# Introduction to record linkage with diyar

#### 12 November 2023

Consolidating information from multiple sources is often the first step in these investigations. This vignette gives a brief introduction to the basics of record linkage as implemented by `diyar`.

Let’s begin by reviewing `missing_staff_id` - a sample dataset containing incomplete staff information.

    data(missing_staff_id)
    missing_staff_id
    #>   r_id staff_id age initials hair_colour     branch_office source_1 source_2
    #> 1    1       NA  30     G.D.       Brown Republic of Ghana        A        3
    #> 2    2       NA  30     B.G.        Teal            France        A        1
    #> 3    3       NA  30     X.P.        <NA>              <NA>        A        1
    #> 4    4       NA  30     X.P.       Green              <NA>        B        1
    #> 5    5       NA  30     <NA>       Green            France        A        1
    #> 6    6        2  30     G.D.  Dark brown             Ghana        A        1
    #> 7    7        2  30     G.D.       Brown Republic of Ghana        B        2

A unique identifier that distinguishes one entity (staff) from another is often unavailable or incomplete as is the case with `staff_id` in this example. `links()` can be used to create one. The identifier is created as an `S4` class (`pid`) with useful information about each group in its slots.

The simplest strategy would be to select one attribute as a distinguishing characteristic for each entity. This is the simple deterministic approach to record linkage.

In the example below, we use `initials` and `hair_colour` as distinguishing characteristics.

    missing_staff_id$p1 <- links(criteria = missing_staff_id$initials)
    missing_staff_id$p2 <- links(criteria = missing_staff_id$hair_colour)
    missing_staff_id[c("initials", "hair_colour", "p1", "p2")]
    #>   initials hair_colour            p1            p2
    #> 1     G.D.       Brown P.1 (CRI 001) P.1 (CRI 001)
    #> 2     B.G.        Teal P.2 (No hits) P.2 (No hits)
    #> 3     X.P.        <NA> P.3 (CRI 001) P.3 (No hits)
    #> 4     X.P.       Green P.3 (CRI 001) P.4 (CRI 001)
    #> 5     <NA>       Green P.5 (No hits) P.4 (CRI 001)
    #> 6     G.D.  Dark brown P.1 (CRI 001) P.6 (No hits)
    #> 7     G.D.       Brown P.1 (CRI 001) P.1 (CRI 001)

Unsurprisingly, the uniqueness of identifiers `p1` and `p2` correspond to the uniqueness of the `initials` and `hair_colour` respectively. Both identifiers represent different outcomes - `p1` identifies records 3 and 4 as the same person, while `p2` has it as records 4 and 5.

To maximise coverage, `links()` can implement an ordered multistage deterministic approach to record linkage. For example, we can say that records with matching `initials` should be linked to each other first, then other records with a matching `hair_colour` should then be added to each group. This is referred to as group expansion.

    missing_staff_id$p3 <- links(
      criteria = as.list(missing_staff_id[c("initials", "hair_colour")])
      )
    missing_staff_id[c("initials", "hair_colour", "p1", "p2", "p3")]
    #>   initials hair_colour            p1            p2            p3
    #> 1     G.D.       Brown P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 2     B.G.        Teal P.2 (No hits) P.2 (No hits) P.2 (No hits)
    #> 3     X.P.        <NA> P.3 (CRI 001) P.3 (No hits) P.3 (CRI 001)
    #> 4     X.P.       Green P.3 (CRI 001) P.4 (CRI 001) P.3 (CRI 001)
    #> 5     <NA>       Green P.5 (No hits) P.4 (CRI 001) P.3 (CRI 003)
    #> 6     G.D.  Dark brown P.1 (CRI 001) P.6 (No hits) P.1 (CRI 001)
    #> 7     G.D.       Brown P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)

We see that `p3` now identifies records 3, 4 and 5 as the same person. The logic here is that since record 4 has the same `initial` as record 3 and also has the same `hair_colour` as record 5, all three are therefore linked as part of the same entity. Note that records 3 and 5 have only been linked due to their shared link with record 4. If record 4 is removed from this dataset, and the analysis repeated, records 3 and 5 will not be linked and therefore remain separate entities.

