3.4.1 Probabilistic record linkage

Probabilistic linking is a method for combining information from records on different datasets to form a new linked dataset. It has been described as a process that attempts to link records on different files that have the greatest probability of belonging to the same person/organisation. Whereas deterministic (or exact) linking uses a unique identifier to link datasets, probabilistic linking uses a number of identifiers, in combination, to identify and evaluate links. Probabilistic linking is generally used when a unique identifier is not available or is of insufficient quality.

There are various methods of probabilistic record linkage. - Fellegi and Sunter (1969) -> requires sophisticated software to perform the calculations. References at the end of this sheet provide more information about linking algorithms. - Active Learning -> is an extension to Fellegi and Sunter (1969) + semi-supervised machine learning implementation to probabilistic record linkage

3.4.2 The Fellegi and Sunter method

It is a probabilistic approach to solving record linkage problems based on a decision model. Records in data sources are assumed to represent observations of entities taken from a particular population (individuals, companies, enterprises, farms, geographic regions, families, households…). The records are assumed to contain some attributes identifying an individual entity. Examples of identifying attributes are name, address, age, and gender when dealing with people; a firm’s style (or name); legal form, address, number of local units, number of employees, and turnover value when dealing with businesses. According to the method, given two (or more) sources of data, all pairs coming from the Cartesian product of the two sources have to be classified into three independent and mutually exclusive subsets: the set of matches, the set of non-matches, and the set of pairs requiring manual review. In order to classify the pairs, the comparisons on common attributes are used to estimate for each pair the probabilities of belonging to both the set of matches and the set of non-matches. The pair classification criteria are based on the ratio between such conditional probabilities. The decision model aims to minimize both the misclassification errors and the probability of classifying a pair as belonging to the subset of pairs requiring manual review.

The key steps of probabilistic linking (as shown in Diagram 1) are: 1. Data cleaning and standardisation 2. Blocking 3. Linking 4. Clerical review 5. Evaluating data quality

• Blocking – divides datasets into groups, called blocks, in order to reduce the number of comparisons that need to be conducted to find which pairs of records should be linked. Only records in corresponding blocks on each dataset are compared to identify possible links.
• Fields – types of information, such as name, address, and date of birth, on the records in datasets.
• Linked dataset – the result of linking different datasets is a new dataset whose records contain some information from each of the original datasets.
• Links – records that have been combined after being assessed as referring to the same entity (i.e., person/family/organisation/region).
• Unique identifier – a number or code that uniquely identifies a person, business, or organisation, such as passport number or Australian Business Number (ABN).

3.4.3 Active Learning

The main hypothesis in active learning is that if a learning algorithm can choose the data it wants to learn from, it can perform better than traditional methods with substantially less data for training. In active learning, there are typically three scenarios or settings in which the learner will query the labels of instances. The three main scenarios that have been considered in the literature are Membership Query Synthesis, Stream-Based Selective Sampling, and Pool-Based sampling.

Pool-Based sampling: assumes that there is a large pool of unlabelled data, as with the stream-based selective sampling. Instances are then drawn from the pool according to some informativeness measure. This measure is applied to all instances in the pool (or some subset if the pool is very large), and then the most informative instance(s) are selected.

5.1.1 Kenya and Rwanda

5.2.1 Country Comparison

5.2.2 Kenya and Rwanda

5.3.1 Kenya and Rwanda

To identify the key predictors of a learner repeating the WEC - Can we predict how likely a given learner is to re-engage next year? Does participating in one iteration make you more likely to participate in the next one?

## 
## Call:
## roc.formula(formula = Loyalty ~ final.logit$fitted.values, data = model.df1,     plot = TRUE, grid = TRUE, print.auc = TRUE, show.thres = TRUE,     ci = TRUE, boot.n = 100, ci.alpha = 0.9, stratified = FALSE,     main = "ROC Curve", col = "blue")
## 
## Data: final.logit$fitted.values in 7260 controls (Loyalty 1st Time Users) < 2638 cases (Loyalty Repeat Users).
## Area under the curve: 0.6965
## 95% CI: 0.6848-0.7082 (DeLong)