reclin implements methodology for linking records based on inexact keys. It allows for maximum flexibility by giving users full control over each step of the linking procedure. The package is built with performance and scalability in mind: the core algorithms have been implemented in C++ and where necessary, intermediate results are stored or retrieved from disc using an efficient memory mapping scheme.
We will work with a pair of data sets with artificial data. They are tiny, but that allows us to see what happens.
data("linkexample1", "linkexample2")
print(linkexample1)
#> id lastname firstname address sex postcode
#> 1 1 Smith Anna 12 Mainstr F 1234 AB
#> 2 2 Smith George 12 Mainstr M 1234 AB
#> 3 3 Johnson Anna 61 Mainstr F 1234 AB
#> 4 4 Johnson Charles 61 Mainstr M 1234 AB
#> 5 5 Johnson Charly 61 Mainstr M 1234 AB
#> 6 6 Schwartz Ben 1 Eaststr M 6789 XY
print(linkexample2)
#> id lastname firstname address sex postcode
#> 1 2 Smith Gearge 12 Mainstreet <NA> 1234 AB
#> 2 3 Jonson A. 61 Mainstreet F 1234 AB
#> 3 4 Johnson Charles 61 Mainstr F 1234 AB
#> 4 6 Schwartz Ben 1 Main M 6789 XY
#> 5 7 Schwartz Anna 1 Eaststr F 6789 XYWe have two data sets with personal information. The second data set contains a lot of errors, but we will try to link the second data set to the first.
In principle linkage consists of comparing each combination of records from the two data sets and determine which of those combinations (or pairs as we will call them below) belong to the same entity. In case of a perfect linkage key, it is of course, not necessary to compare all combinations of records, but when the linkage keys are imperfect and contain errors, it is in principle necessary to compare all pairs.
However, comparing all pairs can result in an intractable number of pairs: when linking two data sets with a million records there are \(10^{12}\) possible pairs. Therefore, some sort of reduction of the possible pairs is usually applied. In the example below, we apply blocking, which means that pairs are only generated when they agree on the blocking variable (in this case the postcode). This means that pairs of records that disagree on the blocking variable are not considered. Therefore, one will only use variables that can be considered without errors as blocking variable, or link multiple times with different blocking variables and combine both data sets.
The first step in (probabilistic) linkage is, therefore, generating all pairs:
p <- pair_blocking(linkexample1, linkexample2, "postcode", large = FALSE)
print(p)
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y
#> 1 1 1
#> 2 1 2
#> 3 1 3
#> 4 2 1
#> 5 2 2
#> 6 2 3
#> 7 3 1
#> 8 3 2
#> 9 3 3
#> 10 4 1
#> 11 4 2
#> 12 4 3
#> 13 5 1
#> 14 5 2
#> 15 5 3
#> 16 6 4
#> 17 6 5As you can see, record 1 from x (the first data set) is compared to records 1, 2 and 3 from y.
We can now compare the records on their linkage keys:
p <- compare_pairs(p, by = c("lastname", "firstname", "address", "sex"))
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex
#> 1 1 1 TRUE FALSE FALSE NA
#> 2 1 2 FALSE FALSE FALSE TRUE
#> 3 1 3 FALSE FALSE FALSE TRUE
#> 4 2 1 TRUE FALSE FALSE NA
#> 5 2 2 FALSE FALSE FALSE FALSE
#> 6 2 3 FALSE FALSE FALSE FALSE
#> 7 3 1 FALSE FALSE FALSE NA
#> 8 3 2 FALSE FALSE FALSE TRUE
#> 9 3 3 TRUE FALSE TRUE TRUE
#> 10 4 1 FALSE FALSE FALSE NA
#> 11 4 2 FALSE FALSE FALSE FALSE
#> 12 4 3 TRUE TRUE TRUE FALSE
#> 13 5 1 FALSE FALSE FALSE NA
#> 14 5 2 FALSE FALSE FALSE FALSE
#> 15 5 3 TRUE FALSE TRUE FALSE
#> 16 6 4 TRUE TRUE FALSE TRUE
#> 17 6 5 TRUE FALSE TRUE FALSEAs you can see, we don’t need to pass the original data sets although the variables lastname etc. are from those original data sets. This is because a copy of the original data sets are stored with the pairs object p (and should you be worrying about memory: as long as the original data sets are not modified the data sets are not actually copied).
The default comparison function returns TRUE when the linkage keys agree and false when they don’t. However, when looking at the original data sets, we can see that most of our linkage keys are string variables that contain typing errors. The quality of our linkage could be improved if we could use a similarity score to compare the two strings: a high score means that the two strings are very similar a value close to zero means that the strings are very different.
