Combining data with partially overlapping polygon layers? (QGIS)

Question

I am new to QGIS.

I have a dataset with Baltimore neighborhoods, and then a series of datasets for Baltimore census tracts dating back to the 1930s. My goal is to look at how population and the amount of units has varied over the years for each neighborhood. However, neighborhoods and census tracts overlap in imprecise ways so that the following situations occur:

1. Most neighborhoods contain multiple census tracts.
2. Some census tracts overlap multiple neighborhoods.
3. Some census tracts contain more than one complete neighborhood.

I think the best way to handle this will be to aggregate population counts by the weighted ratio of a given census tract area's containment in a given neighborhood. As some examples (see image as well) In the 1940 census, Reservoir Hill (neighborhood) contains 100% of CT 0132 (pop 5,070), 80% of CT 0131 (pop 4,795), 20% of CT 0133 (pop 6263), and a tiny sliver (let's say 2%) of CT 0134 (pop 3,934). So 5070 + (4795*.8) + (6263*.2) + (3934*.02)=10,237.

Parkview/Woodbrook is an entire neighborhood contained within the CT 0134 in 1940. Since maybe 10% of 0134 is contained in the neighborhood, pop 3,934*.1=393.

I know this will introduce some aggregation bias, but I think it's likely a lot more accurate than just finding the center point of each census tract and then assigning the total population to whatever neighborhood contains the center point.

Is there a reasonably feasible way to conduct this type of analysis and calculations w/in QGIS?

Here's sort of what I'd envision as an output of quasi-arrays in the "Neighborhood" shapefile:

Neighborhood	1940s_CT	1940s_CT_Full Pop	1940s_CT_Area_Percentage	1940s_CT_Estimated_Pop
Reservoir Hill	G240510000131,G240510000132,G240510000133,G240510000134	4795,5070,6263,3934	.8,1,.2,.02	10237
Parkview	G240510000134	3934	.1	393.4

This is the most related issue I've found so far, though I've never used PostGIS.

Answer 1

QGIS Expressions:

Use these four expressions to create new (virtual or not) fields in your Neighborhood Shapefile:

• 1940s_CT

  aggregate( '<CT>', 'array_agg', "<ID>", intersects( $geometry, geometry(@parent) ) )
  

• 1940s_CT_Full_Pop

  aggregate( '<CT>', 'array_agg', "<POP>", intersects( $geometry, geometry(@parent) ) )
  

• 1940s_CT_Area_Percentage

  aggregate( '<CT>', 'array_agg', round( area( intersection( $geometry, geometry( @parent ) ) ) / area( $geometry ), 3 ), intersects( $geometry, geometry(@parent) ) )
  

• 1940s_CT_Estimated_Pop

  aggregate( '<CT>', 'sum', floor( "<POP>" * (area( intersection( $geometry, geometry( @parent ) ) ) / area( $geometry ) ) ), intersects( $geometry, geometry(@parent) ) )
  

Don't forget to replace values wrapped in <> with the actual layer/field identifiers.

Answer 2

QGIS Virtual Layer (SpatiaLite SQL):

Personally, I like to leave base data untouched, and have Virtual Layers in place with analytics, rather than duplicated data. Also, personally, I prefer SQL almost everywhere:

SELECT nbh_name AS "Neighborhood",
       GROUP_CONCAT(ct_id) AS "1940s_CT",
       GROUP_CONCAT(ct_pop) AS "1940s_CT_Full Pop",
       GROUP_CONCAT(ROUND(its_area/ct_area, 3)) AS "1940s_CT_Area_Percentage",
       FLOOR(SUM(pop*(its_area/ct_area))) AS "1940s_CT_Estimated_Pop",
       geometry
FROM   (
    SELECT nbh.<name> AS nbh_name,
           ct.<id> AS ct_id,
           ct.<pop> AS ct_pop,
           ST_Area(ct.geometry) AS ct_area,
           ST_Area(ST_Intersection(nbh.geometry, ct.geometry)) AS its_area,
           nbh.geometry
    FROM   <neighborhood> AS nbh
    JOIN   <ct> AS ct
      ON   ST_Intersects(nbh.geometry, ct.geometry)
) q
GROUP BY
       nbh_name, geometry
;

Don't forget to replace values wrapped in <> with the actual layer/field identifiers.