# Blocking records for record linkage

#### Maciej Beręsewicz

# 1 Setup

Read required packages

    library(blocking)
    library(data.table)

# 2 Data

Read the example data from the tutorial on the `reclin` package on the URos 2021 Conference. The data sets are from ESSnet on Data Integration as stated in the repository:

    These totally fictional data sets are supposed to have captured details of
    persons up to the date 31 December 2011.  Any years of birth captured as 2012
    are therefore in error.  Note that in the fictional Census data set, dates of
    birth between 27 March 2011 and 31 December 2011 are not necessarily in error.

    census: A fictional data set to represent some observations from a
            decennial Census
    cis: Fictional observations from Customer Information System, which is
            combined administrative data from the tax and benefit systems

    In the dataset census all records contain a person_id. For some of the records
    in cis the person_id is also available. This information can be used to
    evaluate the linkage (assuming these records from the cis are representable
    all records in the cis).

    data(census)
    data(cis)
    setDT(census)
    setDT(cis)

- `census` object has 25343 rows and 13 columns,
- `cis` object has 24613 rows and 10 columns.

Census data

    head(census)

person_id | pername1 | pername2 | sex | dob_day | dob_mon | dob_year | hse_num | enumcap | enumpc | str_nam | cap_add | census_id
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
DE03US001001 | COUIE | PRICE | M | 1 | 6 | 1960 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001001
DE03US001002 | ABBIE | PVICE | F | 9 | 11 | 1961 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001002
DE03US001003 | LACEY | PRICE | F | 7 | 2 | 1999 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001003
DE03US001004 | SAMUEL | PRICE | M | 13 | 4 | 1990 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001004
DE03US001005 | JOSEPH | PRICE | M | 20 | 4 | 1986 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001005
DE03US001006 | JOSH | PRICE | M | 14 | 2 | 1996 | 1 | 1 WINDSOR ROAD | DE03US | Windsor Road | 1, Windsor Road | CENSDE03US001006

CIS data

    head(cis)

person_id | pername1 | pername2 | sex | dob_day | dob_mon | dob_year | enumcap | enumpc | cis_id
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
PO827ER091001 | HAYDEN | HALL | M |  | 1 |  | 91 CLARENCE ROAD | PO827ER | CISPO827ER091001
LS992DB024001 | SEREN | ANDERSON | F | 1 | 1 |  | 24 CHURCH LANE | LS992DB | CISLS992DB024001
M432ZZ053003 | LEWIS | LEWIS | M | 1 | 1 |  | 53 CHURCH ROAD | M432ZZ | CISM432ZZ053003
SW75TQ018001 | HARRISON | POSTER | M | 5 | 1 |  | 19 HIGHFIELD ROAD | SW75TG | CISSW75TQ018001
EX527TR017006 | MUHAMMED | WATSUN | M | 7 | 1 |  | 17 VICTORIA STREET |  | CISEX527TR017006
SW540RB001001 | RHYS | THOMPSON | M | 7 | 1 |  | 1 SPRINGFIELD ROAD | SW540RB | CISSW540RB001001

We randomly select 12671 records from `census` and 12306 records from `cis`.

    set.seed(2024)
    census <- census[sample(nrow(census), floor(nrow(census) / 2)), ]
    cis <- cis[sample(nrow(cis), floor(nrow(cis) / 2)), ]

We need to create new columns that concatenate variables from `pername1` to `enumpc`.

    census[, txt:=paste0(pername1, pername2, sex, dob_day, dob_mon, dob_year, enumcap, enumpc)]
    cis[, txt:=paste0(pername1, pername2, sex, dob_day, dob_mon, dob_year, enumcap, enumpc)]

# 3 Linking datasets

## 3.1 Using basic functionalities of `blocking` package

The goal of this exercise is to link units from the CIS dataset to the CENSUS dataset.

    result1 <- blocking(x = census$txt, y = cis$txt, verbose = 1)
    #> ===== creating tokens =====
    #> ===== starting search (nnd, x, y: 12671, 12306, t: 1053) =====
    #> ===== creating graph =====

Distribution of distances for each pair.

    hist(result1$result$dist, main = "Distribution of distances between pairs", xlab = "Distances")

Example pairs.

    head(result1$result, n = 10)

x | y | block | dist
--- | --- | --- | ---
1 | 12088 | 8340 | 0.0452079
2 | 12156 | 8378 | 0.2616496
3 | 7243 | 5756 | 0.0460410
3 | 10643 | 5756 | 0.3730645
4 | 8422 | 6453 | 0.3587636
6 | 9442 | 7034 | 0.3189948
6 | 10195 | 7034 | 0.0416667
7 | 745 | 725 | 0.1633400
8 | 3072 | 2770 | 0.2578439
8 | 10717 | 2770 | 0.1235833

Let’s take a look at the first pair. Obviously there is a typo in the `pername1` but all the other variables are the same, so it appears to be a match.

    cbind(t(census[1, c(1:7, 9:10)]), t(cis[12088, 1:9]))
    #>           [,1]              [,2]
    #> person_id "SW122AB001001"   "SW122AB001001"
    #> pername1  "GEURGE"          "GEORGE"
    #> pername2  "HUGHES"          "HUGHES"
    #> sex       "M"               "M"
    #> dob_day   "19"              "19"
    #> dob_mon   "5"               "5"
    #> dob_year  "1942"            "1942"
    #> enumcap   "1 VICTORIA ROAD" "1 VICTORIA ROAD"
    #> enumpc    "SW122AB"         "SW122AB"

## 3.2 Assessing the quality

For some records, we have information about the correct linkage. We can use this information to evaluate our approach.

    matches <- merge(x = census[, .(x=1:.N, person_id)],
                     y = cis[, .(y = 1:.N, person_id)],
                     by = "person_id")
    matches[, block:=1:.N]
    head(matches)

person_id | x | y | block
--- | --- | --- | ---
DE03US001003 | 1357 | 10248 | 1
DE03US008001 | 4506 | 2506 | 2
DE03US012002 | 2706 | 12005 | 3
DE03US012003 | 6317 | 11103 | 4
DE03US013003 | 4388 | 10673 | 5
DE03US014003 | 9463 | 11793 | 6

So in our example we have 5991 pairs.

    result2 <- blocking(x = census$txt, y = cis$txt, verbose = 1,
                        true_blocks = matches[, .(x, y, block)])
    #> ===== creating tokens =====
    #> ===== starting search (nnd, x, y: 12671, 12306, t: 1053) =====
    #> ===== creating graph =====

Let’s see how our approach handled this problem.

    result2
    #> ========================================================
    #> Blocking based on the nnd method.
    #> Number of blocks: 8437.
    #> Number of columns used for blocking: 1053.
    #> Reduction ratio: 0.9999.
    #> ========================================================
    #> Distribution of the size of the blocks:
    #>    2    3    4    5    6    7    8    9
    #> 5567 2086  611  142   23    6    1    1
    #> ========================================================
    #> Evaluation metrics (standard, in %):
    #>      recall   precision         fpr         fnr    accuracy specificity
    #>     99.5326     99.8159      0.0000      0.4674     99.9999    100.0000
    #>    f1_score
    #>     99.6740

It seems that the default parameters of the NND method result in an FNR of 0.47%. We can see if decreasing the `epsilon` parameter as suggested in the Nearest Neighbor Descent vignette will help.

    ann_control_pars <- controls_ann()
    ann_control_pars$nnd$epsilon <- 0.2

    result3 <- blocking(x = census$txt, y = cis$txt, verbose = 1,
                        true_blocks = matches[, .(x, y, block)],
                        control_ann = ann_control_pars)
    #> ===== creating tokens =====
    #> ===== starting search (nnd, x, y: 12671, 12306, t: 1053) =====
    #> ===== creating graph =====

Changing the `epsilon` search parameter from 0.1 to 0.2 decreased the FNR to 0.17%.

    result3
    #> ========================================================
    #> Blocking based on the nnd method.
    #> Number of blocks: 8451.
    #> Number of columns used for blocking: 1053.
    #> Reduction ratio: 0.9999.
    #> ========================================================
    #> Distribution of the size of the blocks:
    #>    2    3    4    5    6    7    8    9
    #> 5592 2079  606  142   25    5    1    1
    #> ========================================================
    #> Evaluation metrics (standard, in %):
    #>      recall   precision         fpr         fnr    accuracy specificity
    #>     99.8331     99.9332      0.0000      0.1669    100.0000    100.0000
    #>    f1_score
    #>     99.8831

Finally, compare the NND and HNSW algorithm for this example.

    result4 <- blocking(x = census$txt, y = cis$txt, verbose = 1,
                        true_blocks = matches[, .(x, y, block)],
                        ann = "hnsw")
    #> ===== creating tokens =====
    #> ===== starting search (hnsw, x, y: 12671, 12306, t: 1053) =====
    #> ===== creating graph =====

It seems that the HNSW algorithm also performed with 0.17% FNR.

    result4
    #> ========================================================
    #> Blocking based on the hnsw method.
    #> Number of blocks: 8447.
    #> Number of columns used for blocking: 1053.
    #> Reduction ratio: 0.9999.
    #> ========================================================
    #> Distribution of the size of the blocks:
    #>    2    3    4    5    6    7    8    9
    #> 5587 2079  606  142   26    5    1    1
    #> ========================================================
    #> Evaluation metrics (standard, in %):
    #>      recall   precision         fpr         fnr    accuracy specificity
    #>     99.8331     99.9332      0.0000      0.1669    100.0000    100.0000
    #>    f1_score
    #>     99.8831

## 3.3 Compare results

Finally, we can compare the results of two ANN algorithms. The overlap between neighbours is given by

    c("no tuning" = mean(result2$result[order(y)]$x == result4$result[order(y)]$x)*100,
      "with tuning" = mean(result3$result[order(y)]$x == result4$result[order(y)]$x)*100)
    #>   no tuning with tuning
    #>    98.74045    99.21177