reclin2 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++.
We will work with a pair of data sets with artificial data. They are tiny, but that allows us to see what happens. In this example we will perform ‘classic’ probabilistic record linkage. When some known true links are known it is also possible to use machine learning methods. This is illustrated in another vignette.
> 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 1012 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:
> pairs <- pair_blocking(linkexample1, linkexample2,
+ "postcode")
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.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. Also note that reclin2 uses the data.table package to efficiently perform some of the computations. Therefore, the pairs object is a data.table.
Other functions to generate pairs are:
pair: generate all possible pairspairs_minsim: generate pairs that have minimum similarity score (e.g. should agree on at least one variable in a set of given variables). Can be computationally intensive as all records have to be compared.We can now compare the records on their linkage keys:
> pairs <- compare_pairs(pairs, on = c("lastname", "firstname",
+ "address", "sex"))
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.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 pairs (and should you be worrying about memory: as long as the original data sets are not modified the data sets are not actually copied).
In the example above the result of compare_pairs was assigned back to pairs. When working with large datasets it can be more efficient to modify pairs in place preventing unnecessary copies. This behaviour can be switched on using the inplace argument which is accepted by most functions.
> compare_pairs(pairs, on = c("lastname", "firstname",
+ "address", "sex"), inplace = TRUE)
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.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 FALSEThe 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:
> compare_pairs(pairs, on = c("lastname", "firstname",
+ "address", "sex"), default_comparator = jaro_winkler(0.9),
+ inplace = TRUE)
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.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 function compare_vars offers more flexibility than compare_pairs. It can for example compare multiple variables at the same time (e.g. compare birth day and month allowing for swaps) or generate multiple results from comparing on one variable.
The 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. Traditionally, the probabilistic linkage framework initially formalised by Fellegi and Sunter tries is used. 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(~lastname + firstname + address +
+ sex, data = pairs)
> print(m)
M- and u-probabilities estimated by the EM-algorithm:
Variable M-probability U-probability
lastname 0.9990000 0.001152679
firstname 0.1999999 0.000100000
address 0.8999206 0.285831118
sex 0.3002011 0.285427112
Matching probability: 0.5885595.These m- and u-probabilities can be used to score the pairs:
> pairs <- predict(m, pairs = pairs, add = TRUE)
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.x .y lastname firstname address sex weights
1: 1 1 1.000000 0.4722222 0.9230769 NA 7.7103862
2: 1 2 0.000000 0.5833333 0.8641026 1 -5.9463949
3: 1 3 0.447619 0.4642857 0.9333333 1 0.8042090
4: 2 1 1.000000 0.8888889 0.9230769 NA 8.6064218
5: 2 2 0.000000 0.0000000 0.8641026 0 -6.3177171
6: 2 3 0.447619 0.5396825 0.9333333 0 0.7937508
7: 3 1 0.447619 0.4722222 0.8641026 NA 0.6017106
8: 3 2 0.952381 0.5833333 0.9230769 1 4.0674910
9: 3 3 1.000000 0.4642857 1.0000000 1 7.9350221
10: 4 1 0.447619 0.6428571 0.8641026 NA 0.7713174
11: 4 2 0.952381 0.0000000 0.9230769 0 3.6961688
12: 4 3 1.000000 1.0000000 1.0000000 0 15.4915816
13: 5 1 0.447619 0.5555556 0.8641026 NA 0.6717426
14: 5 2 0.952381 0.0000000 0.9230769 0 3.6961688
15: 5 3 1.000000 0.8492063 1.0000000 0 8.5458257
16: 6 4 1.000000 1.0000000 0.6111111 1 14.6796595
17: 6 5 1.000000 0.5277778 1.0000000 0 7.9139248With add = TRUE the predictions are added to the pairs object. The higher the weight the more likely the two pairs belong to the same entity/are a match.
The prediction function can also return the m- and u-probabilities and the posterior m- and u-probabilities.
