Partial Match Weights
In the previous article we saw that the Fellegi-Sunter model makes its predictions with a simple calculation: the sum of the partial_match_weightA partial match weight quantifies the importance of a comparison level in the Fellegi-Sunter model. For instance, a Jaro Winkler fuzzy match on first name may have a positive match weight, indicating it adds evidence in favour of a match.s.
But what are partial match weights and where do they come from?1
What are they?
Some columns are more important than others to the calculation of overall match weight.2 This is quantified by the partial match weights.
For example:
- A match on date of birth provides stronger evidence in favour of a match than a match on gender.
- A mismatch on date of birth may provide more evidence against a match than a mismatch on address (because people move house).
Positive values indicate evidence in favour of a match whilst negative values mean evidence against a match.
The concept applies more generally than just to exact matches and non-matches: partial match weights can be estimated for more subtle scenarios like ‘first name not an exact match, but similar’.
These scenarios thus correspond to a definition how information in the record is compared, since similarity will be defined differently for different types of information. For instance, two addresses may be considered similar if they’re geographically close together, whereas two names may be considered similar if they sound the same despite different spellings.
For this reason, we call each scenario a 'comparison levelIn Splink, a model has a set of comparisons, each typically corresponding to a column in the input data such as name, date of birth etc.
Each comparison has multiple comparison levels. A comparison level defines a category of similarity for that column e.g. an 'exact match' or a 'one character difference'.
Each comparison level has an associated partial match weight.'.
In summary:
- The overall model is made up of a set of comparisons
- Each comparison is made up of a set of similarity scenarios known as ‘comparison levels’
- Each comparison level has an associated partial match weight
It is up to the modeller to define the comparison levels and the resultant partial match weights they wish to estimate.
Example: Defining comparison levels for a first name column
As a reminder, here is the example data we are working with:
| first_name | surname | postcode | gender |
|---|---|---|---|
| Robin | Linacre | W1A 1AA | Female |
| Robyn | Linacre | W1A 1AA | Male |
For first name, we could define the following three comparison levels.
- Exact match: First names are identical
- Fuzzy match: First names are similar according to the Jaro WinklerJaro-Winkler similarity measures how similar two strings are, giving more weight to matching prefixes. It is a good similarity metric to use for names. measure.
- All other cases
The estimated partial match weights may look like this:3
Observe that:
- An exact match on first name provides stronger evidence in favour of a match than a fuzzy match
- If the first name is completely different (neither and exact nor fuzzy match), this is evidence against the records being a match.
These comparison levels are mutually exclusive, and are implemented like a sequence of if statements:
if first_name_l == first_name_r:
first_name_partial_match_weight = 7.2
elif jaro_winkler_sim(first_name_l, first_name_r) >= 0.9:
first_name_partial_match_weight = 5.9
else:
first_name_partial_match_weight = -3.3Remaining columns
Similarly, we can define comparisonsIn Splink, a model has a set of comparisons, each typically corresponding to a column in the input data such as name, date of birth etc.
Each comparison has multiple comparison levels. A comparison level defines a category of similarity for that column e.g. an 'exact match' or a 'one character difference'.
Each comparison level has an associated partial match weight. for the remaining columns and estimate the partial match weights of each of their comparison levelsIn Splink, a model has a set of comparisons, each typically corresponding to a column in the input data such as name, date of birth etc.
Each comparison has multiple comparison levels. A comparison level defines a category of similarity for that column e.g. an 'exact match' or a 'one character difference'.
Each comparison level has an associated partial match weight..
The number of comparison levels modelled and their definition can vary depending on the type of information.
For example, since gender is a categorical variable we’d likely have just two comparison levels: match, and non-match.
For date of birth, we may define three comparison levels, but LevenshteinThe Levenshtein distance measures the minimum number of single-character edits needed to transform one string into another. would be more suitable than Jaro WinklerJaro-Winkler similarity measures how similar two strings are, giving more weight to matching prefixes. It is a good similarity metric to use for names. for assessing similarity.
We can plot all the partial match weights in a single chart like this:
This provides a succinct summary of the whole model.
Intuitive interpretation of partial match weights
The partial match weights in the chart have intuitive interpretations.
For example, the partial match weight associated with an exact match on postcode is stronger than the partial match weight associated with gender.
This makes sense: a match on gender doesn’t tell us much about whether two records are a match, whereas a match on postcode is much more informative.
The pattern of negative partial match weights is also intuitive: If gender is recorded as categorical variable, then it may be very accurate. A mismatch would thus be strong evidence against a match.
Conversely, a mismatch on postcode may offer little evidence against a match since people move house, or typos may have been made.
Understanding the partial match weight chart and waterfall chart
Let’s take a look at an example record comparison, and see how the partial match weights are used.
You can edit the data in the below table to see how the calculation changes
The first stage is to calculate which comparison levels apply for each column. For example, are the first names an exact match, a fuzzy match, or neither?
In the below chart, I reproduce the partial match weights chart, but with the activated partial match weights highlighted.
The activated (selected) partial match weights can then be plotted in a waterfall chart, which represents how they are summed up to compute the final match weight:
Alternatively we can represent the calculation of overall match weight as a sum:
The final match weight is a measure of the similarity of the two records.
Next steps
We now have a good qualitative understanding of the meaning of partial match weights.
In the next article we explore how they are calculated, and how to interpret their values.
Footnotes
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In this context, the word ‘partial’ means ‘using only part of the information in the record’ - typically a single column. There is then a partial match weight for each column. ↩
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In this article, for simplicity, there’s a one to one correspondence between columns and partial match weights. Each column is treated as a separate piece of information. In reality, the model allows for more flexibility. We could split a column (e.g. date of birth) into several pieces of information (e.g. day, month, year) and estimate partial match weights for each. Or we could combine several columns (e.g. first, middle and surname) into a single piece of information and estimate a partial match weights for this information. ↩
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A later article will explain how to estimate partial match weights. Here I just assume they have already been estimated. ↩