During group expansion the following rules are applied.

1. Records with unique or missing values for one attribute (or stage) will not be linked. Instead another attempt to match them will be made at the next stage.
2. Records linked at one stage will remain linked even if their attributes at the next stage are different i.e. matches at earlier stages have priority.
3. If a record can be linked to multiple groups i.e. conflicting matches, the following additional ordered rules are used to break ties;
   - assign the record to whichever group was created at the earlier stage
   - assign the record to a preferred group using the `tie_sort` argument.
   - assign the record to the group first encountered in the dataset

At each stage, additional match criteria can be specified. This is done through a `sub_criteria` object. This is an `S3` class containing attributes to be compared and functions for the comparisons. A `sub_criteria` object is used for evaluated, fuzzy and/or nested matches.

For example, we can compare `hair_colour` and `branch_office` without any order (priority) to them. This is the equivalent of saying matching hair color `OR/AND` branch office.

    scri_1 <- sub_criteria(
      missing_staff_id$hair_colour,
      missing_staff_id$branch_office,
      operator = "or"
      )
    scri_2 <- sub_criteria(
      missing_staff_id$hair_colour,
      missing_staff_id$branch_office,
      operator = "and"
      )
    missing_staff_id$p4 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = scri_1),
      recursive = TRUE
      )
    missing_staff_id$p5 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = scri_2),
      recursive = TRUE
      )
    missing_staff_id[c("hair_colour", "branch_office", "p4", "p5")]
    #>   hair_colour     branch_office            p4            p5
    #> 1       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001)
    #> 2        Teal            France P.2 (CRI 001) P.2 (No hits)
    #> 3        <NA>              <NA> P.3 (No hits) P.3 (No hits)
    #> 4       Green              <NA> P.4 (No hits) P.4 (No hits)
    #> 5       Green            France P.2 (CRI 001) P.5 (No hits)
    #> 6  Dark brown             Ghana P.6 (No hits) P.6 (No hits)
    #> 7       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001)

There is no limit to the number of `sub_criteria` that can be specified but each `sub_criteria` must be paired to a `criteria`. Any unpaired `sub_criteria` will be ignored.

As mentioned, a `sub_criteria` can be nested. For example, `scri_3` below is the equivalent of saying (`scri_1`; matching hair colour `OR` branch office) `AND` (matching initials `OR` branch office).

    scri_3 <- sub_criteria(
      scri_1,
      sub_criteria(
        missing_staff_id$initials,
        missing_staff_id$branch_office,
        operator = "or"),
      operator = "and"
      )
    missing_staff_id$p6 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = scri_3),
      recursive = TRUE
      )
    missing_staff_id[c("hair_colour", "branch_office", "p4", "p5", "p6")]
    #>   hair_colour     branch_office            p4            p5            p6
    #> 1       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 2        Teal            France P.2 (CRI 001) P.2 (No hits) P.2 (No hits)
    #> 3        <NA>              <NA> P.3 (No hits) P.3 (No hits) P.3 (No hits)
    #> 4       Green              <NA> P.4 (No hits) P.4 (No hits) P.4 (No hits)
    #> 5       Green            France P.2 (CRI 001) P.5 (No hits) P.5 (No hits)
    #> 6  Dark brown             Ghana P.6 (No hits) P.6 (No hits) P.6 (No hits)
    #> 7       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)

Evaluated matches can be implemented with user-defined functions. The only requirement for this is that they:

- Must be able to compare the attributes.
- Must have two arguments named `x` and `y`, where `y` is the value for one observation being compared against the value of all other observations - `x`.
- Must return either `TRUE` or `FALSE`.

For example, there are variations of the same `hair_colour` and `branch_office` values in `missing_staff_id`. A quick look and we see that using the last word of each value will improve the linkage result. We can create and pass a function to the `sub_criteria` object that will make this comparison. After doing this below (`p7`), we see that record 6 has now been linked with records 1 and 7, which was not the case earlier.

