municipality (sub-admin unit)	Colombia administrative boundaries
i	Index: Census enumeration area	Colombia census
Pi	Count of people	Colombia census
Bi	Count of buildings	Colombia census
Ai	Area (hectares) of census unit	Colombia census
Ci	Building coverage (hectares)	German Aerospace Center
Di	Community estimated count of dwellings	Social cartography workshops
Fi	Community estimated count of families	Social cartography workshops
Ii	Community estimated count of individuals	Social cartography workshops
x1,i	School density (centred, scaled)	Geospatial covariates
x2,i	Poverty index (centred, scaled)	Geospatial covariates
x3,i	Elevation (centred, scaled)	Geospatial covariates
x4,i	Night-time lights (centred, scaled)	Geospatial covariates
x5,i	Distance to populated centre (centred, scaled)	Geospatial covariates
x6,i	Area (hectares) of census unit	Geospatial covariates

Table 2 Definitions of symbols for parameters

Symbol	Definition
${\rho }_i$	People per building for each census enumeration area (i)
${\theta }_i$	Buildings per total area (hectares)
${\varphi }_i$	Building count per building area
${\overline{\rho }}_i$	Expected value of ${\rho }_i$
${\overline{\theta }}_i$	Expected value of ${\theta }_i$
${\overline{\varphi }}_i$	Expected value of ${\varphi }_i$
${\sigma }_1$	Residual variation (i.e. uncertainty)
${\alpha }_d$	Random intercept by department
${\delta }_m$	Random intercept adjustment by municipality
${\beta }_k$	Effect of geospatial covariate k
$\gamma$	Effect of optional covariate(s) (i.e. satellite or community)
$\mu$	Mean of ${\alpha }_d$ among departments
${\sigma }_2$	Variation in ${\alpha }_d$ among departments
${\sigma }_3$	Variation in ${\delta }_{\mathit{m}}$ among municipalities

Figure 4 Predicted counts from the Combined model of population (left-hand panel) and building counts (right-hand panel) for all census enumeration areas where the routes method was conducted, Colombia 2018

Source: National boundaries were obtained from Global Administrative Areas (GADM 2019) and the subnational boundaries from DANE (2022b). The maps were created using ESRI ArcGIS pro v.2.5. See Data subsection for information on data sources used to calculate values displayed in this map.

Table 3 Proportion of out-of-sample observations that were within each model’s prediction intervals

Parameter	Model	Credible interval width
		CI 95	CI 90	CI 80	CI 50
P	Base	0.961	0.955	0.896	0.626
P	Satellite	0.965	0.949	0.894	0.622
P	Community	0.957	0.941	0.904	0.640
P	Combined	0.963	0.953	0.898	0.648
B	Base	0.967	0.939	0.888	0.644
B	Satellite	0.963	0.937	0.879	0.648
B	Community	0.967	0.941	0.879	0.650
B	Combined	0.967	0.943	0.883	0.640

Note: Approximately 95 per cent of observations (i.e. 0.95) should fall within well-specified 95 per cent credible intervals (CI).

Source: See Data subsection for information on data sources used to calculate values in this table.

Figure 5 Comparisons of model fit across four models (Base, Satellite, Community, and Combined) for the two response variables (population and buildings) in each hierarchical model

Notes: Fit statistics were calculated using out-of-sample predictions from 10-fold cross-validations. Bias, imprecision, and inaccuracy are reported as proportions of the predicted values. R-squared values quantify the proportion of variance explained by each model. Note that x-axes do not start at zero.

Source: See Data subsection for information on data sources used to calculate values in this figure.

Figure 6 Model fit for the Combined model showing out-of-sample model predictions vs observed data from census enumeration areas that were fully enumerated (≥90 per cent coverage), Colombia 2018

Notes: The diagonal line is a 1:1 relationship where predictions are equal to observations. Vertical lines show 95 per cent prediction intervals.

Source: See Data subsection for information on data sources used to calculate values in this figure.

Figure 7 Covariate effects ($\dot{\beta }$ and $\dot{\gamma }$) on the expected values of buildings per hectare (${\overline{\theta }}_i$) or buildings per built hectare (${\overline{\varphi }}_i$) for all four models, Colombia

Notes: Covariates are defined in the Methods section and Table 1: Schools (x₁), Poverty (x₂), Elevation (x₃), NightLights (x₄), DistToCenter (x₅), and Area (x₆). BldgCover refers to building coverage.

Source: See Data subsection for information on data sources used to calculate values in this figure.

Figure 8 Covariate effects ($\beta$ and $\gamma$) on the expected values of people per building (${\overline{\rho }}_i$) for all four models, Colombia

Notes: Covariates are defined in the Methods section and Table 1: Schools (x₁), Poverty (x₂), Elevation (x₃), NightLights (x₄), DistToCenter (x₅), and Area (x₆).

Source: See Data subsection for information on data sources used to calculate values in this figure.

[DANE] National Administrative Department of Statistics of Colombia. 2022a. Estimación de la omisión censal a nivel nacional y subnacional a partir de métodos demográficos, econométricos y geoestadísticos, Metodologías Demográficas Aplicada [Estimation of Census Omission at National and Subnational Levels Based on Demographic, Econometric and Geostatistical Methods], Metodologías Demográficas Aplicada 2.

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Global Administrative Areas (GADM). 2019. University of California, Berkeley. Available: http://www.gadm.org (accessed: 10 October 2019).

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[DANE] National Administrative Department of Statistics of Colombia. 2022b. Descarga del Marco Geoestadistico Nacional (MGN). Available: https://geoportal.dane.gov.co/servicios/descarga-y-metadatos/descarga-mgn-marco-geoestadistico-nacional/ (accessed: 21 June 2022).

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