Below we use the jaro_winkler similarity score to compare all fields:
p <- compare_pairs(p, by = c("lastname", "firstname", "address", "sex"),
default_comparator = jaro_winkler(0.9), overwrite = TRUE)
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex
#> 1 1 1 1.000000 0.4722222 0.9230769 NA
#> 2 1 2 0.000000 0.5833333 0.8641026 1
#> 3 1 3 0.447619 0.4642857 0.9333333 1
#> 4 2 1 1.000000 0.8888889 0.9230769 NA
#> 5 2 2 0.000000 0.0000000 0.8641026 0
#> 6 2 3 0.447619 0.5396825 0.9333333 0
#> 7 3 1 0.447619 0.4722222 0.8641026 NA
#> 8 3 2 0.952381 0.5833333 0.9230769 1
#> 9 3 3 1.000000 0.4642857 1.0000000 1
#> 10 4 1 0.447619 0.6428571 0.8641026 NA
#> 11 4 2 0.952381 0.0000000 0.9230769 0
#> 12 4 3 1.000000 1.0000000 1.0000000 0
#> 13 5 1 0.447619 0.5555556 0.8641026 NA
#> 14 5 2 0.952381 0.0000000 0.9230769 0
#> 15 5 3 1.000000 0.8492063 1.0000000 0
#> 16 6 4 1.000000 1.0000000 0.6111111 1
#> 17 6 5 1.000000 0.5277778 1.0000000 0The next step in the process, is to determine which pairs of records belong to the same entity and which do not. There are numerous ways to do this. One possibility is to label some of the pairs as match or no match, and use some machine learning algorithm to predict the match status using the comparison vectors. Another, method, is to score the pairs based on the comparison vectors and select those with a score above some threshold. The simplest way to score the pairs, is to calculate the sum of the comparison vectors. That is what score_simsum does:
p <- score_simsum(p, var = "simsum")
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex simsum
#> 1 1 1 1.000000 0.4722222 0.9230769 NA 2.3952991
#> 2 1 2 0.000000 0.5833333 0.8641026 1 2.4474359
#> 3 1 3 0.447619 0.4642857 0.9333333 1 2.8452381
#> 4 2 1 1.000000 0.8888889 0.9230769 NA 2.8119658
#> 5 2 2 0.000000 0.0000000 0.8641026 0 0.8641026
#> 6 2 3 0.447619 0.5396825 0.9333333 0 1.9206349
#> 7 3 1 0.447619 0.4722222 0.8641026 NA 1.7839438
#> 8 3 2 0.952381 0.5833333 0.9230769 1 3.4587912
#> 9 3 3 1.000000 0.4642857 1.0000000 1 3.4642857
#> 10 4 1 0.447619 0.6428571 0.8641026 NA 1.9545788
#> 11 4 2 0.952381 0.0000000 0.9230769 0 1.8754579
#> 12 4 3 1.000000 1.0000000 1.0000000 0 3.0000000
#> 13 5 1 0.447619 0.5555556 0.8641026 NA 1.8672772
#> 14 5 2 0.952381 0.0000000 0.9230769 0 1.8754579
#> 15 5 3 1.000000 0.8492063 1.0000000 0 2.8492063
#> 16 6 4 1.000000 1.0000000 0.6111111 1 3.6111111
#> 17 6 5 1.000000 0.5277778 1.0000000 0 2.5277778The disadvantage of score_simsum is that it doesn’t take into account that the amount of information in agreement or disagreement on a variable depends on the variable. For example, agreement on sex doesn’t tell us much: when our data sets contain 50% men an 50% women, there is a 50% chance that two random records agree on sex. On the other hand the probability that two random records agree on last name is much lower. Therefore, agreement on last name makes it much more likely that the two records belong to the same entity.
This is what the probabilistic linkage framework initially formalised by Fellegi and Sunter tries to do. The function problink_em uses an EM-algorithm to estimate the so called m- and u-probabilities for each of the linkage variables. The m-probability is the probability that two records concerning the same entity agree on the linkage variable; this means that the m-probability corresponds to the probability that there is an error in the linkage variables. The u-probability is the probability that two records belonging to different entities agree on a variable. For a variable with few categories (such as sex) this probability will be large, while for a variable with a large number of categories (such as last name) this probability will be small.
