R: How to calculate the number of locations nearby a spatial point?

Question

I have a data frame containing a number of projects + their start date + their coordinates(long/lat) and I have a data frame containing a number of (fictional) respondents + the date they were surveyed + their coordinates:

respond_id<- c(1:5)
survey_year<- c(2007, 2005, 2008, 2004, 2005)
lat_1<- c(53.780928, 54.025200, 53.931432, 53.881048, 54.083359)
long_1<- c(9.614991, 9.349862, 9.473498, 10.685581, 10.026894)

project_id<- c(1111:1114)
year_start<- c(2007, 2007, 2006, 2008)
lat_2<- c(54.022881, 54.022881, 53.931753, 53.750523)
long_2<- c(9.381104, 9.381104, 9.505700, 9.666336)

survey<- data.frame(respond_id, survey_year, lat_1, long_1)
projects<- data.frame(project_id, year_start, lat_2, long_2)

Now, I want to create a new variable survey$project_nearby that counts the amount of projects located nearby (here: 5km) the respondents. So the data frame survey should look somewhat like this (other results possible):

> survey

  respond_id survey_year     lat_1    long_1 projects_nearby
1          1        2007 53.780928  9.614991               0
2          2        2005 54.025200  9.349862               0
3          3        2008 53.931432  9.473498               1
4          4        2004 53.881048 10.685581               0
5          5        2005 54.083359 10.026894               0

Special attention needs to be paid to the start years of the projects and the year the surveys were conducted: If a respondent was asked in 2007, but the project nearby was completed in 2008, this project naturally does not count as project nearby.

I thought of creating a distance matrix and then just counting the number of rows containing a distance smaller than 5km... but I don't know how to create this distance matrix. And maybe a for loop would be easier? Could anyone help me or give me a hint, what would be the code for doing this?

EDIT: I edited the expected values of survey$projects_nearby. Now these values should match with actual amount of projects located nearby the respective respondents.

Answer 1

You can use the sp package to find the distances, and then just count the number that are nearby. That is,

library(sp)
survey.loc <- matrix(as.numeric(as.character(unlist(survey[, 3:4]))), ncol = 2)
project.loc <- matrix(as.numeric(as.character(unlist(projects[, 3:4]))), ncol = 2)
distances <- spDists(survey.loc, project.loc, longlat = TRUE)
survey$project_nearby <- apply(distances, 1, function(x) sum(x<5))

I hope this helps!

EDIT:

My apologies for not considering the date.

library(sp)
survey.loc <- matrix(as.numeric(as.character(unlist(survey[, 3:4]))), ncol = 2)
project.loc <- matrix(as.numeric(as.character(unlist(projects[, 3:4]))), ncol = 2)
distances <- spDists(survey.loc, project.loc, longlat = TRUE)
year.diff <- sapply(projects$year_start, function(x) survey$survey_year-x)
year.diff <- ifelse(year.diff < 0, Inf, 1)
survey$project_nearby <- apply(year.diff*distances, 1, function(x) sum(x<5))

Answer 2

I don't think the correct answer is that shown? Below I left_join by the year so that every row of survey will be replicated for every matching projects. Then I filter to rows where the lats are below 5 km. Count them and join back to the original survey.

Slightly confusing results too as project1 and 2 from same year are in same location. I count them twice with this code.

>survey
  respond_id survey_year    lat_1    long_1
1          1        2007 53.78093  9.614991
2          2        2005 54.02520  9.349862
3          3        2008 53.93143  9.473498
4          4        2004 53.88105 10.685581
5          5        2005 54.08336 10.026894


>projects
> projects
  project_id year_start    lat_2   long_2
1       1111       2007 54.02288 9.381104
2       1112       2007 54.02288 9.381104
3       1113       2006 53.93175 9.505700
4       1114       2008 53.75052 9.666336

> left_join(survey, projects, by = c( "survey_year"="year_start")) %>%
+ dplyr::filter( sqrt((lat_1-lat_2)^2 + (long_1-long_2)^2 ) < 5) %>%
+   group_by(respond_id, survey_year, lat_1, long_1) %>%
+   summarise(projects_nearby = n()) %>%
+   right_join(survey)
Joining, by = c("respond_id", "survey_year", "lat_1", "long_1")
Source: local data frame [5 x 5]
Groups: respond_id, survey_year, lat_1 [?]

  respond_id survey_year    lat_1    long_1 projects_nearby
       <int>       <dbl>    <dbl>     <dbl>           <int>
1          1        2007 53.78093  9.614991               2
2          2        2005 54.02520  9.349862              NA
3          3        2008 53.93143  9.473498               1
4          4        2004 53.88105 10.685581              NA
5          5        2005 54.08336 10.026894              NA

.. you can of course change NA to zero if appropriate...

Answer 3

I think you have to convert your lat, long coordinates to coordinates in a plane or using this link below from a previous post:

harvesine distance

https://stackoverflow.com/questions/27928/calculate-distance-between-two-latitude-longitude-points-haversine-formula

Once you have distances to a particular location in the projects data frame, you may need to find similar points using knn or any other technique of your preference.