    # A function to extract the last word in a string
    last_word_wf <- function(x) tolower(gsub("^.* ", "", x))
    # A logical test using `last_word_wf`.
    last_word_cmp <- function(x, y) last_word_wf(x) == last_word_wf(y)

    scri_4 <- sub_criteria(
      missing_staff_id$hair_colour,
      missing_staff_id$branch_office,
      match_funcs = c(last_word_cmp, last_word_cmp),
      operator = "or"
      )
    missing_staff_id$p7 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = scri_4),
      recursive = TRUE
      )
    missing_staff_id[c("hair_colour", "branch_office", "p4", "p5", "p6", "p7")]
    #>   hair_colour     branch_office            p4            p5            p6
    #> 1       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 2        Teal            France P.2 (CRI 001) P.2 (No hits) P.2 (No hits)
    #> 3        <NA>              <NA> P.3 (No hits) P.3 (No hits) P.3 (No hits)
    #> 4       Green              <NA> P.4 (No hits) P.4 (No hits) P.4 (No hits)
    #> 5       Green            France P.2 (CRI 001) P.5 (No hits) P.5 (No hits)
    #> 6  Dark brown             Ghana P.6 (No hits) P.6 (No hits) P.6 (No hits)
    #> 7       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #>              p7
    #> 1 P.1 (CRI 001)
    #> 2 P.2 (CRI 001)
    #> 3 P.3 (No hits)
    #> 4 P.4 (No hits)
    #> 5 P.2 (CRI 001)
    #> 6 P.1 (CRI 001)
    #> 7 P.1 (CRI 001)

A `sub_criteria` can provide a lot of flexibly in terms of how attributes are compared however, it comes at the cost of processing time. This is because `links()` is an iterative function, comparing batches of record-pairs in iterations. This generally leads to a lower maximum memory usage but longer run times needed to analyse the multiple batches. There are three modes of a `batched` analysis with `links()` - `"yes"`, `"semi"` and `"no"`. These help manage the maximum memory usage or maximum number of iterations expended to complete the analyses.

For instance, below is a match criteria for a rolling match of records within three days of each other. With `print()`, we can see the record-pair batches compared at each iteration.

    dfr <- data.frame(x = 1:5)
    roll_window_funx <- function(x, y){
      match <- abs(x - y) <= 2
      print(data.frame(y, x, match))
      cat("\n")
      return(match)
      }
    roll_window_scri <- sub_criteria(
      dfr$x,
      match_funcs = roll_window_funx
      )

With the `"yes"` option, the linkage takes 5 iterations (run time) but only creates 5 record-pairs (max memory usage) are compared at each iteration.

    dfr$b.p1 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = roll_window_scri),
      batched = "yes",
      recursive = TRUE
      )
    #>   y x match
    #> 1 1 1  TRUE
    #> 2 1 2  TRUE
    #> 3 1 3  TRUE
    #> 4 1 4 FALSE
    #> 5 1 5 FALSE
    #>
    #>   y x match
    #> 1 2 2  TRUE
    #> 2 2 3  TRUE
    #> 3 2 4  TRUE
    #> 4 2 5 FALSE
    #> 5 2 1  TRUE
    #>
    #>   y x match
    #> 1 3 3  TRUE
    #> 2 3 4  TRUE
    #> 3 3 5  TRUE
    #> 4 3 1  TRUE
    #> 5 3 2  TRUE
    #>
    #>   y x match
    #> 1 4 4  TRUE
    #> 2 4 5  TRUE
    #> 3 4 1 FALSE
    #> 4 4 2  TRUE
    #> 5 4 3  TRUE
    #>
    #>   y x match
    #> 1 5 5  TRUE
    #> 2 5 1 FALSE
    #> 3 5 2 FALSE
    #> 4 5 3  TRUE
    #> 5 5 4  TRUE

Conversely, the `"no"` option completes the linkage in 1 iteration but creates 15 record-pairs in that single iteration.

    dfr$b.p2 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = roll_window_scri),
      batched = "no"
      )
    #>    y x match
    #> 1  1 1  TRUE
    #> 2  1 2  TRUE
    #> 3  1 3  TRUE
    #> 4  1 4 FALSE
    #> 5  1 5 FALSE
    #> 6  2 2  TRUE
    #> 7  2 3  TRUE
    #> 8  2 4  TRUE
    #> 9  2 5 FALSE
    #> 10 3 3  TRUE
    #> 11 3 4  TRUE
    #> 12 3 5  TRUE
    #> 13 4 4  TRUE
    #> 14 4 5  TRUE
    #> 15 5 5  TRUE

The `"semi"` option is a balance between the `"yes"` and `"no"` options. The number of record-pairs increases as matches are identified. This generally leads to a lower maximum memory usage compared to the `"no"` option and fewer number of iterations compared to the `"yes"` options.

    dfr$b.p3 <- links(
      criteria = "place_holder",
      sub_criteria = list(cr1 = roll_window_scri),
      batched = "semi",
      recursive = TRUE
      )
    #>   y x match
    #> 1 1 1  TRUE
    #> 2 1 2  TRUE
    #> 3 1 3  TRUE
    #> 4 1 4 FALSE
    #> 5 1 5 FALSE
    #>
    #>   y x match
    #> 1 2 2  TRUE
    #> 2 2 3  TRUE
    #> 3 2 4  TRUE
    #> 4 2 5 FALSE
    #> 5 2 1  TRUE
    #> 6 3 3  TRUE
    #> 7 3 4  TRUE
    #> 8 3 5  TRUE
    #> 9 3 1  TRUE
    #>
    #>   y x match
    #> 1 4 4  TRUE
    #> 2 4 5  TRUE
    #> 3 4 1 FALSE
    #> 4 4 2  TRUE
    #> 5 4 3  TRUE
    #> 6 5 5  TRUE
    #> 7 5 1 FALSE
    #> 8 5 2 FALSE
    #> 9 5 3  TRUE
    dfr
    #>   x          b.p1          b.p2          b.p3
    #> 1 1 P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 2 2 P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 3 3 P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 4 4 P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)
    #> 5 5 P.1 (CRI 001) P.1 (CRI 001) P.1 (CRI 001)

There are variations of `links()` such as `links_wf_probabilistic()`, `links_af_probabilistic()` and `links_wf_episodes()` for specific use cases such as probabilistic record linkage and grouping temporal events.

The implementation of probabilistic record linkage is based on Fellegi and Sunter (1969) model for deciding if two records belong to the same entity. In summary, `m_probabilities` and `u_probabilities`, which are the probabilities of a true and false match respectively are used to calculate a final match score for each record-pair. Records below or above a certain `score_threshold` are considered matches or non-matches respectively. See `help(links_wf_probabilistic)` for a more detailed explanation of the method. Below we see the same analysis as above but as a probabilistic record linkage.

    missing_staff_id$p9 <- links_wf_probabilistic(
      attribute = list(missing_staff_id$hair_colour,
                       missing_staff_id$branch_office),
      cmp_func = c(last_word_cmp, last_word_cmp),
      probabilistic = TRUE
      )
    missing_staff_id[c("hair_colour", "branch_office", "p7", "p9")]
    #>   hair_colour     branch_office            p7            p9
    #> 1       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001)
    #> 2        Teal            France P.2 (CRI 001) P.2 (No hits)
    #> 3        <NA>              <NA> P.3 (No hits) P.3 (No hits)
    #> 4       Green              <NA> P.4 (No hits) P.4 (No hits)
    #> 5       Green            France P.2 (CRI 001) P.5 (No hits)
    #> 6  Dark brown             Ghana P.1 (CRI 001) P.1 (CRI 001)
    #> 7       Brown Republic of Ghana P.1 (CRI 001) P.1 (CRI 001)