m <- problink_em(p)
print(m)
#> M- and u-probabilities estimated by the EM-algorithm:
#> Variable M-probability U-probability
#> lastname 0.9995993 1.148282e-03
#> firstname 0.2000808 6.534287e-11
#> address 0.8999198 2.861829e-01
#> sex 0.3001260 2.855427e-01
#>
#> Matching probability: 0.5882748.These m- and u-probabilities can be used to score the pairs:
p <- score_problink(p, model = m, var = "weight")
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex simsum weight
#> 1 1 1 1.000000 0.4722222 0.9230769 NA 2.3952991 7.7138545
#> 2 1 2 0.000000 0.5833333 0.8641026 1 2.4474359 -6.8623638
#> 3 1 3 0.447619 0.4642857 0.9333333 1 2.8452381 0.8024181
#> 4 2 1 1.000000 0.8888889 0.9230769 NA 2.8119658 8.6108449
#> 5 2 2 0.000000 0.0000000 0.8641026 0 0.8641026 -7.2330326
#> 6 2 3 0.447619 0.5396825 0.9333333 0 1.9206349 0.7929395
#> 7 3 1 0.447619 0.4722222 0.8641026 NA 1.7839438 0.6008053
#> 8 3 2 0.952381 0.5833333 0.9230769 1 3.4587912 4.0666230
#> 9 3 3 1.000000 0.4642857 1.0000000 1 3.4642857 7.9375333
#> 10 4 1 0.447619 0.6428571 0.8641026 NA 1.9545788 0.7705671
#> 11 4 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542
#> 12 4 3 1.000000 1.0000000 1.0000000 0 3.0000000 29.7364771
#> 13 5 1 0.447619 0.5555556 0.8641026 NA 1.8672772 0.6709008
#> 14 5 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542
#> 15 5 3 1.000000 0.8492063 1.0000000 0 2.8492063 8.5499432
#> 16 6 4 1.000000 1.0000000 0.6111111 1 3.6111111 28.9246883
#> 17 6 5 1.000000 0.5277778 1.0000000 0 2.5277778 7.9174058The higher the weight the more likely the two pairs belong to the same entity/are a match.
The final step is to select the pairs that are considered to belong to the same entities. The simplest method is to select all pairs above a certain threshold
p <- select_threshold(p, "weight", var = "threshold", threshold = 8)
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex simsum weight threshold
#> 1 1 1 1.000000 0.4722222 0.9230769 NA 2.3952991 7.7138545 FALSE
#> 2 1 2 0.000000 0.5833333 0.8641026 1 2.4474359 -6.8623638 FALSE
#> 3 1 3 0.447619 0.4642857 0.9333333 1 2.8452381 0.8024181 FALSE
#> 4 2 1 1.000000 0.8888889 0.9230769 NA 2.8119658 8.6108449 TRUE
#> 5 2 2 0.000000 0.0000000 0.8641026 0 0.8641026 -7.2330326 FALSE
#> 6 2 3 0.447619 0.5396825 0.9333333 0 1.9206349 0.7929395 FALSE
#> 7 3 1 0.447619 0.4722222 0.8641026 NA 1.7839438 0.6008053 FALSE
#> 8 3 2 0.952381 0.5833333 0.9230769 1 3.4587912 4.0666230 FALSE
#> 9 3 3 1.000000 0.4642857 1.0000000 1 3.4642857 7.9375333 FALSE
#> 10 4 1 0.447619 0.6428571 0.8641026 NA 1.9545788 0.7705671 FALSE
#> 11 4 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542 FALSE
#> 12 4 3 1.000000 1.0000000 1.0000000 0 3.0000000 29.7364771 TRUE
#> 13 5 1 0.447619 0.5555556 0.8641026 NA 1.8672772 0.6709008 FALSE
#> 14 5 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542 FALSE
#> 15 5 3 1.000000 0.8492063 1.0000000 0 2.8492063 8.5499432 TRUE
#> 16 6 4 1.000000 1.0000000 0.6111111 1 3.6111111 28.9246883 TRUE
#> 17 6 5 1.000000 0.5277778 1.0000000 0 2.5277778 7.9174058 FALSEThe select functions add a (logical) variable to the data set indicating whether a pairs is selected or not.