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
> pairs <- select_threshold(pairs, "threshold", score = "weights",
+ threshold = 8)
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.x .y lastname firstname address sex weights threshold
1: 1 1 1.000000 0.4722222 0.9230769 NA 7.7103862 FALSE
2: 1 2 0.000000 0.5833333 0.8641026 1 -5.9463949 FALSE
3: 1 3 0.447619 0.4642857 0.9333333 1 0.8042090 FALSE
4: 2 1 1.000000 0.8888889 0.9230769 NA 8.6064218 TRUE
5: 2 2 0.000000 0.0000000 0.8641026 0 -6.3177171 FALSE
6: 2 3 0.447619 0.5396825 0.9333333 0 0.7937508 FALSE
7: 3 1 0.447619 0.4722222 0.8641026 NA 0.6017106 FALSE
8: 3 2 0.952381 0.5833333 0.9230769 1 4.0674910 FALSE
9: 3 3 1.000000 0.4642857 1.0000000 1 7.9350221 FALSE
10: 4 1 0.447619 0.6428571 0.8641026 NA 0.7713174 FALSE
11: 4 2 0.952381 0.0000000 0.9230769 0 3.6961688 FALSE
12: 4 3 1.000000 1.0000000 1.0000000 0 15.4915816 TRUE
13: 5 1 0.447619 0.5555556 0.8641026 NA 0.6717426 FALSE
14: 5 2 0.952381 0.0000000 0.9230769 0 3.6961688 FALSE
15: 5 3 1.000000 0.8492063 1.0000000 0 8.5458257 TRUE
16: 6 4 1.000000 1.0000000 0.6111111 1 14.6796595 TRUE
17: 6 5 1.000000 0.5277778 1.0000000 0 7.9139248 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:
> pairs <- compare_vars(pairs, "truth", on_x = "id",
+ on_y = "id")
> print(pairs)
First data set: 6 records
Second data set: 5 records
Total number of pairs: 17 pairs
Blocking on: 'postcode'
.x .y lastname firstname address sex weights threshold truth
1: 1 1 1.000000 0.4722222 0.9230769 NA 7.7103862 FALSE FALSE
2: 1 2 0.000000 0.5833333 0.8641026 1 -5.9463949 FALSE FALSE
3: 1 3 0.447619 0.4642857 0.9333333 1 0.8042090 FALSE FALSE
4: 2 1 1.000000 0.8888889 0.9230769 NA 8.6064218 TRUE TRUE
5: 2 2 0.000000 0.0000000 0.8641026 0 -6.3177171 FALSE FALSE
6: 2 3 0.447619 0.5396825 0.9333333 0 0.7937508 FALSE FALSE
7: 3 1 0.447619 0.4722222 0.8641026 NA 0.6017106 FALSE FALSE
8: 3 2 0.952381 0.5833333 0.9230769 1 4.0674910 FALSE TRUE
9: 3 3 1.000000 0.4642857 1.0000000 1 7.9350221 FALSE FALSE
10: 4 1 0.447619 0.6428571 0.8641026 NA 0.7713174 FALSE FALSE
11: 4 2 0.952381 0.0000000 0.9230769 0 3.6961688 FALSE FALSE
12: 4 3 1.000000 1.0000000 1.0000000 0 15.4915816 TRUE TRUE
13: 5 1 0.447619 0.5555556 0.8641026 NA 0.6717426 FALSE FALSE
14: 5 2 0.952381 0.0000000 0.9230769 0 3.6961688 FALSE FALSE
15: 5 3 1.000000 0.8492063 1.0000000 0 8.5458257 TRUE FALSE
16: 6 4 1.000000 1.0000000 0.6111111 1 14.6796595 TRUE TRUE
17: 6 5 1.000000 0.5277778 1.0000000 0 7.9139248 FALSE FALSEWe 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):
> pairs <- select_greedy(pairs, "weights", variable = "greedy",
+ threshold = 0)
> table(pairs$truth, pairs$greedy)
FALSE TRUE
FALSE 13 0
TRUE 0 4> pairs <- select_n_to_m(pairs, "weights", variable = "ntom",
+ threshold = 0)
> table(pairs$truth, pairs$ntom)
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(pairs, selection = "ntom")
> print(linked_data_set)
Total number of pairs: 4 pairs
.y .x id.x lastname.x firstname.x address.x sex.x postcode.x id.y
1: 1 2 2 Smith George 12 Mainstr M 1234 AB 2
2: 2 3 3 Johnson Anna 61 Mainstr F 1234 AB 3
3: 3 4 4 Johnson Charles 61 Mainstr M 1234 AB 4
4: 4 6 6 Schwartz Ben 1 Eaststr M 6789 XY 6
lastname.y firstname.y address.y sex.y postcode.y
1: Smith Gearge 12 Mainstreet <NA> 1234 AB
2: Jonson A. 61 Mainstreet F 1234 AB
3: Johnson Charles 61 Mainstr F 1234 AB
4: Schwartz Ben 1 Main M 6789 XY