In this case we know which records truly belong to each other. We can use that to evaluate the linkage:
p <- add_from_x(p, id_x = "id")
print(p)
#> Compare
#> By: lastname, firstname, address, sex
#>
#> Simple blocking
#> Blocking variable(s): postcode
#> First data set: 6 records
#> Second data set: 5 records
#> Total number of pairs: 17 pairs
#>
#> Showing all pairs:
#> x y lastname firstname address sex simsum weight threshold id_x
#> 1 1 1 1.000000 0.4722222 0.9230769 NA 2.3952991 7.7138545 FALSE 1
#> 2 1 2 0.000000 0.5833333 0.8641026 1 2.4474359 -6.8623638 FALSE 1
#> 3 1 3 0.447619 0.4642857 0.9333333 1 2.8452381 0.8024181 FALSE 1
#> 4 2 1 1.000000 0.8888889 0.9230769 NA 2.8119658 8.6108449 TRUE 2
#> 5 2 2 0.000000 0.0000000 0.8641026 0 0.8641026 -7.2330326 FALSE 2
#> 6 2 3 0.447619 0.5396825 0.9333333 0 1.9206349 0.7929395 FALSE 2
#> 7 3 1 0.447619 0.4722222 0.8641026 NA 1.7839438 0.6008053 FALSE 3
#> 8 3 2 0.952381 0.5833333 0.9230769 1 3.4587912 4.0666230 FALSE 3
#> 9 3 3 1.000000 0.4642857 1.0000000 1 3.4642857 7.9375333 FALSE 3
#> 10 4 1 0.447619 0.6428571 0.8641026 NA 1.9545788 0.7705671 FALSE 4
#> 11 4 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542 FALSE 4
#> 12 4 3 1.000000 1.0000000 1.0000000 0 3.0000000 29.7364771 TRUE 4
#> 13 5 1 0.447619 0.5555556 0.8641026 NA 1.8672772 0.6709008 FALSE 5
#> 14 5 2 0.952381 0.0000000 0.9230769 0 1.8754579 3.6959542 FALSE 5
#> 15 5 3 1.000000 0.8492063 1.0000000 0 2.8492063 8.5499432 TRUE 5
#> 16 6 4 1.000000 1.0000000 0.6111111 1 3.6111111 28.9246883 TRUE 6
#> 17 6 5 1.000000 0.5277778 1.0000000 0 2.5277778 7.9174058 FALSE 6The add_from_x function adds variables from the original x. As was mentioned before the two data sets are stored in p.
p <- add_from_y(p, id_y = "id")
p$true <- p$id_x == p$id_y
table(as.data.frame(p[c("true", "threshold")]))
#> threshold
#> true FALSE TRUE
#> FALSE 12 1
#> TRUE 1 3We see that three of the four matches that should have been found have indeed been found (the recall is 3/4) and we have one false link (sensitivity is 1/4).
Using a threshold, does not take into account the fact that often we know that one record from the first data set can be linked to at most one record from the second data set and vice versa. If we make the threshold low enough we have more links than records in either data set. reclin contains two functions that force one-to-one linkage: select_greedy and select_n_to_m. The first is fast (it selects pairs starting from the highest score; pairs are only selected when each of the records in a pair have not been selected previously); the second is slower, but can lead to better results (it tries to optimise to total score of the selected records under the restriction that each record can be selected only once):
p <- select_greedy(p, "weight", var = "greedy", threshold = 0)
table(as.data.frame(p[c("true", "greedy")]))
#> greedy
#> true FALSE TRUE
#> FALSE 13 0
#> TRUE 0 4p <- select_n_to_m(p, "weight", var = "ntom", threshold = 0)
table(as.data.frame(p[c("true", "ntom")]))
#> ntom
#> true FALSE TRUE
#> FALSE 13 0
#> TRUE 0 4Perfection!
The real final step is to create the linked data set. We now know which pairs are to be linked, but we still have to actually link them. link does that (the optional arguments all_x and all_y control the type of linkage):
linked_data_set <- link(p)
print(linked_data_set)
#> id.x lastname.x firstname.x address.x sex.x postcode.x id.y lastname.y
#> 1 2 Smith George 12 Mainstr M 1234 AB 2 Smith
#> 2 3 Johnson Anna 61 Mainstr F 1234 AB 3 Jonson
#> 3 4 Johnson Charles 61 Mainstr M 1234 AB 4 Johnson
#> 4 6 Schwartz Ben 1 Eaststr M 6789 XY 6 Schwartz
#> 5 1 Smith Anna 12 Mainstr F 1234 AB NA <NA>
#> 6 5 Johnson Charly 61 Mainstr M 1234 AB NA <NA>
#> 7 NA <NA> <NA> <NA> <NA> <NA> 7 Schwartz
#> firstname.y address.y sex.y postcode.y
#> 1 Gearge 12 Mainstreet <NA> 1234 AB
#> 2 A. 61 Mainstreet F 1234 AB
#> 3 Charles 61 Mainstr F 1234 AB
#> 4 Ben 1 Main M 6789 XY
#> 5 <NA> <NA> <NA> <NA>
#> 6 <NA> <NA> <NA> <NA>
#> 7 Anna 1 Eaststr F 6789 XYThe functions have been designed to be usable with pipe operators, so the entire linkage process